ShantanuT01/DACTYL-Pretraining huggingface dataset:
New results on conditional joint probability distributions of first exit times are presented for a continuous-time stochastic process defined as the mixture of Markov jump processes moving at different speeds on the same finite state space, while the mixture occurs at a random time. Such mixture was first proposed by Frydman \cite{Frydman2005} and Frydman and Schuermann \cite{Frydman2008} as a generalization of the mover-stayer model of Blumen et at. \cite{Blumen}, and was recently extended by Surya \cite{Surya2018}, in which explicit distributional identities of the process are given, in particular in the presence of an absorbing state. We revisit \cite{Surya2018} for a finite mixture with overlapping absorbing sets. The contribution of this paper is two fold. First, we generalize distributional properties of the mixture discussed in \cite{Frydman2008} and \cite{Surya2018}. Secondly, we give distributional identities of the first exit times explicitly in terms of intensity matrices of the underlying Markov processes and the Bayesian updates of switching probability and of the probability distribution of states, despite the fact that the mixture itself is non-Markov. They form non-stationary functions of time and have the ability to capture heterogeneity and path dependence when conditioning on the available information (either full or partial) of the process. In particular, initial profile of the distributions forms of a generalized mixture of multivariate phase-type distributions of Assaf et al. \cite{Assaf1984}. When the underlying processes move at the same speed, in which case the mixture becomes a simple Markov process, these features are removed, and the initial distributions reduce to \cite{Assaf1984}. Some explicit and numerical examples are discussed to illustrate the main results.
We theoretically study the creation of single- and multi-phonon Fock states and arbitrary superpositions of quantum phonon states in a nanomechanical carbon nanotube (CNT) resonator. In our model, a doubly clamped CNT resonator is initialized in the ground state and a single electron is trapped in a quantum dot which is formed by a electric gate potential and brought into the magnetic field of a micro-magnet. The preparation of arbitrary quantum phonon states is based on the coupling between the mechanical motion of the CNT and the electron spin which acts as a non-linearity. We assume that electrical driving pulses with different frequencies are applied on the system. The quantum information is transferred from the spin qubit to the mechanical motion by the spin-phonon coupling and the electron spin qubit can be reset by the single-electron spin resonance. We describe Wigner tomography which can be applied at the end to obtain the phase information of the prepared phonon states.
We evaluate the intersection numbers of loaded cycles and twisted forms associated with an n-fold Selberg-type integral. The result is deeply related with the geometry of the configuration space of n+3 points in the projective line.
The theory of highly super-Eddington black hole accretion was developed in the 1980s in Warsaw by Paczynski and his collaborators in terms of "Polish doughnuts", i.e. low viscosity, rotating accretion flows that are optically thick, radiation pressure supported, cooled by advection, and radiatively very inefficient. Polish doughnuts resemble fat tori with two narrow funnels along rotation axis. The funnels collimate radiation into beams with highly super-Eddington luminosities. "Slim disks" introduced later by Abramowicz, Lasota and collaborators, have only moderately super-Eddington accretion rates, rather disk-like shapes, and almost thermal spectra.
We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables.
We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.
In this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem. We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.
We report the results of a study exploring the stellar populations of 13 luminous (L>L*), spectroscopically confirmed, galaxies in the redshift interval 5.5<z<6.5, all with WFC3/IR and IRAC imaging from the HST/CANDELS and Spitzer/SEDS surveys. Based on fitting the observed photometry with SED templates covering a wide range of different star-formation histories, and a self consistent treatment of Lyman-alpha emission, we find that the derived stellar masses lie within the range 10^9 Msun < M*< 10^10 Msun and are robust to within a factor of two. In contrast, we confirm previous reports that the ages of the stellar populations are poorly constrained. Although the best-fitting models for three objects have ages >= 300 Myr, the degeneracies introduced by dust extinction mean that only two of these objects actually require a >300 Myr old stellar population to reproduce the observed photometry. Moreover, when considering only smoothly-varying star-formation histories, we observe a clear tension between the data and models such that a galaxy SED template with an old age is often chosen in order to try and fit objects with blue UV-slopes but red UV-to-optical colours. To break this tension we explore SED fitting with two-component models (burst plus on-going star-formation) and allow for nebular emission. On average, the inclusion of nebular emission leads to lower stellar-mass estimates (median offset 0.18 dex), moderately higher specific star-formation rates, and allows for a wider range of plausible stellar ages. However, based on our SED modelling, we find no strong evidence for extremely young ages in our sample (<50 Myr). Finally, considering all of the different star-formation histories explored, we find that the median best-fitting ages are of the order 200-300 Myr and that the objects with the tightest constraints indicate ages in the range 50-200 Myr (Abridged).
Weyl semimetal (WSM) is a newly discovered quantum phase of matter that exhibits topologically protected states characterized by two separated Weyl points with linear dispersion in all directions. Here, via combining theoretical analysis and magneto-infrared spectroscopy of an archetypal Weyl semimetal, niobium phosphide, we demonstrate that the coupling between Weyl points can significantly modify the electronic structure of a WSM and provide a new twist to the protected states. These findings suggest that the coupled Weyl points should be considered as the basis for analysis of realistic WSMs.
We use optical and near-infrared spectroscopy to observe rest-UV emission lines and estimate the black hole mass of WISEA J224607.56-052634.9 (W2246-0526) at z = 4.601, the most luminous hot dust-obscured galaxy yet discovered by WISE. From the broad component of the MgII-2799A emission line, we measure a black hole mass of log (M_BH/M_sun) = 9.6 +- 0.4. The broad CIV-1549A line is asymmetric and significantly blue-shifted. The derived M_BH from the blueshift-corrected broad CIV line width agrees with the MgII result. From direct measurement using a well-sampled SED, the bolometric luminosity is 3.6 * 10^14 L_sun. The corresponding Eddington ratio for W2246-0526 is lambda_Edd = L_AGN / L_Edd = 2.8. This high Eddington ratio may reach the level where the luminosity is saturating due to photon trapping in the accretion flow, and be insensitive to the mass accretion rate. In this case, the M_BH growth rate in W2246-0526 would exceed the apparent accretion rate derived from the observed luminosity.
We detail the continued fraction expansion of the square root of monic sextic polynomials. We note in passing that each line of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. In particular we obtain an associated Somos sequence defined by a three-term recurrence relation of gap~6.
A quantum N-body problem with 2-component in (2+1)-dimension deduced from integrable model in (2+1) dimension is investigated. The Davey-Stewartson 1(DS1) system[Proc. R. Soc. London, Ser. A {\bf 338}, 101 (1974)] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimensions. For latters with the $\delta $-function interactions and being solved by the Bethe-Yang ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solusions is discussed.
We provide new constraints on the connection between galaxies in the local universe, identified by the Sloan Digital Sky Survey (SDSS), and dark matter halos and their constituent substructures in the $\Lambda$CDM model using WMAP7 cosmological parameters. Predictions for the abundance and clustering properties of dark matter halos, and the relationship between dark matter hosts and substructures, are based on a high-resolution cosmological simulation, the Bolshoi simulation. We associate galaxies with halos and subhalos using subhalo abundance matching, performing a comprehensive analysis which investigates the underlying assumptions of this technique including (a) which halo property is most closely associated with galaxy stellar masses and luminosities, (b) how much scatter is in this relationship, and (c) how much subhalos can be stripped before their galaxies are destroyed. The models are jointly constrained by new measurements of the projected two-point galaxy clustering and the observed conditional stellar mass function of galaxies in groups. The data put tight constraints on the satellite fraction of galaxies as a function of galaxy stellar mass, on the scatter between halo and galaxy properties, and on the underlying conditional stellar mass function. These data rule out several halo properties commonly used in abundance matching, largely because the satellite fractions in the models disagree with those data. We show that an abundance matching model that associates galaxies with the peak circular velocity of their halos is in good agreement with the data, when scatter of $0.20 \pm 0.03$ dex in stellar mass at a given peak velocity is included. This will yield important constraints for galaxy formation models, and also provides encouraging indications that the galaxy--halo connection can be modeled with sufficient fidelity for future precision studies of the dark Universe.
White-noise case stochastic heat equation was derived from Dawson-Watanabe superprocess. The pathwise uniqueness of their solutions with non-Lipschitz coefficients has attracted wide attention and in particular, the square-root coefficient case was listed as a long standing open problem in the famous literature (i.e. Perkins \cite{Perkins02} p217.) This short note gives an affirmative answer to this open problem.   Our idea is using the $\varphi_k(x)$ function constructed by Yamada-Watanable to prove that   \beqlb \lab{key}   \E_{\mu}| X_{t}(z)-Y_{t}(z) | = \lim_{k \ra \infty} \E_{\mu}|\int_{\r}\frac{1}{\sqrt{\epsilon_k}} \rho_{\epsilon_k}(z-x)[ X_{t}(x)-Y_{t}(x)]dx |=0 .   \eeqlb   However, $\frac{1}{\sqrt{\epsilon_k}} \rho_{\epsilon_k}(x)=p_{\epsilon_k}(x)$, the stable kernel, is not square-integrable uniformly in $k$ and we cannot directly use the heat kernel or stable kernel convolution transformation. This forces us to go a new way in which we have used the linear and reciprocal linear properties of $\varphi_k$ and $\varphi^{\prime \prime}_k$, respectively, making a $\rho_{\epsilon_k}$ convolution transformation first, then, taking expectation and multiplying singularity factor $\frac{1}{\sqrt{\epsilon_k}}$ and finally letting $k \ra \infty$ to estimate and derive (\ref{key}). In this way, we have avoided the non-uniform square integrability of the stochastic integral terms which involve the singularity. The same idea also can be used to prove the pathwise uniqueness of the nonnegative solutions of stochastic heat equation with $\alpha$ coefficients ($1/2 \leq \alpha$) since by a same idea we can construct the $\varphi_k(x)$ functions with $1/2 \leq \alpha$.
IGR J17454-2919 is a hard X-ray transient discovered by INTEGRAL on 2014 September 27. We report on our 20ks Chandra observation of the source, performed about five weeks after the discovery, as well as on INTEGRAL and Swift monitoring long-term observations. X-ray broad-band spectra of the source are compatible with an absorbed power-law, $\Gamma\sim$1.6-1.8, ${\rm N_H}\sim$(10-12)$\times 10^{22}\,{\rm cm}^{-2}$, with no trace of a cut-off in the data up to about 100keV, and with an average absorbed 0.5-100keV flux of about (7.1-9.7)${\times 10^{-10}~erg~cm^{-2}~s^{-1}}$. With Chandra, we determine the most accurate X-ray position of IGR J17454-2919, $\alpha_{J2000}$=17$^{h}$ 45$^{m}$ 27$^{s}$.69, $\delta_{J2000}$= $-$29$^{\circ}$ 19$^{\prime}$ 53$^{\prime \prime}$.8 (90% uncertainty of 0$^{\prime\prime}$.6), consistent with the NIR source 2MASS J17452768-2919534. We also include NIR investigations from our observations of the source field on 2014 October 6 with GROND. With the multi-wavelength information at hand, we discuss the possible nature of IGR J17454-2919.
We present Sunyaev-Zel'dovich (SZ) effect observations of a sample of 25 massive relaxed galaxy clusters observed with the Sunyaev-Zel'dovich Array (SZA), an 8-element interferometer that is part of the Combined Array for Research in Millimeter-wave Astronomy (CARMA). We perform an analysis of new SZA data and archival Chandra observations of this sample to investigate the integrated pressure -- a proxy for cluster mass -- determined from X-ray and SZ observations, two independent probes of the intra-cluster medium. This analysis makes use of a model for the intra-cluster medium introduced by Bulbul (2010) which can be applied simultaneously to SZ and X-ray data. With this model, we estimate the pressure profile for each cluster using a joint analysis of the SZ and X-ray data, and using the SZ data alone. We find that the integrated pressures measured from X-ray and SZ data are consistent. This conclusion is in agreement with recent results obtained using WMAP and Planck data, confirming that SZ and X-ray observations of massive clusters detect the same amount of thermal pressure from the intra-cluster medium. To test for possible biases introduced by our choice of model, we also fit the SZ data using the universal pressure profile proposed by Arnaud (2010), and find consistency between the two models out to r500 in the pressure profiles and integrated pressures.
We report a dynamically evolving low ionization broad absorption line flow in the QSO SDSS J133356.02+001229.1 (at z_em = 0.9197). These observations are part of our ongoing monitoring of low ionization broad absorption line (BAL) QSOs with the 2m telescope at IUCAA Girawali observatory (IGO). The broad Mg II absorption with an ejection velocity of 1.7x10^4 km/s, found in the Sloan Digital Sky Survey (SDSS) spectra, has disappeared completely in our IGO spectra. We found an emerging new component at an ejection velocity of 2.8 x 10^4 km/s. During our monitoring period this component has shown strong evolution both in its velocity width and optical depth and nearly disappeared in our latest observations. Acceleration of a low velocity component seen in SDSS spectrum to a higher velocity is unlikely as the Mg II column densities are always observed to be higher for the new component. We argue that the observed variations may not be related to ionization changes and are consistent with absorption produced by multi-streaming flow transiting across our line of sight. We find a possible connection between flux variation of the QSO and N(Mg II) of the newly emerged component. This could mean the ejection being triggered by changes in the accretion disk or dust reddening due to the outflowing gas.
We study the luminosity function of intermediate-age red-clump stars using deep, near-infrared photometric data covering $\sim$ 20 deg$^2$ located throughout the central part of the Small Magellanic Cloud (SMC), comprising the main body and the galaxy's eastern wing, based on observations obtained with the VISTA Survey of the Magellanic Clouds (VMC). We identified regions which show a foreground population ($\sim$11.8 $\pm$ 2.0 kpc in front of the main body) in the form of a distance bimodality in the red-clump distribution. The most likely explanation for the origin of this feature is tidal stripping from the SMC rather than the extended stellar haloes of the Magellanic Clouds and/or tidally stripped stars from the Large Magellanic Cloud. The homogeneous and continuous VMC data trace this feature in the direction of the Magellanic Bridge and, particularly, identify (for the first time) the inner region ($\sim$ 2 -- 2.5 kpc from the centre) from where the signatures of interactions start becoming evident. This result provides observational evidence of the formation of the Magellanic Bridge from tidally stripped material from the SMC.
In this letter, two different probabilistic teleportations of a two-particle entangled state by pure entangled three-particle state are shown. Their successful probabilities are different.
We use deep $HST$ WFC3/IR imaging to study the Initial Mass Function (IMF) of the ultra faint dwarf galaxy Coma Berenices (Com Ber). Our observations reach the lowest stellar mass ever probed in a resolved galaxy, with 50\% completeness at $\sim 0.17$ M$_{\odot}$. Unresolved background galaxies however limit our purity below $\sim 0.23$ M$_{\odot}$. If modeled with a single power law, we find that the IMF slope is $-1.45^{+0.29}_{-0.3}$ (68\% credible intervals), compared to a Milky Way value of $-2.3$. For a broken power law, we obtain a low-mass slope of $-1.18_{-0.33}^{+0.49}$, a high-mass slope of $-1.88_{-0.49}^{+0.43}$ and a break mass of $0.57_{-0.08}^{+0.12}$ M$_{\odot}$, compared to $-1.3$, $-2.3$ and 0.5 M$_{\odot}$ for a Kroupa IMF. For a log-normal IMF model we obtain values of $0.33_{-0.16}^{+0.15}$ M$_{\odot}$ for the location parameter and of $0.68_{-0.12}^{+0.17}$ for $\sigma$ (0.22 M$_{\odot}$ and 0.57 for the Chabrier system IMF). All three parametrizations produce similar agreement with the data. Our results agree with previous analysis of shallower optical HST data. However analysis of similar optical data of other dwarfs finds IMFs significantly more bottom-light than in the Milky Way. These results suggest two, non mutually exclusive, possibilities: that the discrepancy of the dwarf galaxies IMF with respect to the Milky Way is, at least partly, an artifact of using a single power law model, and that there is real variance in the IMF at low masses between the currently studied nearby dwarfs, with Com Ber being similar to the Milky Way, but other dwarfs differing significantly.
We use recent very extended HI kinematics (out to 48 kpc) along with previous H$\alpha$ kinematics of the spiral galaxy NGC 3198 in order to derive its distribution of dark matter (DM). First, we used a chi-square method to model the rotation curve (RC) of this galaxy in terms of different profiles of its DM distribution: the universal rotation curve (URC) mass model (stellar disk $+$ Burkert halo $+$ gaseous disk), the NFW mass model (stellar disk $+$ NFW halo $+$ gaseous disk) and the baryon $\Lambda$CDM mass model (stellar disk $+$ NFW halo modified by baryonic physics $+$ gaseous disk). Second, to derive the DM halo density distribution, we applied a new method that does not require a global and often uncertain mass modelling. While according to the standard method, both URC and NFW mass models can account for the RC, the new method instead leads to a density profile that is sharply disagrees with the dark halo density distribution predicted within the Lambda cold dark matter ($\Lambda$CDM) scenario. We find that the effects of baryonic physics modify the original $\Lambda$CDM halo densities in such a way that the resulting profile is more compatible with the DM density of NGC 3198 derived using our new method. However, at large distances, r $\sim$ 25 kpc, also this modified baryon $\Lambda$CDM halo profile appears to create a tension with the derived DM halo density.
We report the results of 870-$\mu$m continuum observations, using the Large APEX Bolometer Camera (LABOCA), towards 77 class-II, 6.7-GHz methanol masers identified by the Methanol Multibeam (MMB) survey to map the thermal emission from cool dust towards these objects. These data complement a study of 630 methanol masers associated with compact dense clumps identified from the ATLASGAL survey. Compact dust emission is detected towards 70 sources, which implies a dust-association rate of 99% for the full MMB catalogue. Evaluation of the derived dust and maser properties leads us to conclude that the combined sample represents a single population tracing the same phenomenon. We find median clump masses of a few 10$^3$ M$\odot$ and that all but a handful of sources satisfy the mass-size criterion required for massive star formation. This study provides the strongest evidence of the almost ubiquitous association of methanol masers with massive, star-forming clumps. The fraction of methanol-maser associated clumps is a factor of ~2 lower in the outer Galaxy than the inner Galaxy, possibly a result of the lower metallicity environment of the former. We find no difference in the clump-mass and maser-luminosity distributions of the inner and outer Galaxy. The maser-pumping and clump-formation mechanisms are therefore likely to be relatively invariant to Galactic location. Finally, we use the ratio of maser luminosity and clump mass to investigate the hypothesis that the maser luminosity is a good indicator of the evolutionary stage of the embedded source, however, we find no evidence to support this.
In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than $1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order $n$ that have a multiplicity that is close to the upper bound $\frac{n-3}{2}$, and emphasize the particular role of the algebraic connectivity.