ShantanuT01/DACTYL-Pretraining huggingface dataset:
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the random tree-like object naturally associated with a standard Brownian excursion, may be thought of as a random compact real tree. The continuum random tree is a scaling limit as N tends to infinity of both a critical Galton-Watson tree conditioned to have total population size N as well as a uniform random rooted combinatorial tree with N vertices. The Aldous--Broder algorithm is a Markov chain on the space of rooted combinatorial trees with N vertices that has the uniform tree as its stationary distribution. We construct and study a Markov process on the space of all rooted compact real trees that has the continuum random tree as its stationary distribution and arises as the scaling limit as N tends to infinity of the Aldous--Broder chain. A key technical ingredient in this work is the use of a pointed Gromov--Hausdorff distance to metrize the space of rooted compact real trees.
We study the dyonic charge of type IIA D6-branes interpreted as M-theory Kaluza-Klein monopoles. The connection between the dyonic properties of type IIA D6-branes and the existence of eleven dimensions is discussed. We also study dyonic properties of non-commutative monopoles. Variations of the external antisymmetric B-field generate the electric charge of non-commutative dyons.
We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/YIG) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.
The Classical Jacobian Conjecture claims that any unramified endomorphism of a complex affine space is an automorphism. In order to embed this conjecture in a geometric environment, where one could enjoy the beauty and the richness of tools of algebraic geometry and algebraic D-modules, as his paper [6] proves it, Hyman Bass proposed 25 years ago in [6], page 80 the following statement as the Generalized Jacobian Conjecture: "Any unramified morphism from a complex irreducible affine and unirational variety whose invertible regular functions are all constant to a complex affine space of the same dimension is an isomorphism". On the other hand, without any explicit connection with Bass conjecture, Victor Kulikov published in 1993 (see [18]) a non trivial construction of a complex irreducible rational and simply connected surface and an unramified morphism of geometric degree 3 (and hence which is not an isomorphism) from this surface to the complex affine space, without specifying if this surface is affine or not, or if its invertible regular functions are all constant or not. The main aim of this paper is to bring this precision and thanks to this to expose the complete solution to Bass Generalized Jacobian Conjecture which turned to be true only in dimension one (see Theorem 1 below).
We present ~0.15'' spatial resolution imaging of SHiZELS-14, a massive (M*~10^11 M_sol), dusty, star-forming galaxy at z=2.24. Our rest-frame ~1kpc-scale, matched-resolution data comprise four different widely used tracers of star formation: the H-alpha emission line (from SINFONI/VLT), rest-frame UV continuum (from HST F606W imaging), the rest-frame far-infrared (from ALMA), and the radio continuum (from JVLA). Although originally identified by its modest H-alpha emission line flux, SHiZELS-14 appears to be a vigorously star-forming (SFR~1000 M_sol/yr) example of a submillimeter galaxy, probably undergoing a merger. SHiZELS-14 displays a compact, dusty central starburst, as well as extended emission in $\rm{H}\alpha$ and the rest-frame optical and FIR. The UV emission is spatially offset from the peak of the dust continuum emission, and appears to trace holes in the dust distribution. We find that the dust attenuation varies across the spatial extent of the galaxy, reaching a peak of at least A_H-alpha~5 in the most dusty regions, although the extinction in the central starburst is likely to be much higher. Global star-formation rates inferred using standard calibrations for the different tracers vary from ~10-1000 M_sol/yr, and are particularly discrepant in the galaxy's dusty centre. This galaxy highlights the biased view of the evolution of star-forming galaxies provided by shorter wavelength data.
We critically discuss the recent observations of the binary system at the center of the bipolar planetary nebula Henize 2-428. We find that the proposed explanation of two equal-mass degenerate objects with a total mass larger than the Chandrasekhar limiting mass that supposedly will merge in less than a Hubble time, possibly leading to a SN~Ia, is controversial. This hypothesis relies on the assumption that the variability of the He II 5412A spectral line is due to two absorption components. Instead, we propose that it can be accounted for by a broad absorption line from the central system on top of which there is a narrow emission line from the nebula. This prompted us to study if the binary system can be made of a degenerate star and a low-mass main sequence companion, or of two degenerate objects of smaller mass. We find that although both scenarios can account for the existence of two symmetric broad minima in the light curve, the second one agrees better with observations. We thus argue that the claim that Henize 2-428 provides observational evidence supporting the double-degenerate scenario for SN~Ia is premature.
We study the nature of phase transitions between gaseous and condensed states in the self-gravitating Fermi gas at nonzero temperature in general relativity. The condensed states can represent compact objects such as white dwarfs, neutron stars, or dark matter fermion balls. The caloric curves depend on two parameters: the system size $R$ and the particle number $N$. When $N<N_{\rm OV}$, where $N_{\rm OV}$ is the Oppenheimer-Volkoff limit, there exists an equilibrium state for any value of the temperature $T$ and of the energy $E$ as in the nonrelativistic case [P.H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006)]. Gravitational collapse is prevented by quantum mechanics (Pauli's exclusion principle). When $N>N_{\rm OV}$, there is no equilibrium state below a critical energy and below a critical temperature. In that case, the system is expected to collapse towards a black hole. We plot the caloric curves of the general relativistic Fermi gas, study the different types of phase transitions that occur in the system, and determine the phase diagram in the $(R,N)$ plane. The nonrelativistic results are recovered for $N\ll N_{\rm OV}$ and $R\gg R_{\rm OV}$ with $NR^3$ fixed. The classical results are recovered for $N\gg N_{\rm OV}$ and $R\gg R_{\rm OV}$ with $N/R$ fixed. We highlight a situation of physical interest where a gaseous Fermi gas, by cooling, first undergoes a phase transition towards a compact object (white dwarf, neutron star, dark matter fermion ball), then collapses into a black hole. This situation occurs in the microcanonical ensemble when $N_{\rm OV}<N<3.73\, N_{\rm OV}$. We also relate the phase transitions from a gaseous state to a core-halo state in the microcanonical ensemble to the onset of red-giant structure and to the supernova phenomenon.
We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realisations, using partially-polarising beamsplitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-Z gate in both continuous-wave and pulsed regimes of operation, fully characterising it in each case using quantum process tomography. We also demonstrate a fully-resolving, nondeterministic optical Bell-state analyser based on this controlled-Z gate. This new architecture is ideally suited to guided optics implementations of optical gates.
We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times $T_{1}$ and $T_{2}$ (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with $T_{1}$). To this end, we simply associate the time-dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.
The current cosmological structure formation models predict that galaxies evolve through frequent mergers. During these events, the supermassive black holes (SMBHs) residing in the centres of the galaxies shrink to the central region, while losing energy via dynamical friction. Detection of SMBHs in these galaxy mergers is straightforward if they are actively accreting matter from their surroundings as active galactic nuclei (AGN). Currently, only a few dual AGN are known. One way to identify dual AGN candidates is by detecting double-peaked emission lines in their spectra. If these are broad spectral lines, it may indicate the existence of two broad line regions associated with two AGN. 2MASS J165939.7+183436 is a merging system, where the detected double-peaked broad emission lines can be explained by a dual AGN with an estimated separation of $0.085"$. Radio emission from this object was detected in the Faint Images of the Radio Sky at Twenty-centimeters survey with a flux density of 2.6 mJy. We used the European Very Long Baseline Interferometer Network and the enhanced Multi-Element Remotely Linked Interferometer Network to image 2MASS J165939.7+183436 at 1.7 GHz. We did not detect compact radio emission from the source.
It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (``Bell Locality'') and the empirically well-supported predictions of quantum theory for the standard EPR-Bell setup. The demonstrated hidden variables are precisely those needed for the derivation of the Bell Inequalities. We thus refute the widespread view that empirical violations of Bell Inequalities leave open a choice of whether to reject (i) locality or (ii) hidden variables. Both principles are indeed assumed in the derivation of the inequalities, but since, as we demonstrate here, (ii) actually follows from (i), there is no choice but to blame the violation of Bell's Inequality on (i). Our main conclusion is thus that no Bell Local theory can be consistent with what is known from experiment about the correlations exhibited by separated particles. Aside from our conclusion being based on a different sense of locality this conclusion resembles one that has been advocated recently by H.P. Stapp. We therefore also carefully contrast the argument presented here to that proposed by Stapp.
Leading-order electromagnetic loop corrections to the one-pion-exchange potential are computed within the framework of chiral perturbation theory. These corrections generate an effective nucleon-nucleon potential, $V_{\pi \gamma}$, which supplements the sum of OPEP and the nucleon-nucleon Coulomb potential. This potential is charge dependent and its construction is demonstrated to be gauge invariant. The potential $V_{\pi \gamma}$ has been included in the Nijmegen partial-wave analysis of np data. A particular renormalization scheme is chosen that leads to a negligible change in the charged-piNN coupling constant and in the np 1S0 scattering length and effective range.
We present the submission of Samsung AI Centre Cambridge to the CVPR2020 EPIC-Kitchens Action Recognition Challenge. In this challenge, action recognition is posed as the problem of simultaneously predicting a single `verb' and `noun' class label given an input trimmed video clip. That is, a `verb' and a `noun' together define a compositional `action' class. The challenging aspects of this real-life action recognition task include small fast moving objects, complex hand-object interactions, and occlusions. At the core of our submission is a recently-proposed spatial-temporal video attention model, called `W3' (`What-Where-When') attention~\cite{perez2020knowing}. We further introduce a simple yet effective contextual learning mechanism to model `action' class scores directly from long-term temporal behaviour based on the `verb' and `noun' prediction scores. Our solution achieves strong performance on the challenge metrics without using object-specific reasoning nor extra training data. In particular, our best solution with multimodal ensemble achieves the 2$^{nd}$ best position for `verb', and 3$^{rd}$ best for `noun' and `action' on the Seen Kitchens test set.
Galaxy clusters are valuable cosmological probes. However, cluster mass estimates rely on observable quantities that are affected by complicated baryonic physics in the intracluster medium (ICM), including feedback from active galactic nuclei (AGN). Cosmological simulations have started to include AGN feedback using subgrid models. In order to make robust predictions, the systematics of different implementations and parametrizations need to be understood. We have developed an AGN subgrid model in FLASH that supports a few different black hole accretion models and feedback models. We use this model to study the effect of AGN on X-ray cluster observables and its dependence on model variations.
A theory of image-potential states is presented for the general case where these surface electronic states are resonant with a bulk continuum. The theory extends the multiple scattering approach of Echenique and Pendry into the strong coupling regime while retaining independence from specific forms of surface and bulk potentials. The theory predicts the existence of a well-resolved series of resonances for arbitrary coupling strengths. Surprisingly, distinct image-potential resonances are thus expected to exist on almost any metal surface, even in the limiting case of jellium.
In this paper we use the homotopy invariants methods to study the global dynamics of the reaction-diffusion systems that are at resonance at infinity. Considering degrees of the resonance for the nonlinear perturbation we establish Landesman-Lazer type conditions and use them to express the Rybakowski-Conley index of the invariant set consisting of all bounded solutions. Obtained results are applied to study the existence of solutions connecting stationary points for the system of nonlinear heat equations.
We propose and constrain with the latest observational data three parameterizations of the deceleration parameter, valid from the matter era to the far future. They are well behaved and do not diverge at any redshift. On the other hand, they are model independent in the sense that in constructing them the only assumption made was that the Universe is homogeneous and isotropic at large scales.
T-duality is one of the essential elements of string theory. Recently, Hull has developed a formalism where the dimension of the target space is doubled so as to make T-duality manifest. This is then supplemented with a constraint equation that allows the connection to the usual string sigma model. This paper analyses the partition function of the doubled formalism by interpreting the constraint equation as that of a chiral scalar and then using holomorphic factorisation techniques to determine the partition function. We find there is quantum equivalence to the ordinary string once the topological interaction term is included.
In high-mobility silicon MOSFET's, the $g^*m^*$ inferred indirectly from magnetoconductance and magnetoresistance measurements with the assumption that $g^*\mu_BH_s=2E_F$ are in surprisingly good agreement with $g^*m^*$ obtained by direct measurement of Shubnikov-de Haas oscillations. The enhanced susceptibility $\chi^* \propto (g^*m^*)$ exhibits critical behavior of the form $\chi^* \propto (n - n_0)^{-\alpha}$. We examine the significance of the field scale $H_s$ derived from transport measurements, and show that this field signals the onset of full spin polarization only in the absence of disorder. Our results suggest that disorder becomes increasingly important as the electron density is reduced toward the transition.
We have observed the unconventional photon blockade effect for microwave photons using two coupled superconducting resonators. As opposed to the conventional blockade, only weakly nonlinear resonators are required. The blockade is revealed through measurements of the second order correlation function $g^{(2)}(t)$ of the microwave field inside one of the two resonators. The lowest measured value of $g^{(2)}(0)$ is 0.4 for a resonator population of approximately $10^{-2}$ photons. The time evolution of $g^{(2)}(t)$ exhibits an oscillatory behavior, which is characteristic of the unconventional photon blockade.
Broad absorption lines (BALs), seen in a small fraction of both the radio-quiet and radio-loud quasar populations, are probably caused by the outflow of gas with high velocities and are part of the accretion process. The presence of BALs is the geometrical effect and/or it is connected with the quasar evolution. Using the final release of FIRST survey combined with a A Catalog of BAL QSOs (SDSS/DR3), we have constructed a new sample of compact radio-loud BAL QSOs, which makes the majority of radio-loud BAL QSOs. The main goal of this project is to study the origin of BALs by analysis the BAL QSOs radio morphology, their orientation and jets evolution, using EVN at 1.6 GHz and VLBA at 5 and 8.4 GHz. We will discuss also the first multi-frequency radio observations of very compact BAL quasar 1045+352 made using the VLBA, EVN, MERLIN and CHANDRA. We speculate that the most probable interpretation of the observed radio structure of 1045+352 is the ongoing process of the jet precession due to internal instabilities within the flow.
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
We analyzed the data of Stokes $I$, $Q$, and $U$ in C- and X-bands and investigated the large-scale magnetic field structure of NGC 3627. The polarization intensity and angle in each band were derived using Stokes $Q$ and $U$ maps. The rotation measure was calculated using the polarization-angle maps. Moreover, the magnetic field strength was calculated by assuming energy equipartition with the cosmic ray electrons. The structure of the magnetic field was well aligned with the spiral arms, which were consistent with those in the former studies. We applied the magnetic vector reconstruction method to NGC 3627 to derive a magnetic vector map, which showed that northern and southern disks were dominant with inward and outward magnetic vectors, respectively. Furthermore, we discussed the large-scale structure of the magnetic field in NGC 3627 and observed that the structure is bi-symmetric spiral in nature, and that the number of magnetic field mode is $ m_{\rm B} = 1 $ in outer region of galaxy. In addition, NGC 3627 has a mode of two spiral arms that were clearly visible in an optical image. The ratio of the mode of spiral arms to that of magnetic field is 2:1. In terms of NGC 3627, the large-scale magnetic field may be generated via the parametric resonance induced by the gravitational potential of the spiral arms.
We consider the effect of electron-electron interaction on the density of states of disordered paramagnetic conductor in the presence of spin accumulation and magnetic field. We show that interaction correction to electron density of states of the paramagnet may exhibit singularities at energies corresponding to the difference between chemical potentials of electrons with opposite spins. We also discuss correlation effects on conductivity in metallic as well as in hopping regimes and show that spin accumulation leads to the negative magnetoconductivity.
Long gamma-ray burst's (LGRB's) association to the death of massive stars suggest they could be used to probe the cosmic star formation history (CSFH) with high accuracy, due to their high luminosities. We utilise cosmological simulations from the First Billion Years project to investigate the biases between the CSFH and the LGRB rate at z>5, assuming various different models and constraints on the progenitors of LGRBs. We populate LGRBs using a selection based on environmental properties and demonstrate that the LGRB rate should trace the CSFH to high redshifts. The measured LGRB rate suggests that LGRBs have opening angles of theta_jet=0.1 deg, although the degeneracy with the progenitor model cannot rule out an underlying bias. We demonstrate that proxies that relate the LGRB rate with global LGRB host properties do not reflect the underlying LGRB environment, and are in fact a result of the host galaxy's spatial properties, such that LGRBs can exist in galaxies of solar metallicity. However, we find a class of host galaxies that have low stellar mass and are metal-rich, and that their metallicity dispersions would not allow low-metallicity environments. Detection of hosts with this set of properties would directly reflect the progenitor's environment. We predict that 10% of LGRBs per year are associated with this set of galaxies that would have forbidden line emission that could be detected by instruments on the James Webb Space Telescope. Such a discovery would place strong constraints on the collapsar model and suggest other avenues to be investigated.