ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that the compatibility of the relative canonical sheaf with base change fails generally in families of normal varieties. Furthermore, it always fails if the general fiber of a family of pure dimension n is Cohen-Macaulay and the special fiber contains a strictly S_{n-1} point. In particular, in moduli spaces with functorial relative canonical sheaves Cohen-Macaulay schemes can not degenerate to S_{n-1} schemes. Another, less immediate consequence is that the canonical sheaf of an S_{n-1}, G_2 scheme of pure dimension n is not S_3.
We investigate the magnetic interface states of graphene quantum dots that contain p-n junctions. Within a tight-binding approach, we consider rectangular quantum dots in the presence of a perpendicular magnetic field containing p-n, as well as p-n-p and n-p-n junctions. The results show the interplay between the edge states associated with the zigzag terminations of the sample and the snake states that arise at the p-n junction, due to the overlap between electron and hole states at the potential interface. Remarkable localized states are found at the crossing of the p-n junction with the zigzag edge having a dumb-bell shaped electron distribution. The results are presented as function of the junction parameters and the applied magnetic flux.
In this paper, a novel model of 3D elastic mesh is presented for image segmentation. The model is inspired by stress and strain in physical elastic objects, while the repulsive force and elastic force in the model are defined slightly different from the physical force to suit the segmentation problem well. The self-balancing mechanism in the model guarantees the stability of the method in segmentation. The shape of the elastic mesh at balance state is used for region segmentation, in which the sign distribution of the points'z coordinate values is taken as the basis for segmentation. The effectiveness of the proposed method is proved by analysis and experimental results for both test images and real world images.
We describe periods of irreducible holomorphic manifolds of $K3^{[n]}$-type with a non-symplectic automorphism of prime order $p\geq 3$. These turn out to lie on complex ball quotients and we are able to give a precise characterization of when the period map is bijective, by introducing the notion of $K(T)$-generality.
The second neighbor correlation functions of the spin-${{1/2}}$ $XXZ$ chain in the ground state are expressed in the form of three dimensional integrals. We show that these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions for ${\Delta >1}$.
The theory of {\Gamma}-species is developed to allow species-theoretic study of quotient structures in a categorically rigorous fashion. This new approach is then applied to two graph-enumeration problems which were previously unsolved in the unlabeled case-bipartite blocks and general k-trees.
We study the massless flow from the critical point (dilute loops) to the low-temperature phase (dense loops) of the O(n) loop gas model when the model is coupled to 2D gravity. The flow is generated by the gravitationally dressed thermal operator \Phi_{1,3} coupled to the renormalized loop tension \lambda ~ T-T_c. We find that the susceptibility as a function of the thermal coupling \lambda and the cosmological constant \mu satisfies a simple transcendental equation.
Machine learning with artificial neural networks is revolutionizing science. The most advanced challenges require discovering answers autonomously. This is the domain of reinforcement learning, where control strategies are improved according to a reward function. The power of neural-network-based reinforcement learning has been highlighted by spectacular recent successes, such as playing Go, but its benefits for physics are yet to be demonstrated. Here, we show how a network-based "agent" can discover complete quantum-error-correction strategies, protecting a collection of qubits against noise. These strategies require feedback adapted to measurement outcomes. Finding them from scratch, without human guidance, tailored to different hardware resources, is a formidable challenge due to the combinatorially large search space. To solve this, we develop two ideas: two-stage learning with teacher/student networks and a reward quantifying the capability to recover the quantum information stored in a multi-qubit system. Beyond its immediate impact on quantum computation, our work more generally demonstrates the promise of neural-network-based reinforcement learning in physics.
Einstein-Rosen waves with two polarizations are cylindrically symmetric solutions to vacuum Einstein equations. Einstein equations in this case reduce to an integrable system. In 1971, Geroch has shown that this system admits an infinite-dimensional group of symmetry transformations known as the Geroch group. The phase space of this system can be parametrized by a matrix-valued function of spectral parameter, called monodromy matrix. The latter admits the Riemann-Hilbert factorization into a pair of transition matrices, i.e. matrix-valued functions of spectral parameter such that one of them is holomorphic in the upper half-plane, and the other is holomorphic in the lower half-plane. The classical Geroch group preserves the determinants of transition and monodromy matrices by construction. The algebraic quantization of the quadratic Poisson algebra generated by transition matrices of Einstein-Rosen system was proposed by Korotkin and Samtleben in 1997. Paternain, Perasa and Reisenberger have recently suggested a quantization of the Geroch group, which can be considered as a symmetry of the quantum algebra of observables. They have shown that commutation relations involving quantum monodromy matrices are preserved by the action of the quantum Geroch group. In present paper we introduce the notion of the determinant of the quantum monodromy matrix. We derive a factorization formula expressing the quantum determinant of the monodromy matrix as a product of the quantum determinants of the transition matrices. The action of the quantum Geroch group is extended from the subalgebra generated by the monodromy matrix onto the full algebra of observables. This extension is used to prove that the quantum determinant of the quantum monodromy matrix is invariant under the action of quantum Geroch group.
In this paper, we determine orbital and linear stability of periodic waves with the mean zero property related to the Intermediate Long Wave equation. Our arguments follow the recent developments in \cite{andrade-pastor}, \cite{natali} and \cite{DK} to deduce the orbital/linear stability of periodic traveling waves.
We present the results of a 8.4 GHz Very Large Array radio survey of early-type galaxies extracted from the ACS Virgo Cluster Survey. The aim of this survey is to investigate the origin of radio emission in early-type galaxies and its link with the host properties in an unexplored territory toward the lowest levels of both radio and optical luminosities. Radio images, available for all 63 galaxies with BT < 14.4, show the presence of a compact radio source in 12 objects, with fluxes spanning from 0.13 to 2700 mJy. The remaining 51 galaxies, undetected at a flux limit of ~0.1 mJy, have radio luminosities L < 4 10E18 W/Hz . The fraction of radio-detected galaxies are a strong function of stellar mass, in agreement with previous results: none of the 30 galaxies with stellar mass M(star) < 1.7 10E10 M(sun) is detected, while 8 of the 11 most massive galaxies have radio cores. There appears to be no simple relation between the presence of a stellar nucleus and radio emission. A multiwavelength analysis of the active galactic nucleus (AGN) emission, combining radio and X-ray data, confirms the link between optical surface brightness profile and radio loudness in the sense that the bright core galaxies are associated with radio-loud AGNs, while non-core galaxies host radio-quiet AGNs. Not all radio-detected galaxies have a X-ray nuclear counter part (and vice-versa). A complete census of AGNs (and supermassive black holes, SMBHs) thus requires observations, at least, in both bands. Nonetheless, there are massive galaxies in the sample, expected to host a large SMBH (M(BH) ~ 10E8 M(sun)), whose nuclear emission eludes detection despite their proximity and the depth and the spatial resolution of the available observations. Most likely this is due to an extremely low level of accretion onto the central SMBH.
We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, their deformations, and we draw some conclusions.   For such a group we can define its Newton polygon (abbreviated NP). This is invariant under isogeny. For an abelian variety (in characteristic p) the Newton polygon of its p-divisible group is ``symmetric''.   In 1963 Manin conjectured that conversely any symmetric Newton polygon is ``algebroid''; i.e., it is the Newton polygon of an abelian variety. This conjecture was shown to be true and was proved with the help of the ``Honda-Serre-Tate theory''. We give another proof.   Grothendieck showed that Newton polygons ``go up'' under specialization: no point of the Newton polygon of a closed fiber in a family is below the Newton polygon of the generic fiber. In 1970 Grothendieck conjectured the converse: any pair of comparable Newton polygons appear for the generic and special fiber of a family. This was extended by Koblitz in 1975 to a conjecture about a sequence of comparable Newton polygons. We prove these conjectures.
The past years have seen a revived interest in the diagrammatic Monte Carlo (DiagMC) methods for interacting fermions on a lattice. A promising recent development allows one to now circumvent the analytical continuation of dynamic observables in DiagMC calculations within the Matsubara formalism. This is made possible by symbolic algebra algorithms, which can be used to analytically solve the internal Matsubara frequency summations of Feynman diagrams. In this paper, we take a different approach and show that it yields improved results. We present a closed-form analytical solution of imaginary-time integrals that appear in the time-domain formulation of Feynman diagrams. We implement and test a DiagMC algorithm based on this analytical solution and show that it has numerous significant advantages. Most importantly, the algorithm is general enough for any kind of single-time correlation function series, involving any single-particle vertex insertions. Therefore, it readily allows for the use of action-shifted schemes, aimed at improving the convergence properties of the series. By performing a frequency-resolved action-shift tuning, we are able to further improve the method and converge the self-energy in a non-trivial regime, with only 3-4 perturbation orders. Finally, we identify time integrals of the same general form in many commonly used Monte Carlo algorithms and therefore expect a broader usage of our analytical solution.
The pinning phenomena of the domain wall in the presence of exchange bias is studied analytically. The analytic solution of the domain wall spin configuration is presented. Unlike the traditional solution which is symmetric, our new solution could exhibit the asymmetry of the domain wall spin profile. Using the solution, the domain wall position, its width, its stability, and the depinning field are discussed analytically.
In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a H\"older continuous function with parameter greater that 1/2 via the Young integration setting. Then some estimates of the solution are obtained, which allow to show that the solution of a delay differential equation driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2 has a smooth density. To this purpose, we use Malliavin calculus based on the Frechet differentiability in the directions of the reproducing kernel Hilbert space associated with fBm.
We present hydrodynamical simulations of major mergers of galaxies and study the effects of winds produced by active galactic nuclei (AGN) on interstellar gas in the AGN's host galaxy. We consider winds with initial velocities ~ 10,000 km/s and an initial momentum (energy) flux of ~ tau_w L/c (~ 0.01 tau_w L), with tau_w ~ 1-10. The AGN wind sweeps up and shock heats the surrounding interstellar gas, leading to a galaxy-scale outflow with velocities ~ 1000 km/s, peak mass outflow rates comparable to the star formation rate, and a total ejected gas mass ~ 3 x 10^9 M_sun. Large momentum fluxes, tau_w > 3, are required for the AGN-driven galactic outflow to suppress star formation and accretion in the black hole's host galaxy. Less powerful AGN winds (tau_w < 3) still produce a modest galaxy-scale outflow, but the outflow has little global effect on the ambient interstellar gas. We argue that this mechanism of AGN feedback can plausibly produce the high velocity outflows observed in post-starburst galaxies and the massive molecular and atomic outflows observed in local ultra-luminous infrared galaxies. Moreover, the outflows from local ultra-luminous infrared galaxies are inferred to have tau_w ~ 10, comparable to what we find is required for AGN winds to regulate the growth of black holes and set the M_BH-sigma relation. We conclude by discussing theoretical mechanisms that can lead to AGN wind mass-loading and momentum/energy fluxes large enough to have a significant impact on galaxy formation.
Warm cores (or hot corinos) around low-mass protostellar objects show a rich chemistry with strong spatial variations. This chemistry is generally attributed to the sublimation of icy mantles on dust grains initiated by the warming effect of the stellar radiation. We have used a model of the chemistry in warm cores in which the sublimation process is based on extensive laboratory data; these data indicate that sublimation from mixed ices occurs in several well-defined temperature bands. We have determined the position of these bands for the slow warming by a solar-mass star. The resulting chemistry is dominated by the sublimation process and by subsequent gas-phase reactions; strong spatial and temporal variations in certain molecular species are found to occur, and our results are, in general, consistent with observational results for the well-studied source IRAS 16293-2422. The model used is similar to one that describes the chemistry of hot cores. We infer that the chemistry of both hot cores and warm cores may be described by the same model (suitably adjusted for different physical parameters).
An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts.
An object detector performs suboptimally when applied to image data taken from a viewpoint different from the one with which it was trained. In this paper, we present a viewpoint adaptation algorithm that allows a trained single-view object detector to be adapted to a new, distinct viewpoint. We first illustrate how a feature space transformation can be inferred from a known homography between the source and target viewpoints. Second, we show that a variety of trained classifiers can be modified to behave as if that transformation were applied to each testing instance. The proposed algorithm is evaluated on a person detection task using images from the PETS 2007 and CAVIAR datasets, as well as from a new synthetic multi-view person detection dataset. It yields substantial performance improvements when adapting single-view person detectors to new viewpoints, and simultaneously reduces computational complexity. This work has the potential to improve detection performance for cameras viewing objects from arbitrary viewpoints, while simplifying data collection and feature extraction.
Sub-structures in the hot gas of galaxy clusters are related to their formation history and to the astrophysical processes at play in the intracluster medium (ICM). The thermal Sunyaev-Zel'dovich (tSZ) effect is directly sensitive to the line-of-sight integrated ICM pressure, and is thus particularly adapted to study ICM sub-structures. We apply structure-enhancement filtering algorithms to high resolution tSZ observations of distant clusters, in order to search for pressure discontinuities, compressions, as well as secondary peaks in the ICM. The same filters are applied to synthetic tSZ images extracted from RHAPSODY-G hydrodynamic simulations, in order to better interpret the extracted features. We also study the noise propagation trough the filters and quantify the impact of systematic effects, point source residuals being identified as the dominant potential contaminant. In 3 of our 6 NIKA clusters we identify features at high S/N that show clear evidence for merger events. In MACSJ0717 (z=0.55), three strong pressure gradients are observed on the E, SE and W sectors, and two main peaks in the pressure distribution are identified. We observe a lack of tSZ compact structure in the cool-core cluster PSZ1G045.85 (z=0.61), and a tSZ gradient ridge dominates in the SE. In the highest z cluster, CLJ1227 (z=0.89), we detect a ~45" (360 kpc) long ridge pressure gradient associated with a secondary pressure peak in the W region. Our results show that current tSZ facilities have now reached the angular resolution and sensitivity to allow an exploration of the details of pressure sub-structures in clusters, even at high z. This opens the possibility to quantify the impact of the dynamical state on the relation between the tSZ signal and the mass of clusters, which is important when using tSZ clusters to test cosmological models. This work also marks the first NIKA cluster sample data release.
We present an improved dynamical model of the X-ray binary and microquasar XTE J1550-564 based on new moderate-resolution optical spectroscopy and near-infrared photometry. By combining our new radial velocity measurements with previous measurements obtained 2001 May at the 8.2m VLT and with light curves, we find an orbital period of P=1.5420333 +/- 0.0000024 days and a radial velocity semiamplitude of K_2=363.14 +/- 5.97$ km/sec, which together imply an optical mass function of f(M)=7.65 +/- 0.38 solar masses. We find that the projected rotational velocity of the secondary star is 55 +/- 5 km/sec, which implies a very extreme mass ratio of Q=M/M_2=30. Using a model of a Roche lobe-filling star and an azimuthally symmetric accretion disk, we fit simultaneously optical light curves from 2001, near-infrared light curves from 2008 and all of the radial velocity measurements to derive system parameters. We find an inclination of 74.7 +/- 3.8 deg and component masses of M_2=0.30 +/- 0.07 solar masses and M=9.10 +/- 0.61 solar masses for the secondary star and black hole, respectively. The radius of the secondary star for the adopted model is 1.75 +/- 0.12 solar radii. Using this radius, the average K_S magnitude, and an extinction of A_K=0.507 +/- 0.050 mag, we find a distance of 4.38^{+0.58}_{-0.41} kpc, which is in good agreement with a recent distance estimate based on HI absorption lines (abstract shortened).
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These probabilities do not display any multifractal properties contrary to previous numerical claims. The explanation for this apparent multifractal behavior is given, and our conclusion are supported by numerical calculations. These exact results are exploited to compute the large time asymptotics of the survival probability (or the density) which is found to decay as $\exp [-Ct^{1/3}\log^{2/3}(t)]$. An exact lower bound for the density is found to decay in a similar way.
We study a non-dissipative hydrodynamical mechanism that can stabilize the spin of the accretor in an ultra-compact double white dwarf binary. This novel synchronization mechanism relies on a nonlinear wave interaction spinning down the background star. The essential physics of the synchronization mechanism is summarized as follows. As the compact binary coalesces due to gravitational wave emission, the largest star eventually fills its Roche lobe and accretion starts. The accretor then spins up due to infalling material and eventually reaches a spin frequency where a normal mode of the star is resonantly driven by the gravitational tidal field of the companion. If the resonating mode satisfies a set of specific criteria, which we elucidate in this paper, it exchanges angular momentum with the background star at a rate such that the spin of the accretor locks at this resonant frequency, even though accretion is ongoing. Some of the accreted angular momentum that would otherwise spin up the accretor is fed back into the orbit through this resonant tidal interaction.   Two modes capable of stabilizing the accretor's spin are the l=4,m=2 and l=5,m=3 CFS unstable hybrid r-modes, which stabilize the spin of the accretor at frequency 2.6 and 1.5 times the binary's orbital frequency respectively. Since the stabilization mechanism relies on continuously driving a mode at resonance, its lifetime is limited since eventually the mode amplitude saturates due to non-linear mode-mode coupling. Rough estimates of the lifetime of the effect lie from a few orbits to millions of years.
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on $\{1,2,\ldots,n\}$. Classical formulas for counting various trees such as rooted trees, bipartite trees, tripartite trees, plane trees, $k$-ary plane trees, $k$-edge colored trees follow immediately from our recursive relations.
We study the main properties of the one-loop vacuum polarization function for massless spinor QED4 in a slab, namely, with fields defined on M in R^(3+1), such that M = {(x0, ..., x3)|0 <= x3 <= epsilon}, and bag-like boundary conditions on the boundary. We evaluate the induced charge density and current due to an external constant electric field normal to the boundary; we also study the effective action for a purely transverse field, identifying its epsilon-dependent contribution.
We observe dressed states and quantum interference effects in a strongly driven three-level quantum dot ladder system. The effect of a strong coupling field on one dipole transition is measured by a weak probe field on the second dipole transition using differential reflection. When the coupling energy is much larger than both the homoge-neous and inhomogeneous linewidths an Autler-Townes splitting is observed. Striking differences are observed when the transitions resonant with the strong and weak fields are swapped, particularly when the coupling energy is nearly equal to the measured linewidth. This result is attributed to quantum interference: a modest destructive or constructive interference is observed depending on the pump / probe geometry. The data demonstrate that coher-ence of both the bi-exciton and the exciton is maintained in this solid-state system, even under intense illumina-tion, which is crucial for prospects in quantum information processing and non-linear optical devices.