ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the classical theory, a famous by-product of the continued fraction expansion of quadratic irrational numbers $\sqrt{D}$ is the solution to Pell's equation for $D$. It is well-known that, once an integer solution to Pell's equation exists, we can use it to generate all other solutions $(u_n,v_n)_{n\in\Zee}$. Our object of interest is the polynomial version of Pell's equation, where the integers are replaced by polynomials with complex coefficients. We then investigate the factors of $v_n(t)$. In particular, we show that over the complex polynomials, there are only finitely many values of $n$ for which $v_n(t)$ has a repeated root. Restricting our analysis to $\Qee[t]$, we give an upper bound on the number of "new" factors of $v_n(t)$ of degree at most $N$. Furthermore, we show that all "new" linear rational factors of $v_n(t)$ can be found when $n\leq 3$, and all "new" quadratic rational factors when $n\leq 6$.
During the recent years, correlation filters have shown dominant and spectacular results for visual object tracking. The types of the features that are employed in these family of trackers significantly affect the performance of visual tracking. The ultimate goal is to utilize robust features invariant to any kind of appearance change of the object, while predicting the object location as properly as in the case of no appearance change. As the deep learning based methods have emerged, the study of learning features for specific tasks has accelerated. For instance, discriminative visual tracking methods based on deep architectures have been studied with promising performance. Nevertheless, correlation filter based (CFB) trackers confine themselves to use the pre-trained networks which are trained for object classification problem. To this end, in this manuscript the problem of learning deep fully convolutional features for the CFB visual tracking is formulated. In order to learn the proposed model, a novel and efficient backpropagation algorithm is presented based on the loss function of the network. The proposed learning framework enables the network model to be flexible for a custom design. Moreover, it alleviates the dependency on the network trained for classification. Extensive performance analysis shows the efficacy of the proposed custom design in the CFB tracking framework. By fine-tuning the convolutional parts of a state-of-the-art network and integrating this model to a CFB tracker, which is the top performing one of VOT2016, 18% increase is achieved in terms of expected average overlap, and tracking failures are decreased by 25%, while maintaining the superiority over the state-of-the-art methods in OTB-2013 and OTB-2015 tracking datasets.
The renormalization of MZV was until now carried out by algebraic means. We show that renormalization in general, of the multiple zeta functions in particular, is more than mere convention. We show that simple calculus methods allow us to compute the renormalized values of multiple zeta functions in any dimension for arguments of the form (1,...,1), where the series do not converge. These values happen to be the coefficients of the asymptotic expansion of the inverse Gamma function. We focus on the geometric interpretation of these values, and on the combinatorics their closed form encodes, which happen to match the combinatorics of the generalized Euler reflection formula discovered by Michael E. Hoffman, which in turn is a kind of analogue of the Cayley-Hamilton theorem for matrices. By means of one single limit formula, we define a function on the positive open half-line which takes exactly the values of the Riemann zeta function, with the additional advantage that it equals the Euler constant when the argument is 1.
We discuss the importance of the real part of the Feynman-Vernon influence action for the analysis of dephasing and decay near the ground state of a system which is coupled to a bath. Using exactly solvable linear quantum dissipative systems, it is shown how the effects of the real and the imaginary part (describing friction and fluctuations, respectively) may cancel beyond lowest-order perturbation theory. The resulting picture is extended to a qualitative discussion of nonlinear systems and dephasing of degenerate fermions. We explain why dephasing rates will, in general, come out finite at zero temperature if they are deduced from the imaginary part of the action alone, a procedure which is reliable only for highly excited states.
The distance energy of a simple connected graph $G$ is defined as the sum of absolute values of its distance eigenvalues. In this paper, we mainly give a positive answer to a conjecture of distance energy of clique trees proposed by Lin, Liu and Lu [H.~Q.~ Lin, R.~F.~Liu, X.~W.~Lu, The inertia and energy of the distance matrix of a connected graph, {\it Linear Algebra Appl.,} 467 (2015), 29-39.]
For an odd prime $p$ and a supersingular elliptic curve over a number field, this article introduces a fine signed residual Selmer group, under certain hypotheses on the base field. This group depends purely on the residual representation at $p$, yet captures information about the Iwasawa theoretic invariants of the signed $p^\infty$-Selmer group that arise in supersingular Iwasawa theory. Working in this residual setting provides a natural framework for studying congruences modulo $p$ in Iwasawa theory.
The interaction of a rotating star's magnetic field with a surrounding plasma disk lies at the heart of many questions posed by neutron stars in X-ray binaries. We consider the opening of stellar magnetic flux due to differential rotation along field lines coupling the star and disk, using a simple model for the disk-opened flux, the torques exerted on the star by the magnetosphere, and the power extracted by the electromagnetic wind. We examine the conditions under which the system enters an equilibrium spin state, in which the accretion torque is instantaneously balanced by the pulsar wind torque alone. For magnetic moments, spin frequencies, and accretion rates relevant to accreting millisecond pulsars, the spin-down torque from this enhanced pulsar wind can be substantially larger than that predicted by existing models of the disk-magnetosphere interaction, and is in principle capable of maintaining spin equilibrium at frequencies less than 1 kHz. We speculate that this mechanism may account for the non-detection of frequency increases during outbursts of SAX J1808.4-3658 and XTE J1814-338, and may be generally responsible for preventing spin-up to sub-millisecond periods. If the pulsar wind is collimated by the surrounding environment, the resulting jet can satisfy the power requirements of the highly relativistic outflows from Cir X-1 and Sco X-1. In this framework, the jet power scales relatively weakly with accretion rate, L_j ~ Mdot^{4/7}, and would be suppressed at high accretion rates only if the stellar magnetic moment is sufficiently low.
Two new bright X-ray sources in globular clusters, and many less luminous ones in globular clusters and in old open clusters, have been discovered with ROSAT. Accurate positions obtained with ROSAT help identification with optical objects, which however is still very incomplete in globular clusters. One dim globular cluster source has been identified with a recycled radio pulsar; several others may be cataclysmic variables. The four brightest X-ray sources identified in the old open cluster M67 are puzzling, as we do not understand why they emit X-rays. In comparison with the two old open clusters studied so far, globular clusters are remarkably underluminous in X-rays.
The common envelope binary interaction remains one of the least understood phases in the evolution of compact binaries, including those that result in Type Ia supernovae and in mergers that emit detectable gravitational waves. In this work we continue the detailed and systematic analysis of 3D hydrodynamic simulations of the common envelope interaction aimed at understanding the reliability of the results. Our first set of simulations replicate the 5 simulations of Passy et al. (a 0.88Msun, 90Rsun RGB primary with companions in the range 0.1 to 0.9Msun) using a new AMR gravity solver implemented on our modified version of the hydrodynamic code Enzo. Despite smaller final separations obtained, these more resolved simulations do not alter the nature of the conclusions that are drawn. We also carry out 5 identical simulations but with a 2.0Msun primary RGB star with the same core mass as the Passy et al. simulations, isolating the effect of the envelope binding energy. With a more bound envelope all the companions in-spiral faster and deeper though relatively less gas is unbound. Even at the highest resolution, the final separation attained by simulations with a heavier primary is similar to the size of the smoothed potential even if we account for the loss of some angular momentum by the simulation. As a result we suggest that a ~2.0$Msun RGB primary may possibly end in a merger with companions as massive as 0.6Msun, something that would not be deduced using analytical arguments based on energy conservation.
We theoretically investigate the formation of $W$ states in a tripartite system composed of three charge qubits coupled to vibrational modes. The electromechanical coupling is responsable for second order virtual processes that result in an effective electron-electron interaction between neighbor qubits, which yields to the formation of $W$ states. Based on the Lang-Firsov transformation and perturbation theory, we analytically solve the quantum dynamics, providing a mathematical expression for the maximally entangled $W$ state. Dephasing is also taken into accout, paying particular attention on the robustness of bipartite entanglement against local dephasing processes.
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential equations. Several possible approaches are examined, along with various improvements over previous efforts. These are then evaluated numerically by comparison to a complicated but analytically known rotation that is motivated by the important astrophysical problem of precessing black-hole binaries. It is shown that a straightforward solution directly using quaternions is most efficient and accurate, and that the norm of the quaternion is irrelevant. Integration of the generator of the rotation can also be made roughly as efficient as integration of the rotation. Both methods will typically be twice as efficient as naive vector- or matrix-based methods. Implementation by means of standard general-purpose numerical integrators is stable and efficient, so that such problems can be readily solved as part of a larger system of differential equations. Possible generalization to integration in other Lie groups is also discussed.
We present a suite of galaxy formation simulations that directly model star cluster formation and disruption. Starting from a model previously developed by our group, here we introduce several improvements to the prescriptions for cluster formation and feedback, then test these updates using a large suite of cosmological simulations of Milky Way mass galaxies. We perform a differential analysis with the goal of understanding how each of the updates affects star cluster populations. Two key parameters are the momentum boost of supernova feedback $f_{\mathrm{boost}}$ and star formation efficiency per freefall time $\epsilon_{\mathrm{ff}}$. We find that $f_{\mathrm{boost}}$ has a strong influence on the galactic star formation rate, with higher values leading to less star formation. The efficiency $\epsilon_{\mathrm{ff}}$ does not have a significant impact on the global star formation rate, but dramatically changes cluster properties, with increasing $\epsilon_{\mathrm{ff}}$ leading to a higher maximum cluster mass, shorter age spread of stars within clusters, and higher integrated star formation efficiencies. We also explore the redshift evolution of the observable cluster mass function, finding that most massive clusters have formed at high redshift $z>4$. Extrapolation of cluster disruption to $z=0$ produces good agreement with both the Galactic globular cluster mass function and age-metallicity relation. Our results emphasize the importance of using small-scale properties of galaxies to calibrate subgrid models of star cluster formation and feedback.
Fundamental errors exist in the above-mentioned article, which attempts to justify previous erroneous claims concerning signature change. In the simplest example, the authors' proposed ``solutions'' do not satisfy the relevant equation, as may be checked by substitution. These ``solutions'' are also different to the authors' originally proposed ``solutions'', which also do not satisfy the equation. The variational equations obtained from the authors' ``actions'' are singular at the change of signature. The authors' ``distributional field equations'' are manifestly ill defined.
Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed states at the lower bound of uncertainty relation is obtained. It is shown, that in case of entropy-bounded uncertainty relations, lower-bound state is thermal, and a transition from one-dimensional problem to multi-dimensional one is trivial. Results of numerical calculation of the relation lower bound for different types of generalized purity are presented. Analytical expressions for general purity-bounded relations for highly mixed states are obtained.
How to detect the skyrmion position is a crucial problem in future skyrmionics since it corresponds to the reading process of information. We propose a method to detect the skyrmion position purely electrically by measuring the Hall conductance in a constricted geometry. The Hall conductance becomes maximum when a skyrmion is at the lead position. It is possible to detect the skyrmion position even at room temperature. We find an optimized width of the sample determined by the skyrmion radius. We also investigate the effects of elastic and inelastic scatterings, and finite temperature. We find that the local density of states become minimum at the skyrmion position. Our results will be a basis of future skyrmion electronics.
High-mass gamma-ray binaries consist of a presumptive pulsar in orbit with a massive star. The intense outflows from the star can absorb radio emission from the pulsar, making the detection of pulsation difficult. In this work, we present the basic geometry and formulae that describe the absorption process of a pulsar in binary with an O/B star and apply our model to two typical and well-studied binaries: PSR~B1259-63/LS~2883 and LS 5039. We investigate the influences of the equatorial disc of LS 2883 with different orientations on the dispersion measure and free-free absorption of the radio pulsation from PSR B1259-63. The observed data are consistent with the disc inserted on the orbital plane with a relatively large inclination angle. For LS 5039, due to its tight orbit, it was believed that the strong wind absorption makes detecting radio emissions from the putative pulsar unlikely. However, considering the wind interaction and orbital motion, a bow shock cavity and a Coriolis shock would be formed, thereby allowing the pulsations to partially avoid stellar outflow absorption. We investigate the dependence of the radio optical depth on the observing frequencies, the orbital inclination angle, and the wind parameters. We suppose that the presumptive pulsar in LS 5039 is similar to PSR B1259-63 with pulsed emission extending to several tens of gigahertz. In that case, there could be a transparent window for radio pulsations when the pulsar is moving around the inferior conjunction. The following deep monitoring of LS 5039 and other systems by radio telescopes at high radio frequencies might reveal the nature of compact objects in the future. Alternatively, even a null detection could still provide further constraints on the properties of the putative pulsar and stellar outflows.
We show that given two hyperbolic Dirichlet to Neumann maps associated to two Riemannian metrics of a Riemannian manifold with boundary which coincide near the boundary are close then the lens data of the two metrics is the same. As a consequence, we prove uniqueness of recovery a conformal factor (sound speed) locally under some conditions on the latter.
Let g >= 1 and let Q be a monic, squarefree polynomial of degree 2g + 1 in Z[x]. For an odd prime p not dividing the discriminant of Q, let Z_p(T) denote the zeta function of the hyperelliptic curve of genus g over the finite field F_p obtained by reducing the coefficients of the equation y^2 = Q(x) modulo p. We present an explicit deterministic algorithm that given as input Q and a positive integer N, computes Z_p(T) simultaneously for all such primes p < N, whose average complexity per prime is polynomial in g, log N, and the number of bits required to represent Q.
We calculate the electronic structure of AA'AA'...-stacked alternating twist N-layer (tNG) graphene for N = 3, 4, 5, 6, 8, 10, 20 layers and bulk alternating twist (AT) graphite systems where the lattice relaxations are modeled by means of molecular dynamics simulations. We show that the symmetric AA'AA'... stacking is energetically preferred among all interlayer sliding geometries for progressively added layers up to N=6. Lattice relaxations enhance electron-hole asymmetry, and reduce the magic angles with respect to calculations with fixed tunneling strengths that we quantify from few layers to bulk AT-graphite. Without a perpendicular electric field, the largest magic angle flat-band states locate around the middle following the largest eigenvalue eigenstate in a 1D-chain model of layers, while the density redistributes to outer layers for smaller magic twist angles corresponding to higher order effective bilayers in the 1D chain. A perpendicular electric field decouples the electronic structure into $N$ Dirac bands with renormalized Fermi velocities with distinct even-odd band splitting behaviors, showing a gap for N=4 while for odd layers a Dirac cone remains between the flat band gaps. The magic angle error tolerance estimated from density of states maxima expand progressively from $0.05^{\circ}$ in t2G to up to $0.2^{\circ}$ in AT-graphite, hence allowing a greater flexibility in multilayers. Decoupling of tNG into t2G with different interlayer tunneling proportional to the eigenvalues of a 1D layers chain allows to map tNG-multilayers bands onto those of periodic bulk AT-graphite's at different $k_z$ values. We also obtain the Landau level density of states in the quantum Hall regime for magnetic fields of up to 50~T and confirm the presence of nearly flat bands around which we can develop suppressed density of states gap regions by applying an electric field in N > 3 systems.
We call $n$ a spoof odd perfect number if $n$ is odd and $n=km$ for two integers $k,m>1$ such that $\sigma(k)(m+1)=2n$, where $\sigma$ is the sum-of-divisors function. In this paper, we show how results analogous to those of odd perfect numbers could be established for spoof odd perfect numbers (otherwise known in the literature as Descartes numbers). In particular, we prove that $k$ is not almost perfect.
We present a spectroscopic survey of Ly$\alpha$ emitters (LAEs) at $z\approx3.1$ in the Subaru MM-Newton Deep Survey Field. This field has deep imaging data in a series of broad and narrow bands, including two adjacent narrow bands NB497 and NB503 that have allowed us to efficiently select LAE candidates at $z\approx3.1$. Using spectroscopic observations on MMT Hectospec and Magellan M2FS, we obtained a sample of 166 LAEs at $z\approx3.1$ over an effective area of $\sim$1.2 deg$^2$, including 16 previously known LAEs. This is so far the largest (spectroscopically confirmed) sample of LAEs at this redshift. We make use of the secure redshifts and multi-band data to measure spectral properties such as Ly$\alpha$ luminosity and rest-frame UV slope. We derive a robust Ly$\alpha$ luminosity function (LF) that spans a luminosity range from $\sim10^{42.0}$ to $>10^{43.5}$ erg s$^{-1}$. Significant overdense and underdense regions are detected in our sample, but the area coverage is wide enough to largely suppress the effect from such cosmic variance. Our Ly$\alpha$ LF is generally consistent with those from previous studies at $z \sim 3.1$. At the brightest end of the LF, there is a tentative detection of a density excess that is not well described by the Schechter function. The comparison with the LFs at other redshifts suggests that the Ly$\alpha$ LF does not show significant evolution at $2<z<5$. Finally, we build the composite spectra of the LAEs and detect the NVI and CIV doublet emission lines at significance of $\sim 4 \sigma$, suggesting very hard radiation fields in (some of) these LAEs.
We explored a variety of brane configurations in our previous paper within the two derivative truncation of the unstable D9-brane effective theory. In this paper we extend our previous results with emphasis on the inclusion of the higher derivative corrections for the tachyon and the gauge fields computed in the boundary string field theories. We give the exact solutions to BPS brane configurations studied in our previous paper and find remarkable exact agreements of their energies and RR-charges with the expected results. We further find a few more solutions that we could not construct in the two derivative truncations, such as a (F,D6) bound state ending on a D8-brane whose existence turns out to be due to a higher derivative effect and also the dielectric brane of Emparan and Myers as a nonsupersymmetric example. These are also in exact agreements with the results obtained in the effective theory of supersymmetric D-branes.
EX Lupi is the prototype for a class of young, pre-main sequence stars which are observed to undergo irregular, presumably accretion-generated, optical outbursts that result in a several magnitude rise of the optical flux. EX Lupi was observed to optically erupt in 2008 January, triggering Chandra ACIS ToO observations shortly thereafter. We find very strong evidence that most of the X-ray emission in the first few months after the optical outburst is generated by accretion of circumstellar material onto the stellar photosphere. Specifically, we find a strong correlation between the decreasing optical and X-ray fluxes following the peak of the outburst in the optical, which suggests that these observed declines in both the optical and X-ray fluxes are the result of declining accretion rate. In addition, in our models of the X-ray spectrum, we find strong evidence for a ~0.4 keV plasma component, as expected for accretion shocks on low-mass, pre-main sequence stars. From 2008 March through October, this cool plasma component appears to fade as EX Lupi returns to its quiescent level in the optical, consistent with a decrease in the overall emission measure of accretion shock-generated plasma. The overall small increase of the X-ray flux during the optical outburst of EX Lupi is similar to what was observed in previous X-ray observations of the 2005 optical outburst of the EX Lupi-type star V1118 Ori but contrasts with the large increase of the X-ray flux from the erupting young star V1647 Ori during its 2003 and 2008 optical outbursts.