ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper presents a novel way to use the algebra of unit quaternions to express arbitrary roots or fractional powers of single-qubit gates, and to use such fractional powers as generators for algebras that combine these fractional input signals, behaving as a kind of nonlinear addition. The method works by connecting several well-known equivalences. The group of all single-qubit gates is $U(2)$, the unitary transformations of $C^2$. Using an appropriate phase multiplier, every element of $U(2)$ can be mapped to a corresponding element of $SU(2)$ with unit determinant, whose quantum mechanical behavior is identical. The group $SU(2)$ is isomorphic to the group of unit quaternions. Powers and roots of unit quaternions can be constructed by extending de Moivre's theorem for roots of complex numbers to the quaternions by selecting a preferred square root of -1. Using this chain of equivalences, for any single-qubit gate $A$ and real exponent $k$, a gate $B$ can be predictably constructed so that $B^k = A$. Different fractions generated in this way can be combined by connecting the individually rotated qubits to a common 'sum' qubit using 2-qubit CNOT gates. Examples of such algebras are explored including those generated by roots of the quaternion $k$ (which corresponds to and $X$-rotation of the Bloch sphere), the quaternion $\frac{\sqrt{2}}{2}(i + k)$ (which corresponds to the Hadamard gate), and a mixture of these. One of the goals of this research is to develop quantum versions of classical components such as the classifier ensembles and activation functions used in machine learning and artificial intelligence. An example application for text classification is presented, which uses fractional rotation gates to represent classifier weights, and classifies new input by using CNOT gates to collect the appropriate classifier weights in a topic-scoring qubit.
The electronic and magnetic properties of single 3d transition-metal(TM) atom (V, Cr, Mn, Fe, Co, and Ni) adsorbed graphdiyne (GDY) and graphyne (GY) are systematically studied using first-principles calculations within the density functional framework. We find that the adsorption of TM atom not only efficiently modulates the electronic structures of GDY/GY system, but also introduces excellent magnetic properties, such as half-metal and spin-select half-semiconductor. Such modulation originates from the charge transfer between TM adatom and the GDY/GY sheet as well as the electron redistribution of the TM intra-atomic s, p, and d orbitals. Our results indicate that the TM adsorbed GDY/GY are excellent candidates for spintronics.
I discuss the Gamma Ray Burst research in the era of SALT and Swift, concentrating on the GRB/SN connection.
Feedback from an active galactic nucleus (AGN) is often implicated as a mechanism that leads to the quenching of galactic star formation. However, AGN-driven quenching is challenging to reconcile with observations that AGN hosts tend to harbour equal (or even excess) amounts of gas compared with inactive galaxies of similar stellar mass. In this paper, we investigate whether AGN feedback happens on sub-galactic (kpc) scales, an effect that might be difficult to detect with global gas measurements. Using kpc-scale measurements of molecular gas (Sigma_H2) and stellar mass (Sigma_*) surface densities taken from the EDGE-CALIFA survey, we show that the gas fractions of central AGN regions are typically a factor of ~2 lower than in star-forming regions. Based on four galaxies with the best spaxel statistics, the difference between AGN and star-forming gas fractions is seen even within a given galaxy, indicating that AGN feedback is able to deplete the molecular gas reservoir in the central few kpc.
We use a strong-disorder renormalization group (SDRG) method and ground-state quantum Monte Carlo (QMC) simulations to study S=1/2 spin chains with random couplings, calculating disorder-averaged spin and dimer correlations. The QMC simulations demonstrate logarithmic corrections to the power-law decaying correlations obtained with the SDRG scheme. The same asymptotic forms apply both for systems with standard Heisenberg exchange and for certain multi-spin couplings leading to spontaneous dimerization in the clean system. We show that the logarithmic corrections arise in the valence-bond (singlet pair) basis from a contribution that can not be generated by the SDRG scheme. In the model with multi-spin couplings, where the clean system dimerizes spontaneously, random singlets form between spinons localized at domain walls in the presence of disorder. This amorphous valence-bond solid is asymptotically a random-singlet state and only differs from the random-exchange Heisenberg chain in its short-distance properties.
We present the first detection of para-ammonia masers in NGC 7538: multiple epochs of observation of the 14NH3 (J,K) = (10,8) and (9,8) lines. We detect both thermal absorption and nonthermal emission in the (10,8) and (9,8) transitions and the absence of a maser in the (11,8) transition. The (9,8) maser is observed to increase in intensity by 40% over six months. Using interferometric observations with a synthesized beam of 0.25", we find that the (10,8) and (9,8) masers originate at the same sky position near IRS1. With strong evidence that the (10,8) and (9,8) masers arise in the same volume, we discuss the application of pumping models for the simultaneous excitation of nonmetastable (J > K) para-ammonia states having the same value of K and consecutive values of J. We also present detections of thermal absorption in rotational states ranging in energy from E/k_B ~ 200 K to 2000 K, and several non-detections in higher-energy states. In particular, we describe the populations in eight adjacent rotational states with K=6, including two maser transitions, along with the implications for ortho-ammonia pumping models. An existing torus model for molecular gas in the environment of IRS1 has been applied to the masers; a variety of maser species are shown to agree with the model. Historical and new interferometric observations of 15NH3 (3,3) masers in the region indicate a precession of the rotating torus at a rate comparable to continuum-emission-based models of the region. We discuss the general necessity of interferometric observations for diagnosing the excitation state of the masers and for determining the geometry of the molecular environment.
We obtain infinite product expansions in the sense of Borcherds for theta functions associated with certain positive-definite binary quadratic and binary hermitian forms. Among other things, we show that every weight 1 binary theta function is a Borcherds product. In particular, binary theta functions have zeros only at quadratic irrationalities.
We develop a gluing theory in the sense of Koll\'{a}r for slc surfaces and threefolds in positive characteristic. For surfaces we are able to deal with every positive characteristic $p$, while for threefolds we assume that $p>5$. Along the way we study nodes in characteristic $2$ and establish a theory of sources and springs \`a la Koll\'{a}r for threefolds. We also give applications to the topology of lc centers on slc threefolds, and to the projectivity of the moduli space of stable surfaces in characteristic $p>5$.
Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. Let $E$ be a vector bundle over $B$ and $X={\mathbb P} (E)$. It is easily seen that a power of any endomorphism of $X$ takes fibers to fibers. We prove that if $X$ admits an endomorphism which is of degree greater than one on the fibers then $E$ splits into a direct sum of line bundles.
Quantum anomalous Hall (QAH) phases in magnetic topological insulators are characterized by the scattering-free chiral edge currents protected by their nontrivial bulk band topology. To fully explore these intriguing phenomena and application of topological insulators, high temperature material realization of QAH phases is crucial. In this paper, based on extensive first-principles density functional theory calculations, we predict that perovskite bilayers (LaXO$_3$)$_{2}$ (X = Pd, Pt) imbedded in the (111) (LaXO$_3$)$_{2}$/(LaAlO$_3$)$_{10}$ superlattices are high Curie temperature ferromagnets that host both QAH and Dirac semimetal phases, depending on the biaxial strain and onsite electron correlation. In particular, both the direction (the sign of Chern number) and spin-polarization of the chiral edge currents are tunable by either onsite electron correlation or biaxial in-plane strain. Furthermore, the nontrivial band gap can be enhanced up to 92 meV in the LaPdO$_3$ bilayer by the compressive in-plane strain, and can go up to as large as 242 meV when the Pd atoms are replaced by the heavier Pt atoms. Finally, the microscopic mechanisms of the ferromagnetic coupling and other interesting properties of the bilayers are uncovered by analyzing their underlying electronic band structures.
We present the power spectrum analysis of clustering in the Durham/UKST Galaxy Redshift Survey, which covers 1450 square degrees and consists of 2501 galaxy redshifts sampled at a rate of 1 in 3 to b_J = 17. The fluctuations that we measure can be expressed as sigma_{8} = 1.01 +/- 0.17 . We find remarkably good agreement between the power spectrum measured for the Durham/UKST Survey and those from other optical studies, in spite of the very different sampling rates, magnitude limits and survey geometries employed, on scales up to lambda = (2 pi)/k = 80/h Mpc. On scales larger than this we find good agreement with the power measured from the Stromlo-APM Survey (Tadros & Efstathiou), but find more power than estimated from the Las Campanas Redshift Survey (Lin et al). We apply a simple model for redshift space distortions to the real space APM Galaxy Survey power spectrum and find a shape and amplitude that is in very good agreement with the power spectrum of the Durham/UKST Survey. This implies beta=Omega^{0.6}/b=0.60 +/- 0.35, where Omega is the density parameter and b is the bias between fluctuations in the galaxy and mass distributions, and also suggests a one dimensional velocity dispersion of sigma = 320 +/-140 km/s. We find that for any choice of normalisation, the standard CDM model has a shape that cannot be reconciled with the Durham/UKST Survey power spectrum, unless either unacceptably high values of the one dimensional velocity dispersion are adopted or the assumption that bias is constant is invalid on scales greater than 20/h Mpc. Over the range of wavenumbers for which we have a robust measurement of the power spectrum, we find the best agreement is obtained for a critical density CDM model in which the shape of the power spectrum is modified. (Abridged)
We describe a simple scheme for calculating the fidelity of a composite pulse when considered as a universal rotor.
A collision-induced magnetic reconnection (CMR) mechanism was recently proposed to explain the formation of a filament in the Orion A molecular cloud. In this mechanism, a collision between two clouds with antiparallel magnetic fields produces a dense filament due to the magnetic tension of the reconnected fields. The filament contains fiber-like sub-structures and is confined by a helical magnetic field. To show whether the dense filament is capable of forming stars, we use the \textsc{Arepo} code with sink particles to model star formation following the formation of the CMR-filament. First, the CMR-filament formation is confirmed with \textsc{Arepo}. Second, the filament is able to form a star cluster after it collapses along its main axis. Compared to the control model without magnetic fields, the CMR model shows two distinctive features. First, the CMR-cluster is confined to a factor of $\sim4$ smaller volume. The confinement is due to the combination of the helical field and gravity. Second, the CMR model has a factor of $\sim2$ lower star formation rate. The slower star formation is again due to the surface helical field that hinders gas inflow from larger scales. Mass is only supplied to the accreting cluster through streamers.
We present dynamical distribution functions for evolved stars in the inner galactic plane. We use an axisymmetric, two-component Stackel potential that satisfies recent constraints on the galactic potential, amongst others a slightly declining local rotation curve. We show that this potential is adequate to model stellar-kinematic samples with radial extent ranging from \~100 pc to ~5 kpc in the Galaxy. The two-integral model that gives the best fit to the first three projected moments provides a very good global representation of the data but fails to reproduce the central dispersion, the central apparent scaleheight and the cylindrical rotation at intermediate longitudes. All these features are fitted well by a three--integral model. We discuss various properties of the 2I- and 3I models and the implications for galactic structure. A somewhat thicker disk component is needed to explain the distribution of older AGB stars in the plane; this component also fits the kinematics at higher latitudes better. We find that the Disk and the Bulge, as traced by AGB stars, are very similar dynamically and could well be one and the same component. There is a dynamically distinct component in the inner 100 pc of the Bulge, however.
We present Giant Metrewave Radio Telescope and Very Large Array observations of HI 21-cm absorption in ten z<=0.2 galaxy mergers that host strong radio sources. Seven of these mergers show strong absorption [with N(HI) ~10^{21-22} cm^{-2}, for spin temperature of 100 K and unit covering factor], leading to a total detection rate of 83 +/- 17% in low-z radio-loud galaxy mergers. This is ~3-4 times higher than that found for intrinsic HI 21-cm absorption in low-z radio sources in general. The fraction of intrinsic absorbers that are associated with mergers increases with increasing N(HI) threshold, i.e. ~40% and 100% of the absorbers with N(HI) >10^{21} cm^{-2} and >10^{22} cm^{-2} arise from mergers, respectively. The distribution of N(HI) among the mergers is significantly different from that found in isolated systems, with mergers giving rise to six times stronger absorption on average. The fraction of redshifted absorption components (with respect to the systemic velocity of the radio source obtained from optical emission lines) among mergers is found to be higher by two to three times compared to that found for non-interacting systems. Follow-up spatially-resolved multi-wavelength spectroscopy is essential to understand the exact connection between the presence of circumnuclear neutral gas and the AGN activity in these mergers.
Cygnus X-1 is the archetypal black hole (BH) binary system in our Galaxy. We report the main results of an extensive search for transient gamma-ray emission from Cygnus X-1 carried out in the energy range 100 MeV - 3 GeV by the AGILE satellite, during the period 2007 July - 2009 October. The total exposure time is about 300 days, during which the source was in the "hard" X-ray spectral state. We divided the observing intervals in 2 or 4 week periods, and searched for transient and persistent emission. We report an episode of significant transient gamma-ray emission detected on 2009, October 16 in a position compatible with Cygnus X-1 optical position. This episode, occurred during a hard spectral state of Cygnus X-1, shows that a 1-2 day time variable emission above 100 MeV can be produced during hard spectral states, having important theoretical implications for current Comptonization models for Cygnus X-1 and other microquasars. Except for this one short timescale episode, no significant gamma-ray emission was detected by AGILE. By integrating all available data we obtain a 2$\sigma$ upper limit for the total integrated flux of $F_{\gamma,U.L.} = 3 \times 10^{-8} \rm ph cm^{-2} s^{-1}$ in the energy range 100 MeV - 3 GeV. We then clearly establish the existence of a spectral cutoff in the energy range 1-100 MeV that applies to the typical hard state outside the flaring period and that confirms the historically known spectral cutoff above 1 MeV.
The evolution of electron conductance in the presence of inelastic effects is studied as an atomic gold contact is formed evolving from a low-conductance regime (tunneling) to a high-conductance regime (contact). In order to characterize each regime, we perform density functional theory (DFT) calculations to study the geometric and electronic structures, together with the strength of the atomic bonds and the associated vibrational frequencies. The conductance is calculated by first evaluating the transmission of electrons through the system, and secondly by calculating the conductance change due to the excitation of vibrations. As found in previous studies [Paulsson et al., Phys. Rev. B. 72, 201101(R) (2005)] the change in conductance due to inelastic effects permits to characterize the crossover from tunneling to contact. The most notorious effect being the crossover from an increase in conductance in the tunneling regime to a decrease in conductance in the contact regime when the bias voltage matches a vibrational threshold. Our DFT-based calculations actually show that the effect of vibrational modes in electron conductance is rather complex, in particular when modes localized in the contact region are permitted to extend into the electrodes. As an example, we find that certain modes can give rise to decreases in conductance when in the tunneling regime, opposite to the above mentioned result. Whereas details in the inelastic spectrum depend on the size of the vibrational region, we show that the overall change in conductance is quantitatively well approximated by the simplest calculation where only the apex atoms are allowed to vibrate. Our study is completed by the application of a simplified model where the relevant parameters are obtained from the above DFT-based calculations.
Deep neural network (DNN) predictions have been shown to be vulnerable to carefully crafted adversarial perturbations. Specifically, image-agnostic (universal adversarial) perturbations added to any image can fool a target network into making erroneous predictions. Departing from existing defense strategies that work mostly in the image domain, we present a novel defense which operates in the DNN feature domain and effectively defends against such universal perturbations. Our approach identifies pre-trained convolutional features that are most vulnerable to adversarial noise and deploys trainable feature regeneration units which transform these DNN filter activations into resilient features that are robust to universal perturbations. Regenerating only the top 50% adversarially susceptible activations in at most 6 DNN layers and leaving all remaining DNN activations unchanged, we outperform existing defense strategies across different network architectures by more than 10% in restored accuracy. We show that without any additional modification, our defense trained on ImageNet with one type of universal attack examples effectively defends against other types of unseen universal attacks.
The linear cosmological perturbation theory of almost homogeneous and isotropic perfect fluid and scalar field universes is reconsidered and formally simplified. Using the existence of a covariant conserved quantity on large perturbation scales, a closed integral expression for comoving energy density perturbations is obtained for arbitrary equations of state. On this basis we establish a simple relation between fluid energy density perturbations at `reentry' into the horizon and the corresponding scalar field quantities at the first Hubble scale crossing during an early de Sitter phase of a standard inflationary scenario.
The C-Band All-Sky Survey (C-BASS) is an experiment to image the whole sky in intensity and polarization at 5 GHz. The primary aim of C-BASS is to provide low-frequency all-sky maps of the Galactic emission which will enable accurate component separation analysis of both existing and future CMB intensity and polarization imaging surveys. Here we present an overview of the experiment and an update on the current status of observations. We present simulation results showing the expected improvement in the recovery of CMB and foreground signals when including C-BASS data as an additional low-frequency channel, both for intensity and polarization. We also present preliminary results from the northern part of the sky survey.
Let f be a newform of weight 2k-2 and level 1. In this paper we provide evidence for the Bloch-Kato conjecture for modular forms. We demonstrate an implication that under suitable hypothesis if a prime divides the algebraic part of L(k,f), then the prime divides the order of the Selmer group associated to f. We demonstrate this by establishing a congruence between the Saito-Kurokawa lift of f and a cuspidal Siegel eigenform that is not a Saito-Kurokawa lift. We then examine what this congruence says in terms of Galois representations to produce a non-trivial p-torsion element in the Selmer group.
To understand the formation mechanism of large plumes in solar prominences, we investigate the formation process of two such phenomena. We studied the dynamic and thermal properties of two large plumes using observations from New Vacuum Solar Telescope, the Solar Dynamic Observatory, and the Solar Terrestrial Relations Observatory-Ahead. We find that two large plumes observed with high-resolution data are quite different from previously studied small-scale plumes. They are born at the top of a prominence bubble with a large projected area of 10-20 Mm^2 . Before the occurrence of each large plume, the bubble expands and takes on a quasi-semicircular appearance. Meanwhile, the emission intensity of extreme-ultra-violet (EUV) bands increases in the bubble. A small-scale filament is found to erupt in the bubble during the second large plume. At the point at which the height of the bubble is comparable with half the width of the bubble, the bubble becomes unstable and generates the plumes. During the formation of plumes, two side edges of the top of the bubble, which are dominated by opposite Doppler signals, approach each other. The large plume then emerges and keeps rising up with a constant speed of about 13-15 km/s. These two large plumes have temperatures of 1.3 x 10^6 Kelvin and densities of 2.0 x 10^9 cm^-3, two orders hotter and one order less dense than the typical prominence. We also find that the bubble is a hot, low-density volume instead of a void region beneath the cold and dense prominence. Therefore, we conclude that these two large plumes are the result of the breakup of the prominence bubble triggered by an enhancement of thermal pressure; they separate from the bubble, most likely by magnetic reconnection.
We give a new, geometric proof of the section conjecture for fixed points of finite group actions on projective curves of positive genus defined over the field of complex numbers, as well as its natural nilpotent analogue. As a part of our investigations we give an explicit description of the abelianised section map for groups of prime order in this setting. We also show a version of the 2-nilpotent section conjecture.
We analyze the nonequilibrium Kondo model at finite voltage and temperature by using a new formulation of the real-time renormalization group method with the Laplace variable as the flow parameter. We evaluate the energy-dependent spin relaxation rate and nonlinear conductance, and derive an approximate form for the universal line shape for the latter in the whole crossover regime from weak to strong coupling. The results are shown to agree well with exact methods in equilibrium, Fermi-liquid theory, weak-coupling expansions, and recent experiments. For the transient spin dynamics we find a universal exponential decay in the long-time limit along with a truncation-dependent pre-exponential power law. For multichannel models a pure power-law decay typical for non-Fermi-liquid behaviour is predicted.