ShantanuT01/DACTYL-Pretraining huggingface dataset:
With the third order Monge-Amp\`ere equation as an example, we show that there exists an infinite number of nonlocal conserved charges associated with the Witten-Dijkgraaf-Verlinde-Verlinde equations. A general prescription for the construction of these charges is given and the charge algebra is calculated bringing out various other interesting features associated with such systems.
A Newman polynomial has all the coefficients in $\{ 0,1\}$ and constant term 1, whereas a Littlewood polynomial has all coefficients in $\{-1,1\}$. We call $P(X)\in\mathbb{Z}[X]$ a Borwein polynomial if all its coefficients belong to $\{ -1,0,1\}$ and $P(0)\neq 0$. By exploiting an algorithm which decides whether a given monic integer polynomial with no roots on the unit circle $|z|=1$ has a non-zero multiple in $\mathbb{Z}[X]$ with coefficients in a finite set $\mathcal{D} \subset \mathbb{Z}$, for every Borwein polynomial of degree at most 9 we determine whether it divides any Littlewood or Newman polynomial. In particular, we show that every Borwein polynomial of degree at most 8 which divides some Newman polynomial divides some Littlewood polynomial as well. In addition to this, for every Newman polynomial of degree at most 11, we check whether it has a Littlewood multiple, extending the previous results of Borwein, Hare, Mossinghoff, Dubickas and Jankauskas.
Yang-Mills theory at finite temperature is rewritten as a theory of plasmons which provides a Hamiltonian framework for perturbation theory with resummation of hard thermal loops.
Hadronic phase in $\pi \pi$ and $K \bar K$ channels are calculated a la Regge. At the D mass one finds $\delta_{\pi \pi} \approx \pi/3$ and $\delta_{K \bar K} \approx -\pi/6$ in good agreement with the CLEO data while at the B mass these angles are predicted to be, respectively, $11^\circ$ and $-7^\circ$. With the hadronic phase $e^{i \delta_{K \bar K}}$ taken into account, a quark diagram decomposition of the isospin invariant amplitudes in $D \to K \bar K$ decays fits the data provided the exchange diagram contribution is about 1/3 of the tree level one.
This paper is a natural continuation of [8], where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in $L_{d+1}(\mathbb{R}^{d+1})$. Here we study some properties of these processes such as higher summability of Green's functions, boundedness of resolvent operators in Lebesgue spaces, establish It\^o's formula, and so on.
We introduce a method to speed up adiabatic protocols for creating entanglement between two qubits dispersively coupled to a transmission line, while keeping fidelities high and maintaining robustness to control errors. The method takes genuinely adiabatic sweeps, ranging from a simple Landau-Zener drive to boundary cancellation methods and local adiabatic drivings, and adds fast oscillations to speed up the protocol while canceling unwanted transitions. We compare our protocol with existing adiabatic methods in a state-of-the-art parameter range and show substantial gains. Numerical simulations emphasize that this strategy is efficient also beyond the rotating-wave approximation and that the method is robust against random static biases in the control parameters and with respect to damping and decoherence effects.
We have investigated the magnetic damping of precessional spin dynamics in defect-controlled epitaxial grown Fe$_3$O$_4$(111)/Yttria-stabilized Zirconia (YSZ) nanoscale films by all-optical pump-probe measurements. The intrinsic damping constant of the defect-free Fe$_3$O$_4$ film is found to be strikingly larger than that of the as-grown Fe$_3$O$_4$ film with structural defects. We demonstrate that the population of the first-order perpendicular standing spin wave (PSSW) mode, which is exclusively observed in the defect-free film under sufficiently high external magnetic fields, leads to the enhancement of the magnetic damping of the uniform precession (Kittel) mode. We propose a physical picture in which the PSSW mode acts as an additional channel for the extra energy dissipation of the Kittel mode. The energy transfer from Kittel mode to PSSW mode increases as in-plane magnetization precession becomes more uniform, resulting in the unique intrinsic magnetic damping enhancement in the defect-free Fe$_3$O$_4$ film.
We use 3D radiation magnetohydrodynamic models to investigate how the thermodynamic quantities in the simulation are encoded in observable quantities, thus exploring the diagnostic potential of the 133.5 nm lines. We find that the line core intensity is correlated with the temperature at the formation height but the correlation is rather weak, especially when the lines are strong. The line core Doppler shift is a good measure of the line-of-sight velocity at the formation height. The line width is both dependent on the width of the absorption profile (thermal and non-thermal width) and an opacity broadening factor of 1.2-4 due to the optically thick line formation with a larger broadening for double peak profiles. The 133.5 nm lines can be formed both higher and lower than the core of the Mg II k line depending on the amount of plasma in the 14-50 kK temperature range. More plasma in this temperature range gives a higher 133.5 nm formation height relative to the Mg II k line core. The synthetic line profiles have been compared with IRIS observations. The derived parameters from the simulated line profiles cover the parameter range seen in observations but on average the synthetic profiles are too narrow. We interpret this discrepancy as a combination of a lack of plasma at chromospheric temperatures in the simulation box and too small non-thermal velocities. The large differences in the distribution of properties between the synthetic profiles and the observed ones show that the 133.5 nm lines are powerful diagnostics of the upper chromosphere and lower transition region.
Bertrand theorem permits closed orbits in 3d Euclidean space only for 2 types of central potentials. These are of Kepler-Coulomb and harmonic oscillator type. Volker Perlick recently extended Bertrand theorem. He designed new static spherically symmetric (Bertrand) spacetimes obeying Einsteins equations and supporting closed orbits. In this work we prove that the topology and geometry of these spacetimes permits to solve quantum many-body problem for any atom of periodic system exactly. The computations of spectrum for any atom of periodic system becomes analogous to that for hydrogen atom. Initially the exact solution of the Schr\"odinger equation for any multielectron atom was obtained by Tietz in 1956. However, neither himself nor others fully comprehended what actually was obtained. We recalculated Tietz results by applying the methodology consistent with new (different from that developed by Fock in 1936) way of solving Schro"odingers equation for hydrogen atom. In the light of this new result it had become possible to demonstrate rigorously that the Tietz-type Schro"odingers equation is in fact describing the quantum motion in Bertrand spacetime. As a bonus, we obtained the analytical proof of the Madelung rule defined in the text
The ESA gamma-ray observatory INTEGRAL, launched on 17 October 2002, continues to produce a wealth of discoveries and new results on compact high energy Galactic objects, nuclear gamma-ray line emission, diffuse line and continuum emission, cosmic background radiation, AGN, high energy transients and sky surveys. The mission's technical status is healthy and INTEGRAL is continuing its scientific operations well beyond its 5-year technical design lifetime until, at least, 31 December 2014. This paper describes the current status of INTEGRAL including the spacecraft technical state-of-health and the scientific observing programme including its on-going and future multi-year "legacy" programmes.
We discuss the impact of the recent precision measurements at LEP on the minimal supersymmetric standard model. We show that the values of $\tan\beta$ necessary to induce large positive corrections to $R_b$ are the same as the ones preferred by the unification of the bottom and $\tau$ Yukawa couplings in the MSSM for the current measured value of $M_t$. We discuss the relevance of the preferred parameter space for the Higgs and sparticle searches at LEP2. Remarkably, it follows that the LEP measurements can provide information about the structure of soft supersymmetry breaking parameters at $M_{GUT}$. Finally, we briefly discuss the properties of a supersymmetric model with four generations, for which the fit to $R_b$ naturally improves with respect to the one in the Standard Model.
An analysis of null geodesics in Schwarzschild de Sitter space is presented with special attention to their global `bending angles', local measurable angles, and the involvement of the cosmological constant. We make use of a general technique which allows for finding observable intersection angles of null trajectories analytically. A general relativistic aberration relationship is established as one of its applications. The question of whether or not the cosmological constant, $\Lambda$, contributes to orbits of light and to related observable quantities is addressed in detail. We also discuss the ongoing debate on this issue and respond to some recent papers on the topic. The dependence of measurable quantities on the motion of observers is stressed throughout. Exact formulas for measurable intersection angles, as well as gravitational lens equations for observers in the Schwarzschild de Sitter background are provided.
The black hole X-ray binary V4641 Sgr experienced an outburst in 2002 May which was detected at X-ray, optical, and radio wavelengths. The outburst lasted for only 6 days, but the object remained active for the next several months. Here we report on the detailed properties of light curves during the outburst and the post-outburst active phase. We reveal that rapid optical variations of ~100 s became more prominent when a thermal flare weakened and the optical spectrum flattened in the Ic, Rc, and V-band region. In conjunction with the flat spectrum in the radio range, this strongly indicates that the origin of rapid variations is not thermal emission, but synchrotron emission. Just after the outburst, we detected repeated flares at optical and X-ray wavelengths. The optical and X-ray light curves exhibited a strong correlation, with the X-rays, lagging by about 7 min. The X-ray lag can be understood in terms of a hot region propagating into the inner region of the accretion flow. The short X-ray lag, however, requires modifications of this simple scenario to account for the short propagation time. We also detected rapid optical variations with surprisingly high amplitude 50 days after the outburst, which we call optical flashes. During the most prominent optical flash, the object brightened by 1.2 mag only within 30 s. The released energy indicates that the emission source should be at the innermost region of the accretion flow.
Thanks to the advances in the technology of low-cost digital cameras and the popularity of the self-recording culture, the amount of visual data on the Internet is going to the opposite side of the available time and patience of the users. Thus, most of the uploaded videos are doomed to be forgotten and unwatched in a computer folder or website. In this work, we address the problem of creating smooth fast-forward videos without losing the relevant content. We present a new adaptive frame selection formulated as a weighted minimum reconstruction problem, which combined with a smoothing frame transition method accelerates first-person videos emphasizing the relevant segments and avoids visual discontinuities. The experiments show that our method is able to fast-forward videos to retain as much relevant information and smoothness as the state-of-the-art techniques in less time. We also present a new 80-hour multimodal (RGB-D, IMU, and GPS) dataset of first-person videos with annotations for recorder profile, frame scene, activities, interaction, and attention.
We define a transformation that associates certain exponential moment sequences with ordinary moment sequences in a natural way. The ingredients of this transformation are series reversion, the Sumudu transform (a variant of the Laplace transform), and the inverting of generating functions. This transformation also has a simple interpretation in terms of continued fractions. It associates lattice path objects with permutation objects, and in particular it associates the Narayana triangle with the Eulerian triangle.
Objects in aerial images have greater variations in scale and orientation than in typical images, so detection is more difficult. Convolutional neural networks use a variety of frequency- and orientation-specific kernels to identify objects subject to different transformations; these require many parameters. Sampling equivariant networks can adjust sampling from input feature maps according to the transformation of the object, allowing a kernel to extract features of an object under different transformations. Doing so requires fewer parameters, and makes the network more suitable for representing deformable objects, like those in aerial images. However, methods like deformable convolutional networks can only provide sampling equivariance under certain circumstances, because of the locations used for sampling. We propose sampling equivariant self-attention networks which consider self-attention restricted to a local image patch as convolution sampling with masks instead of locations, and design a transformation embedding module to further improve the equivariant sampling ability. We also use a novel randomized normalization module to tackle overfitting due to limited aerial image data. We show that our model (i) provides significantly better sampling equivariance than existing methods, without additional supervision, (ii) provides improved classification on ImageNet, and (iii) achieves state-of-the-art results on the DOTA dataset, without increased computation.
With bolometric luminosities exceeding $10^{48}$ erg s$^{-1}$, powerful jets and supermassive black holes at their center, MeV blazars are some of the most extreme sources in the Universe. Recently, the Fermi-Large Area Telescope detected five new $\gamma$-ray emitting MeV blazars beyond redshift $z=3.1$. With the goal of precisely characterizing the jet properties of these extreme sources, we started a multiwavelength campaign to follow them up with joint NuSTAR, Swift and SARA observations. We observe six high-redshift quasars, four of them belonging to the new $\gamma$-ray emitting MeV blazars. Thorough X-ray analysis reveals spectral flattening at soft X-ray for three of these objects. The source NVSS J151002$+$570243 also shows a peculiar re-hardening of the X-ray spectrum at energies $E>6\,\rm keV$. Adopting a one-zone leptonic emission model, this combination of hard X-rays and $\gamma$-rays enables us to determine the location of the Inverse Compton peak and to accurately constrain the jet characteristics. In the context of the jet-accretion disk connection, we find that all six sources have jet powers exceeding accretion disk luminosity, seemingly validating this positive correlation even beyond $z>3$. Our six sources are found to have $10^9 \rm M_{\odot}$ black holes, further raising the space density of supermassive black holes in the redshift bin $z=[3,4]$.
We introduce a multipartite extension of an information-theoretic distance first introduced in [Nature 341, 119 (1989)]. We use this new distance to derive entropic tests of multipartite nonlocality for three and for an arbitrary even number of qubits as well as a test of state-independent contextuality. In addition, we re-derive the tripartite Mermin inequality and a state-independent non-contextuality inequality by Cabello [Phys. Rev. Lett. 101, 210401 (2008)]. This suggests that the information-theoretic distance approach to multipartite nonlocality and state-independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions.
The analytic method for deriving the equation of state of a cell fluid model in the region above the critical temperature ($T \geqslant T_\text{c}$) is elaborated using the renormalization group transformation in the collective variables set. Mathematical description with allowance for non-Gaussian fluctuations of the order parameter is performed in the vicinity of the critical point on the basis of the $\rho^4$ model. The proposed method of calculation of the grand partition function allows one to obtain the equation for the critical temperature of the fluid model in addition to universal quantities such as critical exponents of the correlation length. The isothermal compressibility is plotted as a function of density. The line of extrema of the compressibility in the supercritical region is also represented.
The statistical state of any (classical or quantum) system with non-trivial time evolution can be interpreted as the pointer of a clock. The quality of such a clock is given by the statistical distinguishability of its states at different times. If a clock is used as a resource for producing another one the latter can at most have the quality of the resource. We show that this principle, formalized by a quasi-order, implies constraints on many physical processes. Similarly, the degree to which two (quantum or classical) clocks are synchronized can be formalized by a quasi-order of synchronism.   Copying timing information is restricted by quantum no-cloning and no-broadcasting theorems since classical clocks can only exist in the limit of infinite energy. We show this quantitatively by comparing the Fisher timing information of two output systems to the input's timing information. For classical signal processing in the quantum regime our results imply that a signal looses its localization in time if it is amplified and distributed to many devices.
Polarisation effects in the microcavity parametric oscillator are studied using a simple model in which two chi-three optical parametric oscillators are coupled together. It is found that there are, in general, a number of steady states of the model under continuous pumping. There are both continuous and discontinuous thresholds, at which new steady-states appear as the driving intensity is increased: at the continuous thresholds, the new state has zero output intensity, whereas at the discontinuous threshold it has a finite output intensity. The discontinuous thresholds have no analog in the uncoupled device. The coupling also generates rotations of the linear polarisation of the output compared with the pump, and shifts in the output frequencies as the driving polarisation or intensity is varied. For large ratios of the interaction between polarisations to the interaction within polarisations, of the order of 5, one of the thresholds has its lowest value when the pump is elliptically polarised. This is consistent with recent experiments in which the maximum output was achieved with an elliptically polarised pump.
We introduce an alternative type of quantum repeater for long-range quantum communication with improved scaling with the distance. We show that by employing hashing, a deterministic entanglement distillation protocol with one-way communication, one obtains a scalable scheme that allows one to reach arbitrary distances, with constant overhead in resources per repeater station, and ultrahigh rates. In practical terms, we show that also with moderate resources of a few hundred qubits at each repeater station, one can reach intercontinental distances. At the same time, a measurement-based implementation allows one to tolerate high loss, but also operational and memory errors of the order of several percent per qubit. This opens the way for long-distance communication of big quantum data.
In the framework of the Sen conjectures a construction of vacuum superstring field theory on a non-BPS brane is discussed. A distinguished feature of this theory is a presence of a ghost kinetic operator mixing GSO+/- sectors. A candidate for such kinetic operator with zero cohomology is discussed.
We present a theoretical study of the ballistic magnetoresistance in Ni contacts using first-principles, atomistic electronic-structure calculations. In particular we investigate the role of defects in the contact region in order to explain the recently observed spectacular magnetoresistance ratio. Our results predict that possible presence of spin polarized oxygen in the contact region, could explain conductance changes by an order of magnitude. Electronic transport essentially occurs through spin-polarized oxygen p states, and this mechanism gives a much higher magnetoresistance than that obtained assuming clean atomically sharp domain walls alone.
The paper concerned with higher order asymptotic expansion of solutions to the Cauchy problem of abstract hyperbolic equations of the form $u''+Au+u'=0$ in a Hilbert space, where $A$ is a nonnegative selfadjoint operator. The result says that by assuming the regularity of initial data, asymptotic profiles (of arbitrary order) are explicitly written by using the semigroup $e^{-tA}$ generated by $-A$. To prove this, a kind of maximal regularity for $e^{-tA}$ is used.
Planck was successfully launched on May 14th, 2009, from the Kourou space port, in French Guyana. After recalling the objectives that we set out - back in 1996 - to fulfill with this project, I recall some of the technological breakthroughs which needed to be made and report on the exciting scientific outlook of the project in light of the knowledge we now have of the actual performances of the two on-board instruments. I also include one of our more recent results even though it was not yet available at the time of the conference.
We propose a general scheme determining the quantum pointer basis of a macroscopic object interacting with environment. Unlike the decoherence program, our pointer basis does not require robustness against entanglement, but require robustness on the object state itself. The proposed pointer basis does not rely on master equations, and so is easily calculable since it has a time-local analytic formula. We show that, as a convincing example, the proposed formula gives an satisfactory pointer basis of a macroscopic flying body such as a bullet whose pointer states should have well-defined momentum as well as highly-localized position.
Damping in magnetization dynamics characterizes the dissipation of magnetic energy and is essential for improving the performance of spintronics-based devices. While the damping of ferromagnets has been well studied and can be artificially controlled in practice, the damping parameters of antiferromagnetic materials are nevertheless little known for their physical mechanisms or numerical values. Here we calculate the damping parameters in antiferromagnetic dynamics using the generalized scattering theory of magnetization dissipation combined with the first-principles transport computation. For the PtMn, IrMn, PdMn and FeMn metallic antiferromagnets, the damping coefficient associated with the motion of magnetization ($\alpha_m$) is one to three orders of magnitude larger than the other damping coefficient associated with the variation of the N\'eel order ($\alpha_n$), in sharp contrast to the assumptions made in the literature.