ShantanuT01/DACTYL-Pretraining huggingface dataset:
We review a proof of the well know result stating that moduli spaces of stable sheaves with fixed Chern character on a polarized $K3$ surface are deformations of a hyperk\"ahler variety of Type $K3^{[n]}$ (if a suitable numerical hypothesis is satisfied). In a recent work we have adapted that proof in order to prove results on moduli of vector bundles on polarized hyperk\"ahler varieties of Type $K3^{[2]}$ - this is the content of the second part of the paper.
We present broadband X-ray spectral-timing analysis of the new Galactic X-ray transient MAXI~J1348--630 using five simultaneous {\it AstroSat} and {\it NICER} observations. Spectral analysis using {\it AstroSat} data identify the source to be in the soft state for the first three observations and in a faint and bright hard state for the next two. Quasi-periodic oscillations at $\sim 0.9$ and $\sim 6.9$\,Hz, belonging to the type-C and type-A class are detected. In the soft state, the power density spectra are substantially lower (by a factor $> 5$) for the {\it NICER} (0.5--12 keV) band compared to the {\it AstroSat}/LAXPC (3--80 keV) one, confirming that the disk is significantly less variable than the Comptonization component. For the first time, energy-dependent fractional rms and time lag in the 0.5--80 keV energy band was measured at different Fourier frequencies, using the bright hard state observation. Hard time lag is detected for the bright hard state, while the faint one shows evidence for soft lag. A single-zone propagation model fits the LAXPC results in the energy band 3--80 keV with parameters similar to those obtained for Cygnus X--1 and MAXI J1820+070. Extending the model to lower energies, reveals qualitative similarities but having quantitative differences with the {\it NICER} results. These discrepancies could be because the {\it NICER} and {\it AstroSat} data are not strictly simultaneous and because the simple propagation model does not take into account disk emission. The results highlight the need for more joint coordinated observations of such systems by {\it NICER} and {\it AstroSat}.
One of the key factors behind the recent success in visual tracking is the availability of dedicated benchmarks. While being greatly benefiting to the tracking research, existing benchmarks do not pose the same difficulty as before with recent trackers achieving higher performance mainly due to (i) the introduction of more sophisticated transformers-based methods and (ii) the lack of diverse scenarios with adverse visibility such as, severe weather conditions, camouflage and imaging effects.   We introduce AVisT, a dedicated benchmark for visual tracking in diverse scenarios with adverse visibility. AVisT comprises 120 challenging sequences with 80k annotated frames, spanning 18 diverse scenarios broadly grouped into five attributes with 42 object categories. The key contribution of AVisT is diverse and challenging scenarios covering severe weather conditions such as, dense fog, heavy rain and sandstorm; obstruction effects including, fire, sun glare and splashing water; adverse imaging effects such as, low-light; target effects including, small targets and distractor objects along with camouflage. We further benchmark 17 popular and recent trackers on AVisT with detailed analysis of their tracking performance across attributes, demonstrating a big room for improvement in performance. We believe that AVisT can greatly benefit the tracking community by complementing the existing benchmarks, in developing new creative tracking solutions in order to continue pushing the boundaries of the state-of-the-art. Our dataset along with the complete tracking performance evaluation is available at: https://github.com/visionml/pytracking
A wide range of recent observations have shown that AGN-driven cavities may provide the energy source that balances the cooling observed in the centres of cool-core galaxy clusters. One tool for better understanding the physics of these cavities is their observed morphological evolution, which is dependent on such poorly-understood properties as the turbulent density field and the impact of magnetic fields. Here we combine numerical simulations that include subgrid turbulence and software that produces synthetic X-ray observations to examine the evolution of X-ray cavities in the absence of magnetic fields. Our results reveal an anisotropic size evolution of that is dramatically different from simplified, analytical predictions. These differences highlight some of the key issues that must be accurately quantified when studying AGN-driven cavities, and help to explain why the inferred pV energy in these regions appears to be correlated with their distance from the cluster center. Interpreting X- ray observations will require detailed modeling of effects including mass-entrainment, distortion by drag forces, and pro jection. Current limitations do not allow a discrimination between purely hydrodynamic and magnetically-dominated models for X-ray cavities.
This work presents an exposition of both the internal structure of derived category of an abelian category D*(A) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D*(A) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D*(A) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.
We extend Faltings's "almost purity theorem" on finite etale extensions of perfectoid algebras (as generalized by Scholze and Kedlaya-Liu) to the ramified case, without restriction on the discriminant. The key point is a perfectoid version of Riemann's extension theorem. Categorical aspects of uniform Banach algebras and perfectoid algebras are revisited beforehand.
Accurate 3D object detection from point clouds has become a crucial component in autonomous driving. However, the volumetric representations and the projection methods in previous works fail to establish the relationships between the local point sets. In this paper, we propose Sparse Voxel-Graph Attention Network (SVGA-Net), a novel end-to-end trainable network which mainly contains voxel-graph module and sparse-to-dense regression module to achieve comparable 3D detection tasks from raw LIDAR data. Specifically, SVGA-Net constructs the local complete graph within each divided 3D spherical voxel and global KNN graph through all voxels. The local and global graphs serve as the attention mechanism to enhance the extracted features. In addition, the novel sparse-to-dense regression module enhances the 3D box estimation accuracy through feature maps aggregation at different levels. Experiments on KITTI detection benchmark demonstrate the efficiency of extending the graph representation to 3D object detection and the proposed SVGA-Net can achieve decent detection accuracy.
Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving the hydrodynamic equations uses quantum trajectories as the computational tool. The trajectory equations of motion are described and methods for implementation are discussed, including fitting of the fields to gaussian clusters.
We present a NIR polarimetric map of the 1deg by 1deg region toward the Galactic center. Comparing Stokes parameters between highly reddened stars and less reddened ones, we have obtained a polarization originating from magnetically aligned dust grains at the central region of our Galaxy. The distribution of position angles shows a peak at the parallel direction to the Galactic plane, suggesting a toroidal magnetic field configuration. However, at high Galactic latitudes, the peak of the position angles departs from the direction of the Galactic plane. This may be a transition of a large-scale magnetic field configuration from toroidal to poloidal.
The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The region of validity of the Faddeev-Popov-DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two "equivalent" unconstrained systems: the "dynamic" (with "dynamic" evolution parameter as the metric scale factor) and "geometric" (given by the Levi-Civita type canonical transformation to the action-angle variables where the energy constraint converts into a new momentum). "Big Bang", the Hubble evolution, and creation of matter fields by the "geometric" vacuum are described by the inverted Levi-Civita (LC) transformation of the geomeric system into the dynamic one. The particular case of the LC transformations are the Bogoliubov ones of the particle variables (diagonalizing the dynamic Hamiltonian) to the quasiparticles (diagonalizing the equations of motion). The choice of initial conditions for the "Big Bang" in the form of the Bogoliubov (squeezed) vacuum reproduces all stages of the evolution of the Friedmann-Robertson-Walker Universe in their conformal (Hoyle-Narlikar) versions.
It is known after Jouanolou that a general holomorphic foliation of degree $\geq2$ in projective space has no algebraic leaf. We give formulas for the degrees of the subvarieties of the parameter space of one-dimensional foliations that correspond to foliations endowed with some invariant subvariety of degree 1 or 2 and dimension $\geq1$.
We present a matrix solution to the full equations of statistical equilibrium that give the energy level populations of collisionally-excited ions in photoionised gaseous nebulae. The rationale for such a calculation is to maintain a parity between improvements in the quantum-mechanically evaluated values for collision strengths and transition probabilities from the Iron and Opacity Projects on the one hand, and 3D photoionisation codes such as MOCASSIN and astrophysical software for producing nebular diagnostics such as the Nebular package for IRAF, on the other. We have taken advantage of the fact that mathematics programs such as MATLAB and Mathematica have proven to be very adept at symbolic manipulation providing a route to exact solutions for the n-level ion. In particular, we have avoided the substitution of estimated values. We provide the matrix solution for the 5-level ion as an example and show how the equations faithfully reduce to the exact solution for the 3-level ion. Through the forbidden line ratio R23, we compare the exact solution with a) that obtained from the observed emission of the spherical planetary nebula Abell 39, b) 3D Monte-Carlo photoionisation modelling of the same nebula, c) the approximate 5-level program TEMDEN and d) the exact 3-level ion. The general solution presented here means that programs for the calculation of level populations can obtain solutions for ions with a user-specified number of excited levels. The use of a separate and updatable database of atomic and ionic constants such as that provided by NIST, means that software of more general application can now be made available; particularly for the study of high excitation objects such as active galactic nebulae (AGNs) and supernovae (SNs) where higher excited levels become significant.
De Raedt et al. (Eur. Phys. J. B 53: 139-142, 2006) have claimed to provide a local realist model for correlations of the singlet state in the familiar Einstein-Podolsky-Rosen-Bohm (EPRB) experiment when time-coincidence is used to decide which detection events should count in the analysis, and furthermore that this suggests that it is possible to construct local realistic models that can reproduce the quantum mechanical expectation values. In this letter we show that these conclusions cannot be upheld since their model exploits the so-called coincidence-time loophole. When this is properly taken into account no startling conclusions can be drawn about local realist modelling of quantum mechanics.
We analyze the Bragg regime of the two-particle Kapitza-Dirac arrangement, completing the basic theory of this effect. We provide a detailed evaluation of the detection probabilities for multi-mode states, showing that a complete description must include the interaction time in addition to the usual dimensionless parameter w. The arrangement can be used as a massive two-particle beam splitter. In this respect, we present a comparison with Hong-Ou-Mandel-type experiments in quantum optics. The analysis reveals the presence of dips for massive bosons and a differentiated behavior of distinguishable and identical particles in an unexplored scenario. We suggest that the arrangement can provide the basis for symmetrization verification schemes.
The Schinzel Hypothesis is a celebrated conjecture in number theory linking polynomial values and prime numbers. In the same vein we investigate the common divisors of values $P_1(n),\ldots, P_s(n)$ of several polynomials. We deduce this coprime version of the Schinzel Hypothesis: under some natural assumption, coprime polynomials assume coprime values at infinitely many integers. Consequences include a version "modulo an integer" of the original Schinzel Hypothesis, with the Goldbach conjecture, again modulo an integer, as a special case.
We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, and this direction is opposite for the two transitions. The waveguide is terminated by a mirror which coherently feeds the photon stream emitted by one transition back to the atom. First, we are interested in the dynamics of the atom in the Markovian limit where the time-delay in the feedback is negligible. Specifically, we study the conditions under which the atom evolves towards a pure "dark" stationary state, where the photons emitted by both transitions interfere destructively thanks to the coherent feedback, and the overall emission vanishes. This is a single-atom analog of the quantum dimer, where a pair of laser-driven two-level atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current state-of-the-art experiments. Second, we extend our study to non-Markovian regimes and investigate the effect of the feedback retardation on the steady-state.
Can a non self-complementary graph have the same chromatic polynomial as its complement? The answer to this question of Akiyama and Harrary is positive and was given by J. Xu and Z. Liu. They conjectured that every such graph has the same degree sequence as its complement. In this paper we show that there are infinitely many graphs for which this conjecture does not hold. We then solve a more general variant of the Akiyama-Harary problem by showing that there exists infinitely many non self-complementary graphs having the same Tutte polynomial as their complements.
The susceptible-exposed-infectious-susceptible (SEIS) model is well-known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The compartment model is well studied, but the corresponding particle system has so far received no attention. For the particle system model in one spatial dimension, we give upper and lower bounds on the critical values, prove convergence of critical values in the limit of small and large latent time, and identify a limiting process to which the SEIS model converges in the limit of large latent time.
Myocardial Infarction is one of the leading causes of death worldwide. This paper presents a Convolutional Neural Network (CNN) architecture which takes raw Electrocardiography (ECG) signal from lead II, III and AVF and differentiates between inferior myocardial infarction (IMI) and healthy signals. The performance of the model is evaluated on IMI and healthy signals obtained from Physikalisch-Technische Bundesanstalt (PTB) database. A subject-oriented approach is taken to comprehend the generalization capability of the model and compared with the current state of the art. In a subject-oriented approach, the network is tested on one patient and trained on rest of the patients. Our model achieved a superior metrics scores (accuracy= 84.54%, sensitivity= 85.33% and specificity= 84.09%) when compared to the benchmark. We also analyzed the discriminating strength of the features extracted by the convolutional layers by means of geometric separability index and euclidean distance and compared it with the benchmark model.
We investigate the properties of the environment around 20 powerful radio galaxies and quasars at redshifts between 0.45 and 1. Using XMM-Newton and Chandra observations we probe the spatial distribution and the temperature of the cluster gas. We find that more than 60 per cent of powerful radio sources in the redshift range of our sample lie in a cluster of X-ray luminosity greater than 10^44 erg/s, and all but one of the narrow-line radio galaxies, for which the emission from the nucleus is obscured by a torus, lie in a cluster environment. Within the statistical uncertainties we find no significant difference in the properties of the environment as a function of the orientation to the line of sight of the radio jet. This is in agreement with unification schemes. Our results have important implications for cluster surveys, as clusters around powerful radio sources tend to be excluded from X-ray and Sunyaev-Zeldovich surveys of galaxy clusters, and thus can introduce an important bias in the cluster luminosity function. Most of the radio sources are found close to pressure balance with the environment in which they lie, but the two low-excitation radio galaxies of the sample are observed to be under-pressured. This may be the first observational indication for the presence of non-radiative particles in the lobes of some powerful radio galaxies. We find that the clusters around radio sources in the redshift range of our sample have a steeper entropy-temperature relation than local clusters, and the slope is in agreement with the predictions of self-similar gravitational heating models for cluster gas infall. This suggests that selection by AGN finds systems less affected by AGN feedback than the local average.(Abridged)
In this paper, we prove lower and upper bounds on the achromatic and the pseudoachromatic indices of the $n$-dimensional finite projective space of order $q$.
Here we aim to show that the ratio of the momentum spectra of $K^{+}$ at small transverse momentum measured for symmetric systems of different sizes can be such an observable.
Since the first reports of oscillations in prominences in 1930s there have been major theoretical and observational advances to understand the nature of these oscillatory phenomena leading to a whole new field of so called "prominence seismology". There are two types of oscillatory phenomena observed in prominences; "small amplitude oscillations" (~2-3 km s$^{-1}$) which are quite common and "large amplitude oscillations" ($>$20 km s$^{-1}$) for which observations are scarce. Large amplitude oscillations have been found as "winking filament" in H$\alpha$ as well as motion in the sky plane in H$\alpha$, EUV, micro-wave and He 10830 observations. Historically, it was suggested that the large amplitude oscillations in prominences were triggered by disturbances such as fast-mode MHD waves (Moreton wave) produced by remote flares. Recent observations show, in addition, that near-by flares or jets can also create such large amplitude oscillations in prominences. Large amplitude oscillations, which are observed both in transverse as well as longitudinal direction, have a range of periods varying from tens of minutes to a couple of hours. Using the observed period of oscillation and simple theoretical models, the obtained magnetic field in prominences has shown quite a good agreement with directly measured one and therefore, justifies prominences seismology as a powerful diagnostic tool. On rare occasions, when the large amplitude oscillations have been observed before or during the eruption, the oscillations may be applied to diagnose the stability and the eruption mechanism. Here we review the recent developments and understanding in the observational properties of large amplitude oscillations and their trigger mechanisms and stability in the context of prominence seismology.
A model of nuclear fusion consisting of a wave packet impinging into a well located between square one dimensional barriers is treated analytically. The wave function inside the well is calculated exactly for the assisted tunneling induced by a perturbation mimicking a constant electric field with arbitrary time dependence. Conditions are found for the enhancement of fusion.
While averages and typical fluctuations often play a major role to understand the behavior of a non-equilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of the system is being done. In this context, the statistics of extreme fluctuations in contrast to the average plays an important role, as has been discussed in fields ranging from statistical and mathematical physics to climate, finance and ecology. Herein, we study Extreme Value Statistics (EVS) of stochastic resetting systems which have recently gained lot of interests due to its ubiquitous and enriching applications in physics, chemistry, queuing theory, search processes and computer science. We present a detailed analysis for the finite and large time statistics of extremals (maximum and arg-maximum i.e., the time when the maximum is reached) of the spatial displacement in such system. In particular, we derive an exact renewal formula that relates the joint distribution of maximum and arg-maximum of the reset process to the statistical measures of the underlying process. Benchmarking our results for the maximum of a reset-trajectory that pertain to the Gumbel class for large sample size, we show that the arg-maximum density attains to a uniform distribution regardless of the underlying process at a large observation time. This emerges as a manifestation of the renewal property of the resetting mechanism. The results are augmented with a wide spectrum of Markov and non-Markov stochastic processes under resetting namely simple diffusion, diffusion with drift, Ornstein-Uhlenbeck process and random acceleration process in one dimension. Rigorous results are presented for the first two set-ups while the latter two are supported with heuristic and numerical analysis.