ShantanuT01/DACTYL-Pretraining huggingface dataset:
We start with an i.i.d. sequence and consider the product of two polynomial-forms moving averages based on that sequence. The coefficients of the polynomial forms are asymptotically slowly decaying homogeneous functions so that these processes have long memory. The product of these two polynomial forms is a stationary nonlinear process. Our goal is to obtain limit theorems for the normalized sums of this product process in three cases: exclusion of the diagonal terms of the polynomial form, inclusion, or the mixed case (one polynomial form excludes the diagonals while the other one includes them). In any one of these cases, if the product has long memory, then the limits are given by Wiener chaos. But the limits in each of the cases are quite different. If the diagonals are excluded, then the limit is expressed as in the product formula of two Wiener-It\^{o} integrals. When the diagonals are included, the limit stochastic integrals are typically due to a single factor of the product, namely the one with the strongest memory. In the mixed case, the limit stochastic integral is due to the polynomial form without the diagonals irrespective of the strength of the memory.
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the summation method within the normally ordered product of operators we propose and show that the completeness relation can also be represented or partitioned in terms of some mixed states, such as binomial states and negative binomial states. Thus the view on the structure of Fock space is widen and the connotation of Fock space is enriched. See the matter in this sight, experimentalists may have interests to prepare the binomial- and negative binomial states.
Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A) of an abelian variety A defined over Q_p. These conditions are stated on the filtered (\phi,G)-module attached to V.
The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix $D(G)$. A graph is called distance integral if all of its distance eigenvalues are integers. Let $n \geq 3$ be an integer. A crown graph $Cr(n)$ is a graph obtained from the complete bipartite graph $K_{n,n}$ by removing a perfect matching. Let $L(Cr(n))$ denote the line graph of the crown graph $Cr(n)$. In this paper, by using the orbit partition method in algebraic graph theory, we determine the set of all distance eigenvalues of $L(Cr(n))$ and show that this graph is distance integral.
The mechanisms of magnesium hydride formation and thermal decomposition are directly examined using in-situ imaging.
Given a zero-dimensional scheme Z, the higher-rank interpolation problem asks for the classification of slopes of vector bundles cohomologically orthogonal to the ideal sheaf of Z. In this paper, we solve this problem for all zero-dimensional monomial schemes in the projective plane. As a corollary, we obtain detailed information on the stable base loci of divisors on the Hilbert scheme of points on the plane. We prove the correspondence between walls in the Bridgeland stability manifold and walls in the Mori chamber decomposition of the effective cone conjectured by Arcara-Bertram-Coskun-Huizenga for monomial schemes. We determine the Harder-Narasimhan filtration of ideal sheaves of monomial schemes for suitable Bridgeland stability conditions and, as a consequence, obtain a new resolution better suited for cohomology computations than other standard resolutions such as the minimal free resolution.
This work is a modern revisitation of a classical paper by Alessandro Terracini, going back to 1915, which suggests an elementary but powerful method for studing Grassmann defective varieties. In particular, the case of Veronese surfaces is completely understood, giving an positive answer to the so-called Waring problem for pairs of homogeneous polynomials in three variables.
This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [10] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the importance sampling method, we rely on Robbins-Monro type stochastic algorithms. On the one hand, we extend our previous work [2] to the Multilevel Monte Carlo setting. On the other hand, we improve [2] by providing a new adaptive algorithm avoiding the discretization of any additional process. Furthermore, from a technical point of view, the use of the same stochastic algorithms as in [2] appears to be problematic. To overcome this issue, we employ an alternative version of stochastic algorithms with projection (see e.g. Laruelle, Lehalle and Pag\`es [20]). In this setting, we show innovative limit theorems for a doubly indexed stochastic algorithm which appear to be crucial to study the asymptotic behavior of the new adaptive Multilevel Monte Carlo estimator. Finally, we illustrate the efficiency of our method through applications from quantitative finance.
We study the conditions under which the nucleons inside a deformed nucleus can undergo chaotic motion. To do this we perform self-consistent calculations in semiclassical approximation utilizing a multipole-multipole interaction of the Bohr-Mottelson type for quadrupole and octupole deformations. For the case of harmonic and non-harmonic static potentials, we find that both multipole deformations lead to regular motion of the collective coordinate, the multipole moment of deformation. However, despite this regular collective motion, we observe chaotic single particle dynamics.
The optical absorption spectra in the region of the \fd transition energies of epitaxial layers of of EuTe and \PbEuTe, grown by molecular beam epitaxy, were studied using circularly polarized light, in the Faraday configuration. Under \sigmam polarization a sharp symmetric absorption line (full width at half-maximum 0.041 eV) emerges at the low energy side of the band-edge absorption, for magnetic fields intensities greater than 6 T. The absorption line shows a huge red shift (35 meV/T) with increasing magnetic fields. The peak position of the absorption line as a function of magnetic field is dominated by the {\em d-f} exchange interaction of the excited electron and the \Euion spins in the lattice. The {\em d-f} exchange interaction energy was estimated to be $J_{df}S=0.15\pm 0.01$ eV. In \PbEuTe the same absorption line is detected, but it is broader, due to alloy disorder, indicating that the excitation is localized within a finite radius. From a comparison of the absorption spectra in EuTe and \PbEuTe the characteristic radius of the excitation is estimated to be $\sim 10$\AA.
Galactic and extragalactic relativistic jets have rich environments that are full of moving objects, such as stars and dense clumps. These objects can enter into the jets and generate shocks and non-thermal emission. We characterize the emitting properties of the downstream region of a standing shock formed due to the interaction of a relativistic jet with an obstacle. We focus on the case of red giants interacting with an extragalactic jet. We perform relativistic axisymmetric hydrodynamical simulations of a relativistic jet meeting an obstacle of very large inertia. The results are interpreted in the framework of a red giant whose dense and slow wind interacts with the jet of an active galactic nucleus. Assuming that particles are accelerated in the standing shock generated in the jet as it impacts the red giant wind, we compute the non-thermal particle distribution, the Doppler boosting enhancement, and the non-thermal luminosity in gamma rays. The available non-thermal energy from jet-obstacle interactions is potentially enhanced by a factor of $\sim 100$ when accounting for the whole surface of the shock induced by the obstacle, instead of just the obstacle section. The observer gamma-ray luminosity, including the flow velocity and Doppler boosting effects, can be ~300(g/10)^2 times higher than when the emitting flow is assumed at rest and only the obstacle section is considered, where g is the jet Lorentz factor. For a whole population of red giants inside the jet of an AGN, the predicted persistent gamma-ray luminosities may be potentially detectable for a jet pointing to the observer. Obstacles interacting with relativistic outflows, for instance clouds and populations of stars for extragalactic jets, or stellar wind inhomogeneities in microquasar jets and in winds of pulsars in binaries, should be taken into account when investigating the non-thermal emission from these sources.
Photons of a laser beam driving the upper motional sideband of an optomechanical cavity can decay into photon-phonon pairs by means of an optomechanical parametric process. The phononic state can subsequently be mapped to a photonic state by exciting the lower sideband, hence creating photon-photon pairs out of an optomechanical system. We here demonstrate that these pairs can violate a Bell inequality when they are measured with photon counting techniques preceded by small displacement operations in the phase space. Our results show how to detect non-local light-mechanical correlations and open the way for device-independent quantum optomechanics where non-classical light-mechanical correlations can be certified without assumptions on the state structure or on the measurement devices.
We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing `big crunch', can accommodate singularities of only one kind, namely, those having a non-integrable Hubble parameter, $H$. We analyze several examples from recent literature which illustrate this result and show that such behaviour may arise in a number of different ways. We also discuss the existence of new types of lapse singularities in inhomogeneous models, impossible to meet in the isotropic ones.
In the spirit of Berestycki and Lions, we prove the existence of saddle type nodal solutions for the Choquard equation \[   -\Delta u + u= \big(I_\alpha \ast F(u)\big)F'(u)\qquad \text{ in }\;\mathbb{R}^N \] where $N\geq 2$ and $I_\alpha$ is the Riesz potential of order $\alpha\in (0,N)$. Without any compact setting, we construct saddle solutions in a unified way for the Choquard equation whose nodal domains are of cone shapes demonstrating Coxeter's symmetric configurations in $\mathbb R^N$. Moreover, if $F'$ is odd and has constant sign on $(0,+\infty)$, then the saddle solution maintains signed on the fundamental domain of the corresponding Coxeter group and receives opposite signs on any two adjacent domains. These results further complete the variational framework in constructing sign-changing solutions for the Choquard equation but still require a quadratic or super-quadratic growth on $F$ near the origin.
Recent studies have argued that galaxy mergers are not important drivers for the evolution of S0's, on the basis that mergers cannot preserve the coupling between the bulge and disk scale-lengths observed in these galaxies and the lack of correlation of their ratio with the S0 Hubble type. We investigate whether the remnants resulting from collision-less N-body simulations of intermediate and minor mergers onto S0 galaxies evolve fulfilling global structural relations observed between the bulges and disks of these galaxies. Different initial bulge-to-disk ratios of the primary S0 have been considered, as well as different satellite densities, mass ratios, and orbits of the encounter. We have analysed the final morphology of the remnants in images simulating the typical observing conditions of S0 surveys. We derive bulge+disk decompositions of the final remnants to compare their global bulge-to-disk structure with observations. We show that all remnants present undisturbed S0 morphologies according to the prescriptions of specialized surveys. The dry intermediate and minor mergers induce noticeable bulge growth (S0c --> S0b and S0b --> S0a), but affect negligibly to the bulge and disk scale-lengths. Therefore, if a coupling between these two components exists prior to the merger, the encounter does not break this coupling. This fact provides a simple explanation for the lack of correlation between the ratio of bulge and disk scale-lengths and the S0 Hubble type reported by observations. These models prove that dry intermediate and minor mergers can induce global structural evolution within the sequence of S0 Hubble types compatible with observations, meaning that these processes should not be discarded from the evolutionary scenarios of S0's just on the basis of the strong coupling observed between the bulge and disk scale-lengths in these galaxies (abridged).
Multispectral imaging is an important technique for improving the readability of written or printed text where the letters have faded, either due to deliberate erasing or simply due to the ravages of time. Often the text can be read simply by looking at individual wavelengths, but in some cases the images need further enhancement to maximise the chances of reading the text. There are many possible enhancement techniques and this paper assesses and compares an extended set of dimensionality reduction methods for image processing. We assess 15 dimensionality reduction methods in two different manuscripts. This assessment was performed both subjectively by asking the opinions of scholars who were experts in the languages used in the manuscripts which of the techniques they preferred and also by using the Davies-Bouldin and Dunn indexes for assessing the quality of the resulted image clusters. We found that the Canonical Variates Analysis (CVA) method which was using a Matlab implementation and we have used previously to enhance multispectral images, it was indeed superior to all the other tested methods. However it is very likely that other approaches will be more suitable in specific circumstance so we would still recommend that a range of these techniques are tried. In particular, CVA is a supervised clustering technique so it requires considerably more user time and effort than a non-supervised technique such as the much more commonly used Principle Component Analysis Approach (PCA). If the results from PCA are adequate to allow a text to be read then the added effort required for CVA may not be justified. For the purposes of comparing the computational times and the image results, a CVA method is also implemented in C programming language and using the GNU (GNUs Not Unix) Scientific Library (GSL) and the OpenCV (OPEN source Computer Vision) computer vision programming library.
We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the D-brane is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling of A- and B-model in loop amplitudes. Our calculations in the A-model involve an adapted version of existing localization techniques, and give predictions for the real enumerative geometry of higher genus curves in Calabi-Yau manifolds. In the B-model, we introduce an extension of the holomorphic anomaly equation to unoriented strings.
For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the L\'evy measure of the inverse local time is subexponential this distribution behaves asymtotically as a multiple of the L\'evy measure. Using spectral representations we find the exact value of the multiple. For this we also need a result on the asymptotic behavior of the convolution of a subexponential distribution and an arbitrary distribution on $\R_+.$ The exact knowledge of the asymptotic behavior of the distribution of the local time allows us to analyze the process derived via a penalization procedure with the local time. This result generalizes the penalizations obtained in Roynette, Vallois and Yor \cite{rvyV} for Bessel processes.
The stellar content of the debris field around M81 is investigated using deep images obtained with MegaCam on the Canada-France-Hawaii Telescope. Three new concentrations of bright main sequence stars and red supergiants are identified within ~ 20 kpc of M81. These systems have integrated brightnesses M_V ~ -11 and surface brightnesses ~ 27 - 28 mag per arcsec^2 in V. The main sequence turn-offs are consistent with an age of ~ 30 Myr, while the presence of a well-developed red supergiant plume indicates that their stellar content is not coeval, as they also formed stars ~ 100 Myr in the past. The photometric properties of the red supergiants indicate that the young stars in these systems have metallicities that are comparable to those of other objects in the debris field. The HI density near these groupings comfortably exceeds the threshold required to trigger star formation. Based on the close proximity of these objects to M81, coupled with their extended sizes and low inferred masses, it is argued that they will not be long-lived structures, but will probably dissipate within the next ~ 1 Gyr.
A linear stability analysis of the Navier-Stokes (NS) granular hydrodynamic equations is performed to determine the critical length scale for the onset of vortices and clusters instabilities in granular dense binary mixtures. In contrast to previous attempts, our results (which are based on the solution to the inelastic Enskog equation to NS order) are not restricted to nearly elastic systems since they take into account the complete nonlinear dependence of the NS transport coefficients on the coefficients of restitution $\alpha_{ij}$. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations in flows of strong dissipation ($\alpha_{ij}\geq 0.7$) and moderate solid volume fractions ($\phi\leq 0.2$). We find excellent agreement between MD and kinetic theory for the onset of velocity vortices, indicating the applicability of NS hydrodynamics to polydisperse flows even for strong inelasticity, finite density, and particle dissimilarity.
Let $k$ be a perfect field of characteristic $p$ and set $K=k((t))$. In this paper we study the ramification properties of elements of Aut$_k(K)$. By choosing a uniformizer for $K$ we may interpret our theorems in terms of power series over $k$. The most important tool that we use is the field of norms construction of Fontaine and Wintenberger.
A magnetohydrodynamic model is used to determine conditions under which the Lorentz force accelerates plasma to type 2 spicule speeds in the chromosphere. The model generalizes a previous model to include a more realistic pre-spicule state, and the vertical viscous force. Two cases of acceleration under upper chromospheric conditions are considered. The magnetic field strength for these cases is <= 12.5 and 25 G. Plasma is accelerated to terminal vertical speeds of 66 and 78 km/s in 100 s, compared with 124 and 397 km/s for the case of zero viscosity. The flows are localized within horizontal diameters ~ 80 and 50 km. The total thermal energy generated by viscous dissipation is ~ 10 times larger than that due to Joule dissipation, but the magnitude of the total cooling due to rarefaction is >~ this energy. Compressive heating dominates during the early phase of acceleration. The maximum energy injected into the corona by type 2 spicules, defined as the energy flux in the upper chromosphere, may largely balance total coronal energy losses in quiet regions, possibly also in coronal holes, but not in active regions. It is proposed that magnetic flux emergence in inter-granular regions drives type 2 spicules.
We consider a one-dimensional lattice system of unbounded, real-valued spins. We allow arbitrary strong, attractive, nearest-neighbor interaction. We show that the free energy of the canonical ensemble converges uniformly in $C^2$ to the free energy of the grand canonical ensembles. The error estimates are quantitative. A direct consequence is that the free energy of the canonical ensemble is uniformly strictly convex for large systems. Another consequence is a quantitative local Cram\'er theorem which yields the strict convexity of the coarse-grained Hamiltonian. With small adaptations, the argument could be generalized to systems with finite-range interactions on a graph, as long as the degree of the graph is uniformly bounded and the associated grand canonical ensemble has uniform decay of correlations.
Using soft x-ray spectromicroscopy, we investigate the magnetic domain structure in embedded nanomagnets defined in La$_{0.7}$Sr$_{0.3}$MnO$_3$ thin films and LaFeO$_3$/La$_{0.7}$Sr$_{0.3}$MnO$_3$ bilayers. We find that shape-controlled antiferromagnetic domain states give rise to a significant reduction of the switching field of the rectangular nanomagnets. This is discussed in the framework of competition between an intrinsic spin-flop coupling and shape anisotropy. The data demonstrates that shape effects in antiferromagnets may be used to control the magnetic properties in nanomagnets.
BPS CS 22940-0009 is a helium-rich B-star that shares characteristics with both helium-rich B subdwarfs and extreme helium stars. The optical spectrum of BPS CS 22940-0009 has been analysed from SALT observations. The atmospheric parameters were found to be $T_{\rm eff} = 34970 \pm 370$ K, $\log g/{\rm cm \, s^{-2}} = 4.79 \pm 0.17$, $n_{\rm H}/n_{\rm He} \simeq 0.007$, $n_{\rm C}/n_{\rm He} \simeq 0.007$, $n_{\rm N}/n_{\rm He} \simeq 0.002$, although further improvement to the helium line fits would be desirable. This places the star as a link between the He-sdB and EHe populations in $g$-$T$ space. The abundance profile shows enrichment of N from CNO-processing, and C from $3\alpha$ burning. Depletion of Al, Si, S and a low upper limit for Fe show the star to be intrinsically metal-poor. The results are consistent with BPS CS 22940-0009 having formed from the merger of two helium white dwarfs and currently evolving toward the helium main sequence.
Ground-state properties are examined for an extended two-channel Kondo model where the Hilbert space of the localized states is extended to include a singlet state in addition to the doublet states. By means of zero-th order variational wavefunctions with different symmetries, which are associated with the non-Fermi-liquid and the Fermi-liquid ground states, we demonstrate that the channel exchange coupling via the localized singlet state stabilizes the Fermi-liquid wavefunction. The ground-state phase diagrams, which are in qualitative agreement with the previous study performed by Koga and Shiba, are obtained. The comparison to the structure of the resultant wavefunctions suggests that a unique non-Fermi-liquid (Fermi-liquid) fixed point exists, irrespective of the localized ground state.
We prove that every random walk in a uniformly elliptic random environment satisfying the cone mixing condition and a non-effective polynomial ballisticity condition with high enough degree has an asymptotic direction.