ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0.
Scaling equations for the Kondo lattice in the paramagnetic and magnetically ordered phases are derived to two-loop order with account of spin dynamics. The results are applied to describe various mechanisms of the non-Fermi-liquid (NFL) behavior in the multichannel Kondo-lattice model where a fixed point occurs in the weak-coupling region. The corresponding temperature dependences of electronic and magnetic properties are discussed. The model describes naturally formation of a magnetic state with soft boson mode and small moment value. An important role of Van Hove singularities in the magnon spectral function is demonstrated. The results are rather sensitive to the type of magnetic ordering and space dimensionality, the conditions for NFL behavior being more favorable in the antiferromagnetic and 2D cases.
XTE J1701-407 is a newly discovered X-ray transient source. In this work we investigate its flux variability and study the intermediate long and short bursts discovered by Swift on July 17, and 27, 2008, respectively. So far, only one intermediate long burst, with a duration of ~18 minutes and ten days later a short burst, have been recorded from XTE J1701-407. We analyzed the public available data from Swift and RXTE, and compared the observed properties of the intermediate long burst with theoretical ignition condition and light curves to investigate the possible nuclear burning processes. The intermediate long burst may have exhibited a photospheric radius expansion, allowing us to derive the source distance at 6.2 kpc assuming the empirically derived Eddington luminosity for pure helium. The intermediate long burst decay was best fit by using two exponential functions with e-folding times of \tau_1=40(3) s and \tau_2=221(9) s. The bursts occurred at a persistent luminosity of L_{per}=8.3x10E36 erg/s. For the intermediate long burst the mass accretion rate per unit area onto the NS was \dot{m}=4x10E3 g/cm2/s, and the total energy released was E_{burst}=3.5x10E40 erg. This corresponds to an ignition column depth of y_{ign}=1.8x10E9 g/cm2, for a pure helium burning. We find that the energetics of this burst can be modeled in different ways, as (i) pure helium ignition, as the result of either pure helium accretion or depletion of hydrogen by steady burning during accumulation, or (ii) as ignition of a thick layer of hydrogen-rich material in a source with low metallicity. However, comparison of the burst duration with model light curves suggests that hydrogen burning plays a role during the burst, and therefore this source is a low accretion rate burster with a low metallicity in the accreted material.
We study the one-dimensional Anderson-Hubbard model using the density-matrix renormalization group method. The influence of disorder on the Tomonaga-Luttinger liquid behavior is quantitatively discussed. Based on the finite-size scaling analysis of density-density correlation functions, we find the following results: i) the charge exponent is significantly reduced by disorder at low filling and near half filling, ii) the localization length decays as $\xi \sim \Delta^{-2}$, where $\Delta$ is the disorder strength, independently of the on-site Coulomb interaction as well as band filling, and iii) the localization length is strongly suppressed by the on-site Coulomb interaction near half filling in association with the formation of the Mott plateaus.
In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space $\Cal C$ of elliptic curves with CM by the ring of integers $\OK$ in an imaginary quadratic field $\kay$, on the one hand, and those associated to cycles on the arithmetic surface $\M$ parametrizing 2-dimensional abelian varieties with an action of the maximal order $O_B$ in an indefinite quaternion algebra $B$ over $\Q$, on the other. We show that the arithmetic degree of the pullback to $Cal C$ of the arithmetic theta function of weight 3/2 valued in $\hat CH^1(\M)$ can be expressed as a linear combination of arithmetic theta functions of weight 1 for $\Cal C$ and unary theta series. This identity can be viewed as an arithmetic seesaw identity. In addition, we show that the arithmetic theta series of weight 1 coincide with the central derivative of certain incoherent Eisenstein series for SL(2)/Q, generalizing earlier joint work with M. Rapoport for the case of a prime discriminant.
In this paper, a simple yet efficient activity recognition method for first-person video is introduced. The proposed method is appropriate for representation of high-dimensional features such as those extracted from convolutional neural networks (CNNs). The per-frame (per-segment) extracted features are considered as a set of time series, and inter and intra-time series relations are employed to represent the video descriptors. To find the inter-time relations, the series are grouped and the linear correlation between each pair of groups is calculated. The relations between them can represent the scene dynamics and local motions. The introduced grouping strategy helps to considerably reduce the computational cost. Furthermore, we split the series in temporal direction in order to preserve long term motions and better focus on each local time window. In order to extract the cyclic motion patterns, which can be considered as primary components of various activities, intra-time series correlations are exploited. The representation method results in highly discriminative features which can be linearly classified. The experiments confirm that our method outperforms the state-of-the-art methods on recognizing first-person activities on the two challenging first-person datasets.
With the example of a Stern-Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse - for example, the singleness (or mutual exclusivity) of outcomes. This is done by inserting a quantum two-state system (an ancilla) in each path, capable of responding to the passage of the atom, and thus acting as a virtual detector. We then consider real measurements on the compound system of atomic spin and two ancillae. Nondestructive measurements of a set of compatible joint observables can be performed, one for a superposition and others for collapse properties. A novel perspective is given as to why, within unitary quantum theory, ordinary measurements are blind to such superpositions. Implications for the theory of measurement are discussed.
We consider the optimal quantization problem with R\'enyi-$\alpha$-entropy constraints for centered Gaussian measures on a separable Banach space. For $\alpha = \infty$ we can compute the optimal quantization error by a moment on a ball. For $\alpha \in {}]1,\infty]$ and large entropy bound we derive sharp asymptotics for the optimal quantization error in terms of the small ball probability of the Gaussian measure. We apply our results to several classes of Gaussian measures. The asymptotical order of the optimal quantization error for $\alpha > 1$ is different from the well-known cases $\alpha = 0$ and $\alpha = 1$.
Structural, vibrational and dielectric properties of (Pb1-xBix)(Ti1-xMnx)O3 (PBTM) (0 x 0.50) polycrystalline ceramics have been examined as a function of temperature. Synchrotron-based powder x-ray diffraction was employed to confirm phase purity and crystal structure of samples. Tetragonality (c/a ratio) of the PBTM system exhibit an increase 1.065, 1.066 for x = 0.06 and 0.09 compositions respectively, compare to 1.064 for x = 0 sample. Curie point was found ~763 K and 773 K for x = 0.06 and 0.09 samples respectively. Though, tetragonality start to decreasing from samples with x 0.18, Curie point of the samples started decreasing for x 0.12. Temperature-dependent x-ray diffraction reveals the structural change from tetragonal to cubic structure. Unit cell volume was found to decrease with increasing temperature; indicate these materials are negative thermal expansion type until phase transition temperature, with negative thermal coefficients are -1.571*10-5 /K, -2.44*10-5 /K, and -5.025*10-6 /K for x = 0, 0.06, and 0.09 samples respectively. Raman spectra showed softening of the transverse optical phonon modes and increase in the full width at half maxima with the increase in composition. Field-emission scanning electron microscope equipped with energy dispersive x-ray spectrometer (EDS) confirmed compositional homogeneity and dense type microstructure.
The ON stars are a rare subtype of O stars, of uncertain origin. We report two new, rapidly-rotating ON stars found in data acquired with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST. LS I +61 28 is an ON8.5 Vn dwarf with a projected equatorial rotational velocity of $v_{\textrm e}\sin{i} \simeq 298$ km$\;$s$^{-1}$, while HDE 236672 is an ON9 IVn subgiant with $v_{\textrm e}\sin{i} \simeq 253$ km$\;$s$^{-1}$ The former is the first rapidly-rotating ON dwarf to be found, and the latter is only the third ON subgiant. The luminosity classes of non-supergiant ON stars appear to be influenced by the axial inclination angle $i$: the rapidly-rotating giants are close to equator-on, while ON dwarfs with lower $v_{\textrm e}\sin{i}$ values are viewed more nearly pole-on. Combining parallaxes and proper motions from Gaia DR2 with radial-velocity measurements, we investigate the kinematics of non-supergiant ON stars, and infer that the dynamics, rapid rotation, and surface-nitrogen characteristics may all be consequences of binary interaction.
We compare the CO(1-0) and H$\alpha$ kinematics in 34 nearby galaxies, selected from the ALMaQUEST and EDGE-CALIFA surveys. We use 3-D Barolo, a 3D tilted ring model, to derive the CO and H$\alpha$ rotation curves. Before comparing rotation curves in the 34 nearby galaxies, we found systematics between the MaNGA and the CALIFA data using eight MaNGA-CALIFA overlapping galaxies. We assume the rotation curves based on the MaNGA data are accurate and made the corresponding correction to the CALIFA data. Our result shows that $\sim$56% (19/34) of our galaxies present slower H$\alpha$ rotation curves compared to the CO rotation curves, with a median value of 6.5 km/s. The remaining galaxies (15/34) show consistent CO-H$\alpha$ rotation velocity within uncertainties. As a result, the Ha rotation may underestimate the total dynamical mass by ~6% for a circular velocity of 200 km/s (the median value in our sample). Furthermore, the velocity difference between the CO and H$\alpha$ rotation velocity is found to correlate with the velocity dispersion difference between CO and H$\alpha$, suggesting that the gas pressure plays a role in the velocity discrepancy. After incorporating the effect of pressure support due to the turbulent gas motion to our sample, the median value of the velocity differences decreases to 1.9 km/s, which in turn reduces the underestimation of dynamical mass to $\sim$2%. Finally, we also investigate the role that the extra-planar diffuse ionized gas (eDIG) plays in the CO-H$\alpha$ velocity discrepancy.
We investigate bounds on the dichromatic number of digraphs which avoid a fixed digraph as a topological minor. For a digraph $F$, denote by $\text{mader}_{\vec{\chi}}(F)$ the smallest integer $k$ such that every $k$-dichromatic digraph contains a subdivision of $F$. As our first main result, we prove that if $F$ is an orientation of a cycle then $\text{mader}_{\vec{\chi}}(F)=v(F)$. This settles a conjecture of Aboulker, Cohen, Havet, Lochet, Moura and Thomass\'{e}. We also extend this result to the more general class of orientations of cactus graphs, and to bioriented forests. Our second main result is that $\text{mader}_{\vec{\chi}}(F)=4$ for every tournament $F$ of order $4$. This is an extension of the classical result by Dirac that $4$-chromatic graphs contain a $K_4$-subdivision to directed graphs.
We calculate the linear torque exerted by a planet on a circular orbit on a disc containing a toroidal magnetic field. All fluid perturbations are singular at the so--called magnetic resonances, where the Doppler shifted frequency of the perturbation matches that of a slow MHD wave propagating along the field line. These lie on both sides of the corotation radius. Waves propagate outside the Lindblad resonances, and also in a restricted region around the magnetic resonances. The magnetic resonances contribute to a significant global torque which, like the Lindblad torque, is negative (positive) inside (outside) the planet's orbit. Since these resonances are closer to the planet than the Lindblad resonances, the torque they contribute dominates over the Lindblad torque if the magnetic field is large enough. In addition, if beta=c^2/v_A^2 increases fast enough with radius, the outer magnetic resonance becomes less important and the total torque is then negative, dominated by the inner magnetic resonance. This leads to outward migration of the planet. Even for beta=100 at corotation, a negative torque may be obtained. A planet migrating inward through a nonmagnetized region of a disc would then stall when reaching a magnetized region. It would then be able to grow to become a terrestrial planet or the core of a giant planet. In a turbulent magnetized disc in which the large scale field structure changes sufficiently slowly, a planet may alternate between inward and outward migration, depending on the gradients of the field encountered. Its migration could then become diffusive, or be limited only to small scales.
Tin (II) sulfide (SnS) is a layered mineral found in nature. In this paper, we study the two-dimensional form of this material using a combination of \emph{ab initio} calculation and $\mathbf{k}\cdot\mathbf{p}$ theory. In particular, we address the valley properties and the optical selection rules of 2D SnS. Our study reveals SnS as an extraordinary material for valleytronics, where pairs of equivalent valleys are placed along two perpendicular axes, can be selected exclusively with linear polarized light, and can be separated using non-local electrical measurements.
In the $R$-spread out, $d$-dimensional voter model, each site $x$ of $\mathbb{Z}^d$ has state (or 'opinion') 0 or 1 and, with rate 1, updates its opinion by copying that of some site $y$ chosen uniformly at random among all sites within distance $R$ from $x$. If $d \geq 3$, the set of (extremal) stationary measures of this model is given by a family $\mu_{\alpha, R}$, where $\alpha \in [0,1]$. Configurations sampled from this measure are polynomially correlated fields of 0's and 1's in which the density of 1's is $\alpha$ and the correlation weakens as $R$ becomes larger. We study these configurations from the point of view of nearest neighbor site percolation on $\mathbb{Z}^d$, focusing on asymptotics as $R \to \infty$. In \cite{RV15}, we have shown that, if $R$ is large, there is a critical value $\alpha_c(R)$ such that there is percolation if $\alpha > \alpha_c(R)$ and no percolation if $\alpha < \alpha_c(R)$. Here we prove that, as $R \to \infty$, $\alpha_c(R)$ converges to the critical probability for Bernoulli site percolation on $\mathbb{Z}^d$. Our proof relies on a new upper bound on the joint occurrence of events under $\mu_{\alpha,R}$ which is of independent interest.
The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric representation and our proof is constructive. If the given algebraic surface is translational, then we can compute a standard parametric representation for the surface.
The results of the first observations of Type IV bursts at frequencies 10-30 MHz are presented. These observations were carried out at radio telescopes UTR-2 (Kharkov, Ukraine) and URAN-2 (Poltava, Ukraine) during the period 2003-2006. Detection of Type IV bursts in wide band from 10 to 30MHz with high sensitivity and time resolution allowed to study their properties in details. These bursts have fluxes 10-2000s.f.u. at maximum phase. Their durations are about 1-2 hours and even more. Some of Type IV bursts drift from high to low frequencies with drift rates about 10kHz/s. All observed Type IV bursts have fine structures in the form of sub-bursts with durations from 2s to 20s and frequency drift rates in a majority of 1-2MHz/s. In most cases, sub-bursts with negative drift rates were registered. Sometimes sub-bursts in absorption with durations 10-200s against Type IV burst background have been observed. The Type IV burst observed on July 22, 2004 had zebra structure, in which single zebra stripes had positive, negative and infinite drift rates.
Among solutions of n-Gelfand-Dikii's hierarchy there exists a remarkable solution W, which satisfies the string equation. We call it Witten's solution because according to the Witten conjecture the function F(x_1, x_2, x_3,...) = W(x_1,(x_2)/2, (x_3)/3,...) is the generating function for intersection nambers of Mumford-Morita-Muller cohomological classes of the moduli space of n-spin Riemann surfaces. This conjecture was proved by Kontsevich for n=2 and by Witten himself for surfaces of genus 0.   In this paper we find recurrence relations between coefficients of Taylor series of W. This reduces the Witten's conjecture to conjecture that the Mamford-Morita-Muller numbers satisfy to the same relations. These relations give also an algorithm for calculation of $n$-spin Mamford-Morita-Muller numbers in assuming that the Witten conjecture is true. Moreover we prove that F(x_1,x_2,...,x_{n-1},0,0,...)= W(x_1, (x_2)/2,...,(x_{n-1})/(n-1),0,0,...).
We study some quantum systems described by noncanonical commutation relations formally expressed as [q,p]=ihbar(I + chi H), where H is the associated (harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian (constant) operator, i.e. [H,chi]=0 . In passing, we also consider a simple (chi=0 canonical) model, in the framework of a relativistic Klein-Gordon-like wave equation.
Surface flux transport simulations for the descending phase of cycle 24 using random sources (emerging bipolar magnetic regions) with empirically determined scatter of their properties provide a prediction of the axial dipole moment during the upcoming activity minimum together with a realistic uncertainty range. The expectation value for the dipole moment around 2020 $(2.5\pm1.1\,$G) is comparable to that observed at the end of cycle 23 (about $2\,$G). The empirical correlation between the dipole moment during solar minimum and the strength of the subsequent cycle thus suggests that cycle 25 will be of moderate amplitude, not much higher than that of the current cycle. However, the intrinsic uncertainty of such predictions resulting from the random scatter of the source properties is considerable and fundamentally limits the reliability with which such predictions can be made before activity minimum is reached.
In a previous Letter (J. Phys. A v.47 (2014) 212003) we have presented numerical evidence that a Hamiltonian expressed in terms of the generators of the periodic Temperley-Lieb algebra has, in the finite-size scaling limit, a spectrum given by representations of the Virasoro algebra with complex highest weights. This Hamiltonian defines a stochastic process with a Z_N symmetry. We give here analytical expressions for the partition functions for this system which confirm the numerics. For N even, the Hamiltonian has a symmetry which makes the spectrum doubly degenerate leading to two independent stochastic processes. The existence of a complex spectrum leads to an oscillating approach to the stationary state. This phenomenon is illustrated by an example.
The crucial components of a conventional image registration method are the choice of the right feature representations and similarity measures. These two components, although elaborately designed, are somewhat handcrafted using human knowledge. To this end, these two components are tackled in an end-to-end manner via reinforcement learning in this work. Specifically, an artificial agent, which is composed of a combined policy and value network, is trained to adjust the moving image toward the right direction. We train this network using an asynchronous reinforcement learning algorithm, where a customized reward function is also leveraged to encourage robust image registration. This trained network is further incorporated with a lookahead inference to improve the registration capability. The advantage of this algorithm is fully demonstrated by our superior performance on clinical MR and CT image pairs to other state-of-the-art medical image registration methods.
We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relativity, amongst other results. Finally, we are able to identify modified gravity models which have not been studied in the past. These appear naturally within our setup and would make a interesting starting point for further studies.
The magnetization process of the orthogonal-dimer antiferromagnet SrCu2(BO3)2 is investigated in high magnetic fields of up to 118 T. A 1/2 plateau is clearly observed in the field range 84 to 108 T in addition to 1/8, 1/4 and 1/3 plateaux at lower fields. Using a combination of state-of-the-art numerical simulations, the main features of the high-field magnetization, a 1/2 plateau of width 24 T, a 1/3 plateau of width 34 T, and no 2/5 plateau, are shown to agree quantitatively with the Shastry-Sutherland model if the ratio of inter- to intra-dimer exchange interactions J'/J=0.63. It is further predicted that the intermediate phase between the 1/3 and 1/2 plateau is not uniform but consists of a 1/3 supersolid followed by a 2/5 supersolid and possibly a domain-wall phase, with a reentrance into the 1/3 supersolid above the 1/2 plateau.
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centers of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our approach results in an explicit series solution for any closed measuring surface surrounding a region for which the eigenfunctions of the Dirichlet Laplacian are explicitly known - such as, for example, cube, finite cylinder, half-sphere etc. In addition, we present a fast reconstruction algorithm applicable in the case when the detectors (the centers of the integration spheres) lie on a surface of a cube. This algorithm reconsrtucts 3-D images thousands times faster than backprojection-type methods.