ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report the identification and study of an unusual soft state of the black hole low-mass X-ray binary GRO J1655-40, observed during its 2005 outburst by the Rossi X-ray Timing Explorer. Chandra X-ray grating observations have revealed a high mass-outflow accretion disc wind in this state, and we show that the broadband X-ray spectrum is remarkably similar to that observed in the so-called `hypersoft' state of the high mass X-ray binary Cyg X-3, which possesses a strong stellar wind from a Wolf-Rayet secondary. The power-spectral density (PSD) of GRO J1655-40 shows a bending power-law shape, similar to that of canonical soft states albeit with larger fractional rms. However, the characteristic bend-frequency of the PSD is strongly correlated with the X-ray flux, such that the bend-frequency increases by two decades for less than a factor 2 increase in flux. The strong evolution of PSD bend-frequency for very little change in flux or X-ray spectral shape seems to rule out the suppression of high-frequency variability by scattering in the wind as the origin of the PSD bend. Instead, we suggest that the PSD shape is intrinsic to the variability process and may be linked to the evolution of the scale-height in a slim disc. An alternative possibility is that variability is introduced by variable absorption and scattering in the wind. We further argue that the hypersoft state in GRO J1655-40 and Cyg X-3 is associated with accretion close to or above the Eddington limit.
We consider a scalar field interaction with a cosmic string configuration in a flat 3-brane. The origin of this field is given by a compactification mechanism in the context of a 5-dimensional Brans-Dicke theory. We use the Cosmic Microwave Background Radiation constraint to analyse a possibility of optical activity effect in connection with the Brans-Dicke parameter w and obtain relations between the compactification modes. We show that the dilatons produced by a cosmic string can decay into gauge bosons with masses given by the compactification modes. The Brans- Dicke parameter w imposes stringent constraints on the mass of the dilaton which lives in the brane and help us to understand the energy scales. In this scenario we estimate the lifetime of the dilaton which decays into light gauge bosons and the dependence of this phenomenon with the Brans-Dicke parameter.
We prove the non-rationality of a double cover of $\mathbb{P}^{n}$ branched over a hypersurface $F\subset\mathbb{P}^{n}$ of degree $2n$ having isolated singularities such that $n\ge 4$ and every singular points of the hypersurface $F$ is ordinary, i.e. the projectivization of its tangent cone is smooth, whose multiplicity does not exceed $2(n-2)$.
The effective field theory including the dissipative effect is developed based on the Caldeira-Leggett theory at the classical level. After the integration of the small field fluctuations considered as the field radiation, the integro-differential field equation is given and shown to include the dissipative effects. In that derivation, special cares should be taken for the boundary condition of the integration. Application to the linear sigma model is given, and the decay process of the chiral condensate is calculated with it, both analytically in the linear approximation and numerically. With these results, we discuss the stability of chiral condensates within the quenched approximation.
The magnetization processes of the spin-3/2 antiferromagnet LiInCr4O8 comprising a "breathing" pyrochlore lattice, which is an alternating array of small and large tetrahedra, are studied under ultrahigh magnetic fields of up to 130 T using state-of-the-art pulsed magnets. A half magnetization plateau is observed above 90 T to 130 T, suggesting that LiInCr4O8 has a strong spin-lattice coupling, similar to conventional chromium spinel oxides. The magnetization of LiGa0.125In0.875Cr4O8, in which the structural and magnetic transitions at low temperatures have been completely suppressed, shows a sudden increase above 13 T, indicating that a spin gap of 2.2 meV exists between a tetramer singlet ground state and an excited state with total spin 1, with the latter being stabilized by the application of a magnetic field. The breathing pyrochlore antiferromagnet is found to be a unique frustrated system with strong spin-lattice coupling and bond alternation.
Manin's relations characterize period polynomials of a modular form. In this paper, we propose a finite set of relations checked by bi-period polynomials of a couple of forms. Then we construct an Eisenstein part of depth 2 which essentially completed the set of bi-periods polynomials among polynomials canceled by the relations. By giving a computational description of that part, we prove a result of irrationality of ratio of the periods for some weights.
We report on gamma-ray observations of the Crab Pulsar and Nebula using 8 months of survey data with the Fermi Large Area Telescope (LAT). The high quality light curve obtained using the ephemeris provided by the Nancay and Jodrell Bank radio telescopes shows two main peaks stable in phase with energy. The first gamma-ray peak leads the radio main pulse by (281 \pm 12 \pm 21) mus, giving new constraints on the production site of non-thermal emission in pulsar magnetospheres. The improved sensitivity and the unprecedented statistics afforded by the LAT enable precise measurement of the Crab Pulsar spectral parameters: cut-off energy at E_c = (5.8 \pm 0.5 \pm 1.2) GeV, spectral index of Gamma = (1.97 \pm 0.02 \pm 0.06) and integral photon flux above 100 MeV of (2.09 \pm 0.03 \pm 0.18) x 10^{-6} cm^{-2} s^{-1}. The first errors represent the statistical error on the fit parameters, while the second ones are the systematic uncertainties. Pulsed gamma-ray photons are observed up to ~ 20 GeV which precludes emission near the stellar surface, below altitudes of around 4 to 5 stellar radii in phase intervals encompassing the two main peaks. The spectrum of the nebula in the energy range 100 MeV - 300 GeV is well described by the sum of two power-laws of indices Gamma_{sync} = (3.99 \pm 0.12 \pm 0.08) and Gamma_{IC} = (1.64 \pm 0.05 \pm 0.07), corresponding to the falling edge of the synchrotron and the rising edge of the inverse Compton components, respectively. This latter, which links up naturally with the spectral data points of Cherenkov experiments, is well reproduced via inverse Compton scattering from standard Magnetohydrodynamics (MHD) nebula models, and does not require any additional radiation mechanism.
We have constructed the coherent state of $U(N,1)$, which is an extension of the Barut-Girardello (BG) coherent state of $SU(1,1)$, in our previous paper. However there is a restriction that the eigenvalue of the Casimir operator is natural number. In this paper we construct the coherent state in the analytic representation to overcome this restriction. Next we show that the measure of the BG coherent state is not the symplectic induced measure.
Numerical models of the tidal disruption of the Sagittarius (Sgr) dwarf galaxy have recently been developed that for the first time simultaneously satisfy most observational constraints on the angular position, distance, and radial velocity trends of both leading and trailing tidal streams emanating from the dwarf. We use these dynamical models in combination with extant 3-D position and velocity data for Galactic globular clusters and dSph galaxies to identify those Milky Way satellites that are likely to have originally formed in Sgr and been stripped from it during its extended interaction with the Milky Way. We conclude that the globular clusters Arp 2, M 54, NGC 5634, Terzan 8, and Whiting 1 are likely associated with the Sgr dwarf, and that Berkeley 29, NGC 5053, Pal 12, and Terzan 7 may be as well. The initial Sgr system therefore may have contained 5-9 globular clusters, corresponding to a specific frequency S_N = 5 - 9 for an initial Sgr luminosity M_V = -15.0. Our result is consistent with the 8\pm2 Sgr globular clusters expected from statistical modeling of the Galactic globular cluster distribution and the corresponding false-association rate due to chance alignments with the Sgr streams. These clusters are consistent with previous reconstructions of the Sgr age-metallicity relation, and show no evidence for a second-parameter effect shaping their horizontal branch morphologies. We find no statistically significant evidence to suggest that any of the recently discovered population of ultra-faint dwarf galaxies are conclusively associated with the Sgr tidal streams. (Abridged).
We present a new, model independent method for extracting bounds for the anomalous $\gamma WW$ couplings from hadron collider experiments. At the partonic level we introduce a set of three observables which are constructed from the unpolarized differential cross-section for the process $d\bar{u}\to W^{-}\gamma$ by appropriate convolution with a set of simple polynomials depending only on the center-of-mass angle. One of these observables allows for the direct determination of the anomalous coupling usually denoted by $\Delta\kappa$, without any simplifying assumptions, and without relying on the presence of a radiation zero. The other two observables impose two sum rules on the remaining three anomalous couplings. The inclusion of the structure functions is discussed in detail for both $p\bar{p}$ and $pp$ colliders. We show that, whilst for $p\bar{p}$ experiments this can be accomplished straightforwardly, in the $pp$ case one has to resort to somewhat more elaborate techniques, such as the binning of events according to their longitudinal momenta.
Entropy production in the initial compression stage of relativistic heavy-ion collisions from AGS to SPS energies is calculated within a three-fluid hydrodynamical model. The entropy per participating net baryon is found to increase smoothly and does not exhibit a jump or a plateau as in the 1-dimensional one-fluid shock model. Therefore, the excess of pions per participating net baryon in nucleus-nucleus collisions as compared to proton-proton reactions also increases smoothly with beam energy.
We measure the Balmer decrements of 23 of the brightest planetary nebulae (PNe) in the inner bulge ($r \lesssim 3$ arcmin) of M31 and de-redden the bright end of the region's [O III] $\lambda 5007$ planetary nebula luminosity function. We show that the most luminous PNe produce $\gtrsim 1{,}200 \, \rm{L}_{\odot}$ of power in their [O III] $\lambda 5007$ line, implying central star luminosities of at least $\sim 11{,}000 \, \rm{L}_{\odot}$. Even with the most recent accelerated-evolution post-AGB models, such luminosities require central star masses in excess of $0.66 \, \rm{M}_{\odot}$, and main sequence progenitors of at least $\sim 2.5 \, \rm{M}_{\odot}$. Since M31's bulge has very few intermediate-age stars, we conclude that conventional single-star evolution cannot be responsible for these extremely luminous objects. We also present the circumstellar extinctions for the region's bright PNe and demonstrate that the distribution is similar to that found for PNe in the Large Magellanic Cloud, with a median value of $A_{5007} = 0.71$. Finally, we compare our results to extinction measurements made for PNe in the E6 elliptical NGC 4697 and the interacting lenticular NGC 5128. We show that such extinctions are not unusual, and that the existence of very high-mass PN central stars is a general feature of old stellar populations. Our results suggest that single-star population synthesis models significantly underestimate the maximum luminosities and total integrated light of AGB stars.
We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These two processes commute and both of them commute with the unitary evolution controlled by the systems Hamiltonian. The corresponding memory kernel gives rise to semi-Markov evolution of the diagonal elements of the density matrix. However, the corresponding evolution needs not be completely positive. The role of decoherence generator is to restore complete positivity. Hence, to pose the dynamical problem one needs two processes generated by classical semi-Markov memory kernel and purely quantum decoherence generator. This scheme is illustrated for a qubit evolution.
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders. In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed subintervals of [0,1], and we define a subset of such measures that yield a unique representation. In the semiorder case, we similarly find unique representations by a class of distribution functions.
Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a structural characterisation of the graph states that can be used for quantum information processing. The existence of a gflow (generalized flow) is known to be a requirement for open graphs (graph, input set and output set) to perform uniformly and strongly deterministic computations. We weaken the gflow conditions to define two new more general kinds of MBQC: uniform equiprobability and constant probability. These classes can be useful from a cryptographic and information point of view because even though we cannot do a deterministic computation in general we can preserve the information and transfer it perfectly from the inputs to the outputs. We derive simple graph characterisations for these classes and prove that the deterministic and uniform equiprobability classes collapse when the cardinalities of inputs and outputs are the same. We also prove the reversibility of gflow in that case. The new graphical characterisations allow us to go from open graphs to graphs in general and to consider this question: given a graph with no inputs or outputs fixed, which vertices can be chosen as input and output for quantum information processing? We present a characterisation of the sets of possible inputs and ouputs for the equiprobability class, which is also valid for deterministic computations with inputs and ouputs of the same cardinality.
A finite collection $P$ of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of $P$. We associate with such a tiling a doubly infinite sequence with entries from $P$. The set of all such sequences is a sofic system, called a tiling system. We show that, up to powers of the shift, every shift of finite type can be realized as a tiling system.
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.
We enumerate factorisations of the complete graph into spanning regular graphs in several cases, including when the degrees of all the factors except for one or two are small. The resulting asymptotic behaviour is seen to generalise the number of regular graphs in a simple way. This leads us to conjecture a general formula when the number of factors is vanishing compared to the number of vertices.
Knowledge distillation aims to compress a powerful yet cumbersome teacher model into a lightweight student model without much sacrifice of performance. For this purpose, various approaches have been proposed over the past few years, generally with elaborately designed knowledge representations, which in turn increase the difficulty of model development and interpretation. In contrast, we empirically show that a simple knowledge distillation technique is enough to significantly narrow down the teacher-student performance gap. We directly reuse the discriminative classifier from the pre-trained teacher model for student inference and train a student encoder through feature alignment with a single $\ell_2$ loss. In this way, the student model is able to achieve exactly the same performance as the teacher model provided that their extracted features are perfectly aligned. An additional projector is developed to help the student encoder match with the teacher classifier, which renders our technique applicable to various teacher and student architectures. Extensive experiments demonstrate that our technique achieves state-of-the-art results at the modest cost of compression ratio due to the added projector.
(Abridged).We present the results of MHD simulations of low mass protoplanets interacting with turbulent disks. We calculate the orbital evolution of `planetesimals' and protoplanets with masses in the range 0 < m_p < 30 M_Earth. Planetesimals and protoplanets undergo stochastic migration due to interaction with turbulent density fluctuations. Over run times of ~ 150 planet orbits, stochastic migration dominates over type I migration for many models. Fourier analysis of the torques experienced by planets indicates that the torque fluctuations contain components with significant power whose time scales of variation are similar to the simulation run times. These low frequency fluctuations partly explain the dominance of stochastic torques, and may provide a powerful means of counteracting the type I migration of some planets in turbulent disks. Turbulence is a source of eccentricity driving. Planetesimals attained eccentricities in the range 0.02 < e < 0.14, m_p=1 M_Earth planets attained eccentricities 0.02 < e < 0.08, and m_p=10 M_Earth protoplanets reached 0.02 < e < 0.03. This is in basic agreement with a model in which turbulence drives e-growth, and interaction with disk material at coorbital Lindblad resonances causes e-damping. These results are significant for planet formation. Stochastic migration may prevent some planet cores migrating into their star via type I before becoming gas giants. The growth of planetary cores may be enhanced by preventing isolation. Eccentricity excitation by turbulence, however, may reduce growth rates of planetary cores during the runaway and oligarchic growth stages, and cause collisions between planetesimals to become destructive.
Theoretical background of our proposed relation between the accelerating universe and the time-variability of the fine-structure constant is discussed, based on the scalar-tensor theory, with emphases on the intuitive aspects of underlying physical principles. An important comment is added on the successful understanding of the size of the effective cosmological constant responsible for the acceleration, without appealing to fine-tuning parameters.
We show that a Cram\'er--Wold device holds for infinite divisibility of $\mathbb{Z}^d$-valued distributions, i.e. that the distribution of a $\mathbb{Z}^d$-valued random vector $X$ is infinitely divisible if and only if $\mathcal{L}(a^T X)$ is infinitely divisible for all $a\in \mathbb{R}^d$, and that this in turn is equivalent to infinite divisibility of $\mathcal{L}(a^T X)$ for all $a\in \mathbb{N}_0^d$. A key tool for proving this is a L\'evy--Khintchine type representation with a signed L\'evy measure for the characteristic function of a $\mathbb{Z}^d$-valued distribution, provided the characteristic function is zero-free.
The relations satisfied by period polynomials associated to modular forms yield a way to count dimensions of spaces of cusp forms. After showing how these relations arise from those on the mapping class group $PSL(2, \mathbb{Z})$ of the moduli space $\mathcal{M}_{0,4}$ of genus 0 curves with 4 marked points, the author goes on to define period polynomials associated to Picard modular forms. Relations on these Picard period polynomials are then determined, and via an embedding of a monodromy representation of the moduli space $\mathcal{M}_{0,5}$ of genus 0 curves with 5 marked points in $PU(2,1 ; \mathbb{Z}[\rho])$ (where $\rho$ denotes a third root of unity), they are related to the geometry of $\mathcal{M}_{0,5}.$
Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the quantum states of a single particle remotely, one needs to teleport multilevel (high-dimensional) states. Here, we demonstrate the teleportation of high-dimensional states in a three-dimensional six-photon system. We exploit the spatial mode of a single photon as the high-dimensional system, use two auxiliary entangled photons to realize a deterministic three-dimensional Bell state measurement. The fidelity of teleportation process matrix is F=0.596\pm0.037. Through this process matrix, we can prove that our teleportation is both nonclassical and genuine three dimensional. Our work paves the way to rebuild complex quantum systems remotely and to construct complex quantum networks.
The problem of accretion in the Trojan 1:1 resonance is akin to the standard problem of planet formation, transplanted from a star-centered disk to a disk centered on the Lagrange point. The newly discovered class of Neptune Trojans promises to test theories of planet formation by coagulation. Neptune Trojans resembling the prototype 2001 QR322 (``QR'')--whose radius of ~100 km is comparable to that of the largest Jupiter Trojan--may outnumber their Jovian counterparts by a factor of ~10. We discover that seeding the 1:1 resonance with debris from planetesimal collisions and having the seed particles accrete in situ naturally reproduces the inferred number of QR-sized Trojans. We analyze accretion in the Trojan sub-disk by applying the two-groups method, accounting for kinematics specific to the resonance. We find that a Trojan sub-disk comprising decimeter-sized seed particles and having a surface density 1e-3 that of the local minimum-mass disk produces ~10 QR-sized objects in ~1 Gyr, in accord with observation. Further growth is halted by collisional diffusion of seed particles out of resonance. In our picture, the number and sizes of the largest Neptune Trojans represent the unadulterated outcome of dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the most newly accreted objects in our Solar System, may today have a dispersion in orbital inclination of less than ~10 degrees, despite the existence of niches of stability at higher inclinations. Such a vertically thin disk, born of a dynamically cold environment necessary for accretion, and raised in minimal contact with external perturbations, contrasts with the thick disks of other minor body belts.