ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider redundant analogues of the f- and h-vectors of simplicial complexes and present bases of R^{m+1} related to these ``long'' f- and h-vectors describing the face systems from 2^{1,...,m}; we list the corresponding change of basis matrices. The representations of the long f- and h-vectors of a face system with respect to various bases are expressed based on partitions of the system into Boolean intervals.
The aim of this paper is to present the results of photometric investigations of the central cluster of the W5 E region as well as a follow-up study of the triggered star formation in and around bright-rimmed clouds (BRCs). We have carried out wide field $UBVI_c$ and deep $VI_c$ photometry of the W5 E H{\sc ii} region. A distance of $\sim$2.1 kpc and a mean age of $\sim$1.3 Myr have been obtained for the central cluster. The young stellar objects (YSOs) associated with the region are identified on the basis of near-infrared and mid-infrared observations. We confirmed our earlier results that the average age of the YSOs lying on/inside the rim are younger than those lying outside the rim. The global distribution of the YSOs shows an aligned distribution from the ionising source to the BRCs. These facts indicate that a series of radiation driven implosion processes proceeded from near the central ionising source towards the periphery of the W5 E H{\sc ii} region. We found that, in general, the age distributions of the Class II and Class III sources are the same. This result is apparently in contradiction with the conclusion by Bertout, Siess & Cabrit (2007) and Chauhan et al. (2009) that classical T Tauri stars evolve to weak-line T Tauri stars. The initial mass function of the central cluster region in the mass range $0.4 \le M/M_\odot \le 30$ can be represented by $\Gamma = -1.29 \pm 0.03$. The cumulative mass functions indicate that in the mass range $0.2 \le M/M_\odot \le 0.8$, the cluster region and BRC NW have more low mass YSOs in comparison to BRCs 13 and 14.
We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.
We study the influence of the surface orientation on the wetting behavior of bcc binary alloys, using a semi-infinite lattice model equivalent to a nearest-neighbor Ising antiferromagnet in an external field. The salient feature of the model is the generation of an ``effective'' ordering surface field for symmetry-breaking surface orientations like (100). Such a field couples to the local order parameter at the surface and leads to the occurrence of wetting phenomena below the critical temperature T_c. Utilizing a Ginzburg-Landau continuum model which has been derived earlier from the lattice mean-field theory, the wetting phase diagram is calculated.
We develop an optimization approach to model the magnetic field configuration of magnetic clouds, based on a linear-force free formulation in three dimensions. Such a solution, dubbed the Freidberg solution, is kin to the axi-symmetric Lundquist solution, but with more general "helical symmetry". The merit of our approach is demonstrated via its application to two case studies of in-situ measured magnetic clouds. Both yield results of reduced $\chi^2\approx 1$. Case 1 shows a winding flux rope configuration with one major polarity. Case 2 exhibits a double-helix configuration with two flux bundles winding around each other and rooted on regions of mixed polarities. This study demonstrates the three-dimensional complexity of the magnetic cloud structures.
The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to define partial symmetries in payoff matrices. With this purpose, we introduce the notion of the role a player plays with respect to another one, and combinatorial relations between roles are studied. Building on them, we define relations directly between players, which provide yet another characterization of structural symmetries in the payoff matrices of strategic games.
We investigate correlated electronic transport in single-walled carbon nanotubes with two intramolecular tunneling barriers. We suggest that below a characteristic temperature the long range nature of the Coulomb interaction becomes crucial to determine the temperature dependence of the maximum G_max of the conductance peak. Correlated sequential tunneling dominates transport yielding the power-law G_max ~ T^{\alpha_{end-end}-1}, typical for tunneling between the ends of two Luttinger liquids. Our predictions are in agreement with recent measurements.
In the dimer model, a configuration consists of a perfect matching of a fixed graph. If the underlying graph is planar and bipartite, such a configuration is associated to a height function. For appropriate "critical" (weighted) graphs, this height function is known to converge in the fine mesh limit to a Gaussian free field, following in particular Kenyon's work.   In the present article, we study the asymptotics of smoothed and local field observables from the point of view of families of Cauchy-Riemann operators and their determinants. This allows in particular to obtain a functional invariance principle for the field; characterise completely the limiting field on toroidal graphs as a compactified free field; analyse electric correlators; and settle the Fisher-Stephenson conjecture on monomer correlators.   The analysis is based on comparing the variation of determinants of families of (continuous) CR operators with that of their discrete (finite dimensional) approximations. This relies in turn on estimating precisely inverting kernels, in particular near singularities. In order to treat correlators of "singular" local operators, elements of (multiplicatively) multi-valued discrete holomorphic functions are discussed.
Reactive magnetron sputtering enables the deposition of various thin films to be used for protective as well as optical and electronic applications. However, progressing target erosion during sputtering results in increased magnetic field strengths at the target surface. Consequently, the glow discharge, the target poisoning, and hence the morphology, crystal structure and stoichiometry of the prepared thin films are influenced. Therefore, these effects were investigated by varying the cathode current Im between 0.50 and 1.00 A, the magnetic field strength B between 45 and 90 mT, and the O2/(Ar+O2) flow rate ratio between 0 and 100%. With increasing oxygen flow ratio a sub-stoichiometric TaOx oxide forms at the metallic Ta target surface which further transfers to a non-conductive tantalum pentoxide Ta2O5, impeding a stable DC glow discharge. These two transition zones (from Ta to TaOx and from TaOx to Ta2O5) shift to higher oxygen flow rates for increasing target currents. Contrary, increasing the magnetic field strength (e.g., due to sputter erosion) mainly shifts the TaOx to Ta2O5 transition to lower oxygen flow rates while marginally influencing the Ta to TaOx transition. To allow for a stable DC glow discharge (and to suppress the formation of non-conductive Ta2O5 at the target) even at a flow rate ratio of 100% either a high target current (Im >= 1 A) or a low magnetic field strength (B <= 60 mT) is necessary. These conditions are required to prepare stoichiometric and fully crystalline Ta2O5 films. Our investigations clearly demonstrate the importance of the magnetic field strength, which changes during sputter erosion, on the target poisoning and the resulting film quality.
We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter $K$ that goes to infinity, following a large population assumption. When the birth and natural death parameters are of order $K$, the sequence of stochastic processes indexed by $K$ converges toward a slow-fast dynamics. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches $(0,0)$ almost surely in finite time. We obtain that the population size and the proportion of a given allele converge toward a generalized Wright-Fisher diffusion with varying population size and diploid selection. Using a non trivial change of variables, we next study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting $(0,0)$ admits a unique quasi-stationary distribution. We finally give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.
In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time-dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possible for this Hamiltonian to be non-hermitian. Here, we show that this non-hermiticity results from a time dependence of the position eigenstates that enter into the Schrodinger wave function, and we write the expression for the Hamiltonian that is Hermitian for a general metric when the time-dependence of the metric is not neglected.
Most transition-metal trihalides are dimorphic. The representative chromium-based triad, CrCl3, CrBr3, CrI3, is characterized by the low-temperature phase adopting the trigonal BiI3 type while the structure of the high-temperature phase is monoclinic of AlCl3 type (C2/m). The structural transition between the two crystallographic phases is of the first-order type with large thermal hysteresis in CrCl3 and CrI3. We studied crystal structures and structural phase transitions of vanadium-based counterparts VCl3, VBr3, and VI3 by measuring specific heat, magnetization, and X-ray diffraction as functions of temperature and observed an inverse situation. In these cases, the high-temperature phase has a higher symmetry while the low-temperature structure reveals a lower symmetry. The structural phase transition between them shows no measurable hysteresis in contrast to CrX3. Possible relations of the evolution of the ratio c/a of the unit cell parameters, types of crystal structures, and nature of the structural transitions in V and Cr trihalides are discussed.
Cochlear implants (CIs) are neural prosthetics which are used to treat patients with hearing loss. CIs use an array of electrodes which are surgically inserted into the cochlea to stimulate the auditory nerve endings. After surgery, CIs need to be programmed. Studies have shown that the spatial relationship between the intra-cochlear anatomy and electrodes derived from medical images can guide CI programming and lead to significant improvement in hearing outcomes. However, clinical head CT images are usually obtained from scanners of different brands with different protocols. The field of view thus varies greatly and visual inspection is needed to document their content prior to applying algorithms for electrode localization and intra-cochlear anatomy segmentation. In this work, to determine the presence/absence of inner ears and to accurately localize them in head CTs, we use a volume-to-volume convolutional neural network which can be trained end-to-end to map a raw CT volume to probability maps which indicate inner ear positions. We incorporate a false positive suppression strategy in training and apply a shape-based constraint. We achieve a labeling accuracy of 98.59% and a localization error of 2.45mm. The localization error is significantly smaller than a random forest-based approach that has been proposed recently to perform the same task.
Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly suited to describe evolutions of the total number of customers in (in)homogeneous $M/M/S$ queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared to those known from the literature) under which the methods are applicable, are being formulated. Two numerical examples are given. It is also shown that for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.
General solution of asymptotic conditions, derived previously for n vector-meson parametrization of electromagnetic form factor of any strongly interacting particle with asymptotics 1/t^m (m<n) and combined with a form factor normalization condition, is presented. The special case of m=n and the solution of asymptotic conditions without any form factor normalization are discussed too.
We identify eight z>1 radio sources undetected at 850um but robustly detected at 70um, confirming that they represent ultraluminous infrared galaxies (ULIRGs) with hotter dust temperatures (T_dust=52+-10 K) than Submillimetre Galaxies (SMGs) at similar luminosities and redshifts. These galaxies share many properties with SMGs: ultra-violet (UV) spectra consistent with starbursts, high stellar masses and radio luminosities. We can attribute their radio emission to star formation since high-resolution MERLIN radio maps show extended emission regions (with half light radii of 2-3kpc), which are unlikely to be generated by AGN activity. These observations provide the first direct confirmation of hot, dusty ULIRGs which are missed by current submillimetre surveys. They have significant implications for future observations from the Herschel Space Observatory and SCUBA2, which will select high redshift luminous galaxies with less selection biases.
We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two pinning potential terms of dual fields that stabilize competing orders and allows different types of quantum phase transition to happen between two ordered phases. At the transition point, elementary excitations change from the topological soliton of one of the dual fields to that of the other, thus it can be characterized as a topological transition. We compute the dynamical susceptibilities and the entanglement entropy, which gives us access to the central charge, of the system using a numerical technique of infinite time-evolving block decimation and characterize the universality class of the transition as well as the nature of the order in each phase. The possible realizations of such transitions in experimental systems both for condensed matter and cold atomic gases are also discussed.
A search programme for pulsating subdwarf B stars was conducted with the Nordic Optical Telescope on La Palma over 59 nights between 1999 and 2009. The purpose of the programme was to significantly extend the number of rapidly pulsating sdB stars to better understand the properties of this new group of variable compact stars. Candidates were selected initially from the HS and HE surveys, but were supplemented with additional objects from other surveys. Short sequences of time-series photometry were made on the candidates to determine the presence of rapid pulsations. In total twenty new pulsators were found in this survey, most of which have already been published and some extensively studied. We present four new short period pulsators, bringing the total of such pulsators up to 49. We also give limits on pulsation amplitudes for 285 objects with no obvious periodic variations, summarise the results of the survey, and provide improved physical parameters on the composite pulsators for which only preliminary estimates were published earlier.
Here, cosmology of the late and future universe is obtained from $f(R)$-gravity with non-linear curvature terms $R^2$ and $R^3$ ($R$ being the Ricci scalar curvature). It is different from $f(R)$-dark enrgy models, where non-linear curvature terms are taken as gravitational alternative of dark energy. In the present model, neither linear nor no-linear curvature terms are taken as dark energy. Rather, dark energy terms are induced by curvature terms in the Friedmann equation derived from $f(R)$-gravitational equations. It has advantage over $f(R)$- dark energy models in the sense that the present model satisfies WMAP results and expands as $\sim t^{2/3}$ during matter-dominance. So, it does not have problems due to which $f(R)$-dark energy models are criticized. Curvature-induced dark energy, obtained here, mimics phantom. Different phases of this model, including acceleration and deceleration during phantom phase, are investigated here.It is found that expansion of the universe will stop at the age $(3.87 t_0 + 694.4 {\rm kyr})$ ($t_0$ being the present age of the universe) and after this epoch, it will contract and collapse by the time $(336.87 t_0 + 694.4 {\rm kyr})$. Further,it is shown that universe will escape predicted collapse (obtained using classical mechanics) on making quantum gravity corrections relevant near collapse time due to extremely high energy density and large curvature analogous to the state of very early universe. Interestingly, cosmological constant is also induced here, which is very small in classical domain, but very high in quantum domain.
Under high pressures, phase transition, as well as deformation twins, are constantly reported in many BCC metals, whose interactions are of fundamental importance to understand strengthen mechanism of these metals under extreme conditions. However, the interactions between twins and phase transition in BCC metals are remain largely unexplored. In this work, interactions between coherent twin boundaries and $\alpha \to \epsilon$ phase transition of iron are investigated using both non- equilibrium molecular dynamics simulations and nudge elastic band method. Mechanisms of both twin-assisted phase transition and reverse phase transition are studied and orientation relationships between BCC and HCP phase are found to be <11-1>BCC || <-12-10>HCP and <1-10>BCC || <0001>HCP for both cases. The twin boundary corresponds to after the phase transition. It is amazing that the reverse transition seems to be able to "memory" and recover the initial BCC twins. The memory would partly loss when plastic slips take place in the HCP phase before the reverse transition. In the recovered initial BCC twins, three major twin spacing are observed, which are well explained in terms of energy barriers of the transition from HCP phase to BCC twin. Besides, variant selection rule of the twin assisted phase transition is also discussed. The results of present work could be expected to give some clues for producing ultra-fine grain structure in materials exhibiting martensitic phase transition.
The control of recently observed spintronic effects in topological-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin texture around their interfaces. Here we combine density functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi$_2$Se$_3$ and Co or Cu layers comprising the interface. In contrast to widely assumed but thinly tested Dirac cone gapped by the proximity exchange field, we find that the Rashba ferromagnetic model describes the spectral function on the surface of Bi$_2$Se$_3$ in contact with Co near the Fermi level $E_F^0$, where circular and snowflake-like constant energy contours coexist around which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions injected by metallic layers and pushed, due to charge transfer from Co or Cu layers, few tenths of eV below $E_F^0$ for both Bi$_2$Se$_3$/Co and Bi$_2$Se$_3$/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features explain recent observation [K. Kondou {\em et al.}, Nat. Phys. {\bf 12}, 1027 (2016)] of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of $E_F^0$. Interestingly, three monolayers of Co adjacent to Bi$_2$Se$_3$ host spectral functions very different from the bulk metal, as well as in-plane spin textures signifying the spin-orbit proximity effect. We predict that out-of-plane tunneling anisotropic magnetoresistance in vertical heterostructure Cu/Bi$_2$Se$_3$/Co, where current flowing perpendicular to its interfaces is modulated by rotating magnetization from parallel to orthogonal to current flow, can serve as a sensitive probe of spin texture residing at $E_F^0$.
The data from all observations of RBS 1223 (1RXS J130848.6+212708) conducted by XMM-Newton EPIC pn with the same instrumental setup in 2003-2007 were combined to form spin-phase resolved spectra. A number of complex models of neutron stars with strongly magnetized ($B_{pole} 10^{13}-10^{14}$ G) surface, with temperature and magnetic field distributions around magnetic poles, and partially ionized hydrogen thin atmosphere above it have been implemented into the X-ray spectral fitting package XSPEC for simultaneous fitting of phase-resolved spectra. A Markov-Chain-Monte-Carlo (MCMC) approach is also applied to verify results of fitting and estimating in multi parameter models. The spectra in different rotational phase intervals and light curves in different energy bands with high S/N ratio show a high complexity. The spectra can be parameterized with a Gaussian absorption line superimposed on a blackbody spectrum, while the light curves with double-humped shape show strong dependence of pulsed fraction upon the energy band (13%-42%), which indicates that radiation emerges from at least two emitting areas. A model with condensed iron surface and partially ionized hydrogen thin atmosphere above it allows us to fit simultaneously the observed general spectral shape and the broad absorption feature observed at 0.3 keV in different spin phases of RBS 1223. It allowed to constrain some physical properties of X-ray emitting areas, i.e. the temperatures ($T_{p1} ~ 105$ eV, $T_{p2} ~ 99$ eV), magnetic field strengths ($B_{p1}= B_{p2} ~ 8.6x10^{13}$G) at the poles, and their distributions parameters ($a_{1} 0.61, a_{2} 0.29$, indicating an absence of strong toroidal magnetic field component). In addition, it puts some constraints on the geometry of the emerging X-ray emission and gravitational redshift ($z=0.16^{+0.03}_{-0.01}$) of RBS 1223.