ShantanuT01/DACTYL-Pretraining huggingface dataset:
The paper deals with fluctuations of Kendall random walks, which are extremal Markov chains and iterated integral transforms with the Williamson kernel $\Psi(t) = \left(1-|t|^{\alpha}\right)_+$, $\alpha>0$. We obtain the joint distribution of the first ascending ladder epoch and height over any level $a \geq 0$ and distribution of maximum and minimum for these extremal Markovian sequences solving recursive integral equations. We show that distribution of the first crossing time of level $a \geq0$ is a mixture of geometric and negative binomial distributions. The Williamson transform is the main tool for considered problems connected with the Kendall convolution. All results are described by the Williamson transform of the unit step distribution of Kendall random walks. Using regular variation, we investigate the asymptotic properties of the maximum distribution.
Quite some time ago, at the singularity conference at Carg\`ese 1972 Brieskorn asked the following question:   Is the local fundamental group $\pi_1^{s}(S-D)$ of the discriminant complement inside the semi-universal unfolding $S$ of an isolated hypersurface singularity constant for $s$ in the $\mu$-constant stratum $\Sigma_E$?   We review this question and give an affirmative answer in case of singular plane curve germs of multiplicity at most $3$.
We give a brief account of the development of methods to include thermal fluctuations into lattice Boltzmann algorithms. Emphasis is put on our recent work (Phys. Rev. E 76, 036704 (2007)) which provides a clear understanding in terms of statistical mechanics.
The recent measurements of weak lensing by large-scale structure present significant new opportunities for studies of the matter distribution in the universe. Here, we present a new cosmic shear survey carried out with the Echelle Spectrograph and Imager on the Keck II telescope. This covers a total of 0.6 square degrees in 173 fields probing independent lines of sight, hence minimising the impact of sample variance. We also extend our measurements of cosmic shear with the William Herschel Telescope (Bacon, Refregier & Ellis 2000) to a survey area of 1 square degree. The joint measurements with two independent telescopes allow us to assess the impact of instrument-specific systematics, one of the major difficulties in cosmic shear measurements. For both surveys, we carefully account for effects such as smearing by the point spread function and shearing due to telescope optics. We find negligible residuals in both cases and recover mutually consistent cosmic shear signals, significant at the 5.1 sigma level. We present a simple method to compute the statistical error in the shear correlation function, including non-gaussian sample variance and the covariance between different angular bins. We measure shear correlation functions for all fields and use these to ascertain the amplitude of the matter power spectrum, finding sigma_8 (Omega_m/0.3)^0.68 = 0.97 \pm 0.13 with 0.14<Omega_m<0.65 in a Lambda-CDM model with Gamma=0.21. These 68% CL uncertainties include sample variance, statistical noise, redshift uncertainty, and the error in the shear measurement method. The results from our two independent surveys are both consistent with measurements of cosmic shear from other groups. We discuss how our results compare with current normalisation from cluster abundance.
Light sterile neutrinos of mass about an eV with mixing $\tilde U_{ls}$ of a few percent to active neutrinos may solve some anomalies shown in experimental data related to neutrino oscillation. How to have light sterile neutrinos is one of the theoretical problems which have attracted a lot of attentions. In this article we show that such an eV scale light sterile neutrino candidate can be obtained in a seesaw model in which the right-handed neutrinos satisfy a softly-broken Friedberg-Lee (FL) symmetry. In this model a right-handed neutrino is guaranteed by the FL symmetry to be light comparing with other two heavy right-handed neutrinos. It can be of eV scale when the FL symmetry is softly broken and can play the role of eV scale sterile neutrino needed for explaining the anomalies of experimental data. This model predicts that one of the active neutrino is massless. We find that this model prefers inverted hierarchy mass pattern of active neutrinos than normal hierarchy. An interesting consequence of this model is that realizing relatively large $|{\tilde U}_{es}|$ and relatively small $|{\tilde U}_{\mu s}|$ in this model naturally leads to a relatively small $|{\tilde U}_{\tau s}|$. This interesting prediction can be tested in future atmospheric or solar neutrino experiments.
The contribution Delta_epsilon of extremely small motions of domain walls to small-signal permittivity of a multidomain ferroelectric sample has been a research issue for many years. In ferroelastic ferroelectrics such motions contribute also to their piezoelectric (by Delta_d) and elastic (by Delta_s) properties. Data about their simultaneous existence are scarce but those available point to mutual proportionality of Delta_epsilon, Delta_d and Delta_s, as expected. To understand the magnitude of extrinsic contributions, the origin of the restoring force acting on domain walls must be understood. In the present contribution the theory has been developed based on the model of a plate-like sample in which the ferroelectric- ferroelastic bulk is provided with a nonferroic surface layer. Motion of domain walls in the bulk results in a change of electric and elastic energy both in the bulk and in the layer, which provides the source of restoring force. This makes it possible to determine all mentioned extrinsic contributions. We discuss the applicability of the model to available data for single crystals and also for ceramic grains.
We report the results of molecular dynamics simulation of a spatiotemporal evolution of the locally photoexcited electrons and holes localized in two separate layers. It is shown that the ring-shaped spatial pattern of luminescence forms due to the strong in-layer Coulomb interaction at high photoexcitation power. In addition, the results predict (i) stationary spatial oscillations of the electron density in quasi one-dimensional case and (ii) dynamical phase transition in the expansion of two-dimensional electron cloud when threshold electron concentration is reached. A possible reason of the oscillations and a theoretical interpretation of the transition are suggested.
Previous searches for HI in our Galaxy's dwarf spheroidal companions have not been complete enough to settle the question of whether or not these galaxies have HI, especially in their outer parts. We present VLA observations of three dwarf spheroidals: Fornax, Leo II, and Draco, all of which have known stellar velocities. The new data show no HI emission or absorption. Column density limits in emission are 4--7 x 10^18 atoms/cm^2 in the centers of the galaxies. The importance of the new observations is that they cover larger areas than previous searches and they are less plagued by confusion with foreground (Galactic) HI. The apparent absence of neutral gas in the Fornax dwarf spheroidal is especially puzzling because recent photometry shows evidence of stars only 10^8 years old. We discuss whether the VLA observations could have missed significant amounts of HI.
The Asai (or twisted tensor) $L$-function of a Bianchi modular form $\Psi$ is the $L$-function attached to the tensor induction to $\mathbb{Q}$ of its associated Galois representation. In this paper, when $\Psi$ is ordinary at $p$ we construct a $p$-adic analogue of this $L$-function: that is, a $p$-adic measure on $\mathbb{Z}_p^\times$ that interpolates the critical values of the Asai $L$-function twisted by Dirichlet characters of $p$-power conductor. The construction uses techniques analogous to those used by Lei, Zerbes and the first author in order to construct an Euler system attached to the Asai representation of a quadratic Hilbert modular form.
We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass, quadrupole moment and angular momentum. We investigate the geometric and physical properties of this exact solution of Einstein's vacuum equations, and show that it can be used to describe the exterior gravitational field of rotating, axially symmetric, compact objects.
There is a conjecture in the literature that indicates the tree-level S-matrix elements of graviton become symmetric under the $SL(2,Z)$ transformation after including the loops and the nonperturbative effects. Using the Ward identity corresponding to the global S-duality transformations, this conjecture can be extended to other S-matrix elements as well. While the $SL(2,Z)$ transformation on the background dilaton is nonlinear, the Ward identity dictates the S-duality transformations on external states should be the linearized $SL(2,R)$ transformations. We examine in details various S-matrix elements involving massless closed string and/or open string vertex operators on the world volume of D$_3$-brane in favor of this conjecture.
Data augmentation is critical to the success of modern deep learning techniques. In this paper, we propose Online Hyper-parameter Learning for Auto-Augmentation (OHL-Auto-Aug), an economical solution that learns the augmentation policy distribution along with network training. Unlike previous methods on auto-augmentation that search augmentation strategies in an offline manner, our method formulates the augmentation policy as a parameterized probability distribution, thus allowing its parameters to be optimized jointly with network parameters. Our proposed OHL-Auto-Aug eliminates the need of re-training and dramatically reduces the cost of the overall search process, while establishes significantly accuracy improvements over baseline models. On both CIFAR-10 and ImageNet, our method achieves remarkable on search accuracy, 60x faster on CIFAR-10 and 24x faster on ImageNet, while maintaining competitive accuracies.
We present a brief account of the most salient properties of vortices in dilute atomic Fermi superfluids near a Feshbach resonance.
Let $X_1, X_2,\ldots$ be random elements of the Skorokhod space $D(\mathbb{R})$ and $\xi_1, \xi_2, \ldots$ positive random variables such that the pairs $(X_1,\xi_1), (X_2,\xi_2),\ldots$ are independent and identically distributed. We call the random process $(Y(t))_{t \in \mathbb{R}}$ defined by $Y(t):=\sum_{k \geq 0}X_{k+1}(t-\xi_1-\ldots-\xi_k)1_{\{\xi_1+\ldots+\xi_k\leq t\}}$, $t\in\mathbb{R}$ random process with immigration at the epochs of a renewal process. Assuming that $X_k$ and $\xi_k$ are independent and that the distribution of $\xi_1$ is nonlattice and has finite mean we investigate weak convergence of $(Y(t))_{t\in\mathbb{R}}$ as $t\to\infty$ in $D(\mathbb{R})$ endowed with the $J_1$-topology. The limits are stationary processes with immigration.
The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum channel. At the same time, the entropy of a system evolving via a non-unital channel can, in principle, decrease. Here, we analyze the behavior of the entropy in the context of the H-theorem. As exemplary phenomena, we discuss the action of a Maxwell demon (MD) operating a qubit and the processes of heating and cooling in a two-qubit system. We further discuss how small initial correlations between a quantum system and a reservoir affect the increase in the entropy under the evolution of the quantum system.
We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity automorphic forms, including Eisenstein series, as their weights vary.   We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz's p-adic families of Eisenstein series for Hilbert modular forms.
PSR J1713+0747 is one of the most precisely timed pulsars in the international pulsar timing array experiment. This pulsar showed an abrupt profile shape change between April 16, 2021 (MJD 59320) and April 17, 2021 (MJD 59321). In this paper, we report the results from multi-frequency observations of this pulsar carried out with the upgraded Giant Metrewave Radio Telescope (uGMRT) before and after the event. We demonstrate the profile change seen in Band 5 (1260 MHz - 1460 MHz) and Band 3 (300 MHz - 500 MHz). The timing analysis of this pulsar shows a disturbance accompanying this profile change followed by a recovery with a timescale of $\sim 159$ days. Our data suggest that a model with chromatic index as a free parameter is preferred over models with combinations of achromaticity with DM bump or scattering bump. We determine the frequency dependence to be $\sim\nu^{+1.34}$.
In the present work we have modeled the supernova remnant (SNR) G296.5+10, by means of 3D magnetohydrodynamics (MHD) simulations. This remnant belongs to the bilateral SNR group and has an additional striking feature: the rotation measure (RM) in its eastern and western parts are very different. In order to explain both the morphology observed in radio-continuum and the RM, we consider that the remnant expands into a medium shaped by the superposition of the magnetic field of the progenitor star with a constant Galactic magnetic field. We have also carried out a polarization study from our MHD results, obtaining synthetic maps of the linearly polarized intensity and the Stokes parameters. This study reveals that both the radio morphology and the reported RM for G$296.5+10$ can be explained if the quasi-parallel acceleration mechanism is taking place in the shock front of this remnant.
We discuss the {\it SU}(2) chiral sigma model in the context of nuclear matter using a mean field approach at high density. In this model we include a dynamically generated isoscalar vector field and higher-order terms in the scalar field. With the inclusion of these, we reproduce the empirical values of the nuclear matter saturation density, binding energy, and nuclear incompressibility. The value of the incompressibility is chosen according to recently obtained heavy-ion collision data. We then apply the same dynamical model to neutron-rich matter in beta equilibrium, related to neutron star structure. The maximum mass and corresponding radius of stable non-rotating neutron stars are found to be in the observational limit.
A phenomenological treatment of domain walls based on the Ginzburg-Landau-Devonshire theory is developed for uniaxial, trigonal ferroelectrics lithium niobate and lithium tantalate. The contributions to the domain wall energy from polarization and strain as a function of orientation are considered. Analytical expressions are developed which are analyzed numerically to determine the minimum polarization, strain, and energy configurations of domain walls. It is found that hexagonal y-walls are preferred over x-walls in both materials. This agrees well with experimental observation of domain geometries in stoichiometric composition crystals.
We have made observations of 98 low-Galactic-latitude pulsars to measure pulse broadening caused by multipath propagation through the interstellar medium. Data were collected with the 305-m Arecibo telescope at four radio frequencies between 430 and 2380 MHz. We used a CLEAN-based algorithm to deconvolve interstellar pulse broadening from the measured pulse shapes. We employed two distinct pulse broadening functions (PBFs): PBF$_1$ is appropriate for a thin screen of scattering material between the Earth and a pulsar, while PBF$_2$ is appropriate for scattering material uniformly distributed along the line of sight from the Earth to a pulsar. We found that some observations were better fit by PBF$_1$ and some by PBF$_2$. Pulse broadening times ($\tau_d$) are derived from fits of PBFs to the data, and are compared with the predictions of a smoothed model of the Galactic electron distribution. Several lines of sight show excess broadening, which we model as clumps of high density scattering material. A global analysis of all available data finds that the pulse broadening scales with frequency, $\nu$, as $\taud \propto\nu^{-\alpha}$ where $\alpha\sim 3.9\pm 0.2$. This is somewhat shallower than the value $\alpha=4.4$ expected from a Kolmogorov medium, but could arise if the spectrum of turbulence has an inner cutoff at $\sim $300--800 km. A few objects follow particularly shallow scaling laws (the mean scaling index $\meanalpha \sim 3.1 \pm 0.1$ and $ \sim 3.8 \pm 0.2$ respectively for the case of PBF$_1$ and PBF$_2$), which may arise from large scale refraction or from the truncation of scattering screens transverse to the Earth--pulsar line of sight.
NGC 2915 is a blue compact dwarf galaxy embedded in an extended, low surface brightness HI disk exhibiting a two-armed spiral structure and a central bar-like component. Commonly accepted mechanisms are unable to explain the existence of these patterns and Bureau et al. proposed disk dark matter (scaling with the HI distribution) or a rotating triaxial dark halo as alternative solutions. In an attempt to explore these mechanisms, hydrodynamical simulations were run for each case and compared to observations using customized column density and kinematic constraints. The spiral structure can be accounted for both by an unseen bar or triaxial halo, the former fitting the observations slightly better. However, the large bar mass or halo pattern frequency required make it unlikely that the spiral wave is driven by an external perturber. In particular, the spin parameter is much higher than predicted by current cold dark matter (CDM) structure formation scenarios. The massive disk models show that when the observed gas surface density is scaled up by a factor about 10, the disk develops a spiral structure resembling closely the observed one, in perturbed density as well as perturbed velocity. This is consistent with more limited studies in other galaxies and suggests that the disk of NGC 2915 contains much more mass than is visible, tightly linked to the neutral hydrogen. A classic (quasi-)spherical halo is nevertheless still required, as increasing the disk mass further to fit the circular velocity curve would make the disk violently unstable. Scaling the observed surface density profile by an order of magnitude brings the disk and halo masses to comparable values within the disk radius.
There have been significant advances in neural networks for both 3D object detection using LiDAR and 2D object detection using video. However, it has been surprisingly difficult to train networks to effectively use both modalities in a way that demonstrates gain over single-modality networks. In this paper, we propose a novel Camera-LiDAR Object Candidates (CLOCs) fusion network. CLOCs fusion provides a low-complexity multi-modal fusion framework that significantly improves the performance of single-modality detectors. CLOCs operates on the combined output candidates before Non-Maximum Suppression (NMS) of any 2D and any 3D detector, and is trained to leverage their geometric and semantic consistencies to produce more accurate final 3D and 2D detection results. Our experimental evaluation on the challenging KITTI object detection benchmark, including 3D and bird's eye view metrics, shows significant improvements, especially at long distance, over the state-of-the-art fusion based methods. At time of submission, CLOCs ranks the highest among all the fusion-based methods in the official KITTI leaderboard. We will release our code upon acceptance.
A group of infinite products over low-order rational polynomials evaluated at the sequence of prime numbers is loosely called the Hardy-Littlewood constants. In this manuscript we look at them as factors embedded in a super-product over primes, semiprimes, 3-almost primes etc. Numerical tables are derived by transformation into series over k-almost prime zeta functions. Alternative product representations in a basis of k-almost prime products associated with Euler's formula for the Riemann zeta function are also pointed out.
In this paper, we gave solutions of the Diophantine equations 16^{x}+p^{y}=z^{2}, 64^{x}+p^{y}=z^{2} where p is an odd prime, n is a positive integer and x,y,z are non-negative integers. Finally we gave a generalization of the Diophantine equation (4^{n})^{x}+p^{y}=z^{2}.
A theory for the reliable prediction of the EPR g-tensor for paramagnetic defects in solids is presented. It is based on density functional theory and on the gauge including projector augmented wave (GIPAW) approach to the calculation of all-electron magnetic response. The method is validated by comparison with existing quantum chemical and experimental data for a selection of diatomic radicals. We thenperform the first prediction of EPR ${\rm g} $-tensors in the solid state and find the results to be in excellent agreement with experiment for the $E'_1$ and substitutional P defect centers in quartz.
The entropic pressure in the vicinity of a cubic lattice knot is examined as a model of the entropic pressure near a knotted ring polymer in a good solvent. A model for the scaling of the pressure is developed and this is tested numerically by sampling lattice knots using a Monte Carlo algorithm. Good agreement is found between scaling predictions and numerical experiments.
The aim of this work is to investigate and characterise particle behaviour in a 3D magnetohydrodynamic (MHD) model of a reconnecting magnetic separator. We use a relativistic guiding-centre test-particle code to investigate electron and proton acceleration in snapshots from 3D MHD separator reconnection experiments, and compare the results with findings from an analytical separator reconnection model studied in a previous investigation. The behaviour and acceleration of large distributions of particles are examined in detail for both analytical and numerical separator reconnection models. Accelerated particle orbit trajectories are shown to follow the separator before leaving the system along the separatrix surface of one of the nulls (determined by particle species) in the system of both models. A sufficiently localised electric field about the separator causes the orbits to appear to follow the spine bounding the separatrix surface field lines instead. We analyse and discuss the locations and spread of accelerated particle orbit final positions, which are seen to change over time in the numerical separator reconnection model. We deduce a simple relationship between the final energy range of particle orbits and the model dimensions, and discuss its implications for observed magnetic separators in the solar corona.