ShantanuT01/DACTYL-Pretraining huggingface dataset:
An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and non-extreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regular variation property of the finite-dimensional distributions under assumptions on the marginal tails alone.
We study frustrated quantum spin systems consisting of dimers of spin-1/2 spins. We derive several models that have the exact ground state of the form of the direct product of dimer states. The ground states realized include the product state of dimer singlets, that of dimer triplets with zero magnetization, those of dimer-spin-nematic states, and those of a mixture of the dimer states. Pseudo spin-1/2 operators emerging in each dimer are also introduced.
We study generation of acoustic waves by a precessing spin of a nanoparticle deposited on the surface of a solid. Our approach elucidates macroscopic dynamics of the Einstein - de Haas effect. It is based upon solution of parameter-free equations of motion mandated by the conservation of the total angular momentum: spin + mechanical. We show that the amplitude of the acoustic waves generated by the spin precession may be sufficient for detection by a tunneling electron microscope.
In the present work, we quantize a closed Friedmann-Robertson-Walker model in the presence of a positive cosmological constant and radiation. It gives rise to a Wheeler-DeWitt equation for the scale factor which has the form of a Schr\"{o}dinger equation for a potential with a barrier. We solve it numerically and determine the tunneling probability for the birth of a asymptotically DeSitter, inflationary universe, initially, as a function of the mean energy of the initial wave-function. Then, we verify that the tunneling probability increases with the cosmological constant, for a fixed value of the mean energy of the initial wave-function. Our treatment of the problem is more general than previous ones, based on the WKB approximation. That is the case because we take into account the fact that the scale factor ($a$) cannot be smaller than zero. It means that, one has to introduce an infinity potential wall at $a = 0$, which forces any wave-packet to be zero there. That condition introduces new results, in comparison with previous works.
The application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two-dimensional Kagome staircase magnet, Co3V2O8, induces three quantum phase transitions at low temperatures, ultimately producing a novel high field polarized state, with two distinct sublattices. New time-of-flight neutron scattering techniques, accompanied by large angular access, high magnetic field infrastructure allow the mapping of a sequence of ferromagnetic and incommensurate phases and their accompanying spin excitations. At least one of the transitions to incommensurate phases at \mu 0Hc1~6.25 T and \mu 0Hc2~7 T is discontinuous, while the final quantum critical point at \mu 0Hc3~13 T is continuous.
We establish (Theorem 3.6) polynomial-growth estimates for the   Fourier coefficients of holomorphic logarithmic vector-valued modular forms.
Half-metallicity in materials has been a subject of extensive research due to its potential for applications in spintronics. Ferromagnetic manganites have been seen as a good candidate, and aside from a small minority-spin pocket observed in La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ $(x=0.38)$, transport measurements show that ferromagnetic manganites essentially behave like half metals. Here we develop robust tight-binding models to describe the electronic band structure of the majority as well as minority spin states of ferromagnetic, spin-canted antiferromagnetic, and fully antiferromagnetic bilayer manganites. Both the bilayer coupling between the MnO$_2$ planes and the mixing of the $|x^2 - y^2>$ and $|3z^2 - r^2>$ Mn 3d orbitals play an important role in the subtle behavior of the bilayer splitting. Effects of $k_z$ dispersion are included.
Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see \cite{rg}). In this paper we prove an extension of Mordell's theorem and formulate a conjecture which is stronger than Erdos' conjecture.
The goal of cross-view image based geo-localization is to determine the location of a given street view image by matching it against a collection of geo-tagged satellite images. This task is notoriously challenging due to the drastic viewpoint and appearance differences between the two domains. We show that we can address this discrepancy explicitly by learning to synthesize realistic street views from satellite inputs. Following this observation, we propose a novel multi-task architecture in which image synthesis and retrieval are considered jointly. The rationale behind this is that we can bias our network to learn latent feature representations that are useful for retrieval if we utilize them to generate images across the two input domains. To the best of our knowledge, ours is the first approach that creates realistic street views from satellite images and localizes the corresponding query street-view simultaneously in an end-to-end manner. In our experiments, we obtain state-of-the-art performance on the CVUSA and CVACT benchmarks. Finally, we show compelling qualitative results for satellite-to-street view synthesis.
We give an algorithm for computing Segre classes of subschemes of arbitrary projective varieties by computing degrees of a sequence of linear projections. Based on the fact that Segre classes of projective varieties commute with intersections by general effective Cartier divisors, we can compile a system of linear equations which determine the coefficients for the Segre class pushed forward to projective space. The algorithm presented here comes after several others which solve the problem in special cases, where the ambient variety is for instance projective space; to our knowledge, this is the first algorithm to be able to compute Segre classes in projective varieties with arbitrary singularities.
Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its band dispersion exhibits multiple subbands of partially flat dispersion, originating from the Fermi arc states. Remarkably, the lowest energy flat subbands bear a finite size energy gap, implying that electrons in the Fermi arc surface states are susceptible of the spin Berry phase. This is shown to be a consequence of spin-to-surface locking in the surface electronic states. We verify this behavior and the existence of spin Berry phase in the low-energy effective theory of Fermi arc surface states on a cylindrical nanowire by deriving the latter from a bulk Weyl Hamiltonian. We point out that in any surface state exhibiting a spin Berry phase pi, a zero-energy bound state is formed along a magnetic flux tube of strength, hc/(2e). This effect is highlighted in a surfaceless bulk system pierced by a dislocation line, which shows a 1D chiral mode along the dislocation line.
This paper is a contribution to the description of some congruences on the odd prime factors of the class number of the number fields. An example of results obtained is: Let L/Q be a finite Galois solvable extension with [L:Q]=N, where N > 1 is odd. Let h(L) be the class number of L. Suppose that h(L) > 1. Let p be a prime dividing h(L). Let r be the rank of the p-class group of L. Then the product p\times (p^r-1)\times(p^{r-1}-1)\times ....\times (p-1) and N are not coprime. The proofs are elementary.
A construction for sphere packings is introduced that is parallel to the ``anticode'' construction for codes. This provides a simple way to view Vardy's recent 20-dimensional sphere packing, and also produces packings in dimensions 22, 44--47 that are denser than any previously known.
We use classical/large Nc (number of colors) QCD to study nucleon--antinucleon annihilation at rest. We include pion, rho and omega fields in the classical dynamics, starting from the nonlinear sigma model. We begin with a spherical blob of pionic matter with zero baryon number and energy of twice the nucleon mass. This evolves according to the classical dynamics to pion and vector meson fields into the radiation zone. The radiation fields are quantized using the method of coherent states modified to include isospin and four momentum conservation. Empirical information is extracted from that coherent state. We find good agreement with data for single particle momentum and number spectra, and with branching ratios to many annihilation channels. All this emerges with nearly no free parameters.
A Classical Trajectory Monte Carlo (CTMC) simulation has been made of processes of charge exchange and ionization between an hydrogen atom and fully stripped ions embedded in very strong static electric fields ($O(10^{10}$ V/m$)$), which are thought to exist in cosmic and laser--produced plasmas. Calculations show that the presence of the field affects absolute values of the cross sections, enhancing ionization and reducing charge exchange. Moreover, the overall effect depends upon the relative orientation between the field and the nuclear motion. Other features of a null-field situation, such as scaling laws, are revisited.
We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in arXiv:1801.04036. We propose all the 5-brane web diagrams for these rank 2 theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for $G_2$ gauge theory with six flavors and its dual $Sp(2)$ and $SU(3)$ gauge theories. We also present 5-brane webs for $SU(3)$ theories of Chern-Simons level greater than 5.
We investigate how isospin affects the geometrical shape and energy of classical soliton solutions of topological charges $B=1-4,8$ in the Skyrme model. The novel approach in our work is that we study classically isospinning Skyrmions beyond the rigid-body approximation; that is, we explicitly allow the soliton solutions to deform and to break the symmetries of the static configurations. Our fully three-dimensional relaxation calculations reveal that the symmetries of isospinning Skyrme solitons can differ significantly from the ones of the static configurations. In particular, isospinning Skyrmion solutions can break up into lower-charge Skyrmions, can deform into new solution types that do not exist at vanishing angular frequency $\omega$ or energy degeneracy can be removed. These types of deformations have been largely ignored in previous work on modeling nuclei by quantized Skyrmion solutions.
We study existence of principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term via the Krein-Rutman theorem which based on regularity up to boundary of viscosity solutions. We also show the simplicity of the eigenfunctions in viscosity sense by a nonlocal version of ABP estimate.
The star formation quenching depends on environment, but a full understanding of what mechanisms drive it is still missing. Exploiting a sample of galaxies with masses $M_\ast>10^{9.8}M_\odot$, drawn from the WIde-field Nearby Galaxy-cluster Survey (WINGS) and its recent extension OMEGAWINGS, we investigate the star formation rate (SFR) as a function of stellar mass (M$_*$) in galaxy clusters at $0.04<z<0.07$. We use non-member galaxies at 0.02$<$z$<$0.09 as field control sample. Overall, we find agreement between the SFR-M$_*$ relation in the two environments, but detect a population of cluster galaxies with reduced SFRs which is rare in the field. These {\it transition} galaxies are mainly found within the cluster virial radius ($R_{200}$) but they impact on the SFR-M$_*$ relation only within 0.6R$_{200}$. The ratio of transition to PSF galaxies strongly depends on environment, being larger than 0.6 within 0.3R$_{200}$ and rapidly decreasing with distance, while it is almost flat with $M_*$. As galaxies move downward from the SFR-M$_*$ main sequence, they become redder and present older luminosity and mass weighted ages. These trends, together with the analysis of the star formation histories, suggest that transition galaxies have had a reduced SFR for the past 2-5 Gyr. Our results are consistent with the hypothesis that the interaction of galaxies with the intracluster medium via strangulation causes a gradual shut down of star formation, giving birth to an evolved population of galaxies in transition from being star forming to becoming passive.
We present an improved method for handling off-shell effects in deep inelastic nuclear scattering. With a firm understanding of the effects of the nuclear wave function, including these off-shell corrections as well as binding and nucleon-nucleon correlations, we can begin to examine the role of QCD in nuclei through an analysis of the moments of the nuclear structure function. Our analysis is aimed at extracting the Q^2 dependence of the moments of the nucleon structure function by using the recent high x world Iron data and by properly removing nuclear effects from the perturbative contribution. In addition, we compare quantitatively the behavior of the extracted moments with a simple O(1/Q^2) phenomenological form and we determine the mass term for this parametrization.
Using high-resolution observations from the 1.6 m New Solar Telescope (NST) operating at the Big Bear Solar Observatory (BBSO), we report direct evidence of merging/reconnection of cool H$\alpha$ loops in the chromosphere during two homologous flares (B- and C-class) caused by a shear motion at the footpoint of two loops. The reconnection between these loops caused the formation of an unstable flux rope which showed counterclockwise rotation. The flux rope could not reach the height of torus instability and failed to form a coronal mass ejection. The HMI magnetograms revealed rotation of the negative/positive (N1/P2) polarity sunspots in the opposite directions, which increased the right and left-handed twist in the magnetic structures rooted at N1/P2. Rapid photospheric flux cancellation (duration$\sim$20-30 min, rate$\approx$3.44$\times$10$^{20}$ Mx h$^{-1}$) was observed during and even after the first B6.0 flare and continued until the end of the second C2.3 flare. The RHESSI X-ray sources were located at the site of the loop's coalescence. To the best of our knowledge, such a clear interaction of chromospheric loops along with rapid flux cancellation has not been reported before. These high-resolution observations suggest the formation of a small flux rope by a series of magnetic reconnection within chromospheric loops associated with very rapid flux cancellation.
RGB-thermal salient object detection (SOD) aims to segment the common prominent regions of visible image and corresponding thermal infrared image that we call it RGBT SOD. Existing methods don't fully explore and exploit the potentials of complementarity of different modalities and multi-type cues of image contents, which play a vital role in achieving accurate results. In this paper, we propose a multi-interactive dual-decoder to mine and model the multi-type interactions for accurate RGBT SOD. In specific, we first encode two modalities into multi-level multi-modal feature representations. Then, we design a novel dual-decoder to conduct the interactions of multi-level features, two modalities and global contexts. With these interactions, our method works well in diversely challenging scenarios even in the presence of invalid modality. Finally, we carry out extensive experiments on public RGBT and RGBD SOD datasets, and the results show that the proposed method achieves the outstanding performance against state-of-the-art algorithms. The source code has been released at:https://github.com/lz118/Multi-interactive-Dual-decoder.
In this paper, we study degree conditions for the existence of large matchings in uniform hypergraphs. We prove that for integers $k,l,n$ with $k\ge 3$, $k/2<l<k$, and $n$ large, if $H$ is a $k$-uniform hypergraph on $n$ vertices and $\delta_{l}(H)>{n-l\choose k-l}-{(n-l)-(\lceil n/k \rceil-2)\choose 2}$, then $H$ has a matching covering all but a constant number of vertices. When $l=k-2$ and $k\ge 5$, such a matching is near perfect and our bound on $\delta_l(H)$ is best possible. When $k=3$, with the help of an absorbing lemma of H\'{a}n, Person, and Schacht, our proof also implies that $H$ has a perfect matching, a result proved by K\" uhn, Osthus, and Treglown and, independently, of Kahn.
The Galactic Centre contains a supermassive black hole with a mass of 4 million suns within an environment that differs markedly from that of the Galactic disk. While the black hole is essentially quiescent in the broader context of active galactic nuclei, X-ray observations have provided evidence for energetic outbursts from its surroundings. Also, while the levels of star formation in the Galactic Centre have been approximately constant over the last few hundred Myr, there is evidence of elevated short-duration bursts, strongly influenced by interaction of the black hole with the enhanced gas density present within the ring-like Central Molecular Zone at Galactic longitude |l| < 0.7 degrees and latitude |b| < 0.2 degrees. The inner 200 pc region is characterized by large amounts of warm molecular gas, a high cosmic ray ionization rate, unusual gas chemistry, enhanced synchrotron emission, and a multitude of radio-emitting magnetised filaments, the origin of which has not been established. Here we report radio imaging that reveals bipolar bubbles spanning 1 degree x 3 degrees (140 parsecs x 430 parsecs), extending above and below the Galactic plane and apparently associated with the Galactic Centre. The structure is edge-brightened and bounded, with symmetry implying creation by an energetic event in the Galactic Centre. We estimate the age of the bubbles to be a few million years, with a total energy of 7 x 10^52 ergs. We postulate that the progenitor event was a major contributor to the increased cosmic-ray density in the Galactic Centre, and is in turn the principal source of the relativistic particles required to power the synchrotron emission of the radio filaments within and in the vicinity of the bubble cavities.
We study the non-linear current response of a Dirac model that is coupled to two time-periodic electro-magnetic fields with different frequencies. We distinguish between incommensurable and commensurable frequencies, the latter characterized by their ratio p/q with co-prime integers p and q. Coupling the (effective) two-level system to a dissipative bath ensures a well-defined long-time solution for the reduced density operator and, thus, the current. We then analyze the spatio-temporal symmetries that force certain current components to vanish and close with conclusions for directed average currents.
A system of three coupled quantum dots in a triangular geometry (TQD) with electron-electron interaction and symmetrically coupled to two leads is analyzed with respect to the electron transport by means of the numerical renormalization group. Varying gate potentials this system exhibits extremely rich range of regimes with different many-electron states with various local spin orderings. It is demonstrated how the Luttinger phase changes in a controlled manner which then via the Friedel sum rule formula exactly reproduces the conductance through the TQD system. The analysis of the uncoupled TQD molecule from the leads gives a reliable qualitative understanding of various relevant regimes and gives an insight into the phase diagram with the regular Fermi liquid and singular-Fermi liquid phases.
We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive characteristic.
A review of wind accretion in HMXB is presented. We focus on different regimes of quasi-spherical accretion onto a NS: supersonic (Bondi) accretion, which takes place when the captured matter cools down rapidly and falls supersonically towards the NS magnetosphere, and subsonic (settling) accretion which occurs when the plasma remains hot until it meets the magnetospheric boundary. The two regimes are separated by a limit in X-ray luminosity at about 4 10^{36} erg/s. In subsonic accretion, which works a hot quasi-spherical shell must form around the magnetosphere, and the actual accretion rate onto the NS is determined by the ability of the plasma to enter the magnetosphere due to the Rayleigh-Taylor instability. Two regimes of subsonic accretion are possible, depending on the plasma cooling mechanism (Compton or radiative) near the magnetopshere. The transition from the high-luminosity regime with Compton cooling to the low-luminosity (L_x < 3\times 10^35 erg/s) regime with radiative cooling can be responsible for the onset of the 'off' states repeatedly observed in several X-ray pulsars, such as Vela X-1, GX 301-2 and 4U 1907+09. The triggering of the transition may be due to a switch in the X-ray beam pattern in response to a change in the optical depth in the accretion column with changing luminosity. We also show that in the settling accretion theory, bright X-ray flares (10^{38}-10^{40} ergs) observed in SFXT may be produced by sporadic capture of magnetized stellar-wind plasma. At sufficiently low accretion rates, magnetic reconnection can enhance the magnetospheric plasma entry rate, resulting in copious production of X-ray photons, strong Compton cooling and ultimately in unstable accretion of the entire shell. A bright flare develops on the free-fall time scale in the shell, and the typical energy released in an SFXT bright flare corresponds to the mass of the shell.
We explore the imprint of the cosmological hydrogen recombination lines on the power spectrum of the cosmic microwave background (CMB). In particular, we focus our analysis in the three strongest lines for the Balmer, Paschen and Brackett series of hydrogen. We expect changes in the angular power spectrum due to these lines on the level of $0.3 \mu K$ for the H$\alpha$ line, being maximum at small angular scales ($\ell \approx 870$). The morphology of the signal is very rich. It leads to relatively narrow spectral features ($\Delta \nu / \nu \sim 10^{-1}$), with several regions in the power spectrum showing a characteristic change of sign of the effect as we probe different redshifts or different multipoles by measuring the power spectrum at different frequencies. It also has a very peculiar dependence on the multipole scale, connected with the details of the transfer function at the epoch of scattering. In order to compute the optical depths for these transitions, we have evolved numerically the populations of the levels of the hydrogen atom during recombination, treating simultaneously the evolution of helium. For the hydrogen atom, we follow each angular momentum state separately, up to the level n=10. Foregrounds and other frequency dependent contaminants, as Rayleigh scattering, may be a important limitation for these measurements, although the peculiar frequency and angular dependences of the effect which we are discussing might permit to separate it. Detection of this signal using future narrow-band spectral observations can give information about the details of how the cosmic recombination proceeds, and how Silk damping operates during recombination.