ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we study some new theories of characteristic homology classes for singular complex algebraic varieties. First we introduce a natural transformation T_{y}: K_{0}(var/X) -> H_{*}(X,Q)[y] commuting with proper pushdown, which generalizes the corresponding Hirzebruch characteristic. Here K_{0}(var/X) is the relative Grothendieck group of complex algebraic varieties over X as introduced and studied by Looijenga and Bittner in relation to motivic integration. T_{y} is a homology class version of the motivic measure corresponding to a suitable specialization of the well known Hodge polynomial. This transformation unifies the Chern class transformation of MacPherson and Schwartz (for y=-1) and the Todd class transformation in the singular Riemann-Roch theorem of Baum-Fulton-MacPherson (for y=0). In fact, T_{y} is the composition of a generalized version of this Todd class transformation due to Yokura, and a new motivic Chern class transformation mC_{*}: K_{0}(var/X)-> G_{0}(X)[y], which generalizes the total lambda-class of the cotangent bundle to singular spaces. Here G_{0}(X) is the Grothendieck group of coherent sheaves, and the construction of mC_{*} is based on some results from the theory of algebraic mixed Hodge modules due to M.Saito. In the final part of the paper we use the algebraic cobordism theory of Levine and Morel to lift mC_{*} further up to a natural transformation mC'_{*} from K_{0}(var/X) to a suitable universal Borel-Moore weak homology theory. Moreover, all our results can be extended to varieties over a base field k, which can be embedded into the complex numbers.
Neutron diffraction measurement on the spin glass double perovskite Sr$_2$FeCoO$_6$ reveals site disorder as well as Co$^{3+}$ intermediate spin state. In addition, multiple valence states of Fe and Co are confirmed through M\"{o}ssbauer and X-ray photoelectron spectroscopy. The structural disorder and multiple valence lead to competing ferromagnetic and antiferromagnetic interactions and subsequently to a spin glass state, which is reflected in the form of an additional $T$-linear contribution at low temperatures in specific heat. A clear evidence of Jahn-Teller distortion at the Co$^{3+}$-O$_6$ complex is observed and incorporating the physics of Jahn-Teller effect, the presence of localized magnetic moment is shown. A large, negative and anomalous magnetoresistance of $\approx$ 63% at 14K in 12T applied field is observed for Sr$_2$FeCoO$_6$. The observed magnetoresistance could be explained by applying a semi-empirical fit consisting of a negative and a positive contribution and show that the negative magnetoresistance is due to spin scattering of carriers by localized magnetic moments in the spin glass phase.
Research on automated image enhancement has gained momentum in recent years, partially due to the need for easy-to-use tools for enhancing pictures captured by ubiquitous cameras on mobile devices. Many of the existing leading methods employ machine-learning-based techniques, by which some enhancement parameters for a given image are found by relating the image to the training images with known enhancement parameters. While knowing the structure of the parameter space can facilitate search for the optimal solution, none of the existing methods has explicitly modeled and learned that structure. This paper presents an end-to-end, novel joint regression and ranking approach to model the interaction between desired enhancement parameters and images to be processed, employing a Gaussian process (GP). GP allows searching for ideal parameters using only the image features. The model naturally leads to a ranking technique for comparing images in the induced feature space. Comparative evaluation using the ground-truth based on the MIT-Adobe FiveK dataset plus subjective tests on an additional data-set were used to demonstrate the effectiveness of the proposed approach.
A family of K3 surfaces $\mathscr{X}\rightarrow B$ has the \emph{Franchetta property} if the Chow group of 0-cycles on the generic fiber is cyclic. The generalized Franchetta conjecture proposed by O'Grady asserts that the universal family $\mathscr{X}_g\rightarrow \mathscr{F}_g$ of polarized K3 of degree $2g-2$ has the Franchetta property. While this is known only for small $g$ thanks to \cite{PSY}, we prove that for all $g$ there is a hypersurface in $ \mathscr{F}_g$ such that the corresponding family has the Franchetta property.
In this work a perturbative linear response analysis is performed for the time evolution of the quasi-conserved charge of a scalar field. One can find two regimes, one follows exponential damping, where the damping rate is shown to come from quantum Boltzmann equations. The other regime (coming from multiparticle cuts and products of them) decays as power law. The most important, non-oscillating contribution in our model comes from a 4-particle intermediate state and decays as 1/t^3. These results may have relevance for instance in the context of lepton number violation in the Early Universe.
The Cherenkov effect is a well known phenomenon in the electrodynamics of fast charged particles passing through transparent media. If the particle is faster than the light in a given medium, the medium emits a forward light cone. This beautiful phenomenon has an acoustic counterpart where the role of photons is played by phonons and the role of the speed of light is played by the sound velocity. In this case the medium emits a forward sound cone. Here, we show that in a system with spin-orbit interactions in addition to this {\it normal} Cherenkov sound there appears an {\it anomalous} Cherenkov sound with forward and {\it backward} sound propagation. Furthermore, we demonstrate that the transition from the normal to anomalous Cherenkov sound happens in a {\it singular} way at the Cherenkov cone angle. The detection of this acoustic singularities therefore represents an alternative experimental tool for the measurement of the spin-orbit coupling strength.
The quantum fluctuation of the stress tensor of a quantum field are discussed, as are the resulting spacetime metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the spacetime geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.
We report on microscopic tight-binding modeling of surface states in Bi$_2$Se$_3$ three-dimensional topological insulator, based on a sp$^3$ Slater-Koster Hamiltonian, with parameters calculated from density functional theory. The effect of spin-orbit interaction on the electronic structure of the bulk and of a slab with finite thickness is investigated. In particular, a phenomenological criterion of band inversion is formulated for both bulk and slab, based on the calculated atomic- and orbital-projections of the wavefunctions, associated with valence and conduction band extrema at the center of the Brillouin zone. We carry out a thorough analysis of the calculated bandstructures of slabs with varying thickness, where surface states are identified using a quantitative criterion according to their spatial distribution. The thickness-dependent energy gap, attributed to inter-surface interaction, and the emergence of gapless surface states for slabs above a critical thickness are investigated. We map out the transition to the infinite-thickness limit by calculating explicitly the modifications in the spatial distribution and spin-character of the surface states wavefunction with increasing the slab thickness. Our numerical analysis shows that the system must be approximately forty quintuple-layers thick to exhibit completely decoupled surface states, localized on the opposite surfaces. These results have implications on the effect of external perturbations on the surface states near the Dirac point.
We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, instead of ff=+-8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ff=+-4 is, down to very low fields, weakly dependent on the strength of the magnetic field.
We study metal-insulator transitions between Mott insulators and metals. The transition mechanism completely different from the original dynamical mean field theory (DMFT) emerges from a cluster extension of it. A consistent picture suggests that the quasiparticle weight $Z$ remains nonzero through metals and suddenly jumps to zero at the transition, while the gap opens continuously in the insulators. This is in contrast with the original DMFT, where $Z$ continuously vanishes but the gap opens discontinuously. The present results arising from electron differentiation in momentum space agree with recent puzzling bulk-sensitive experiments on CaVO$_3$ and SrVO$_3$.
We consider the long-time behavior of the mean curvature flow in heterogeneous media with periodic fibrations, modeled as an additive driving force. Under appropriate assumptions on the forcing term, we show existence of generalized traveling waves with maximal speed of propagation, and we prove the convergence of solutions to the forced mean curvature flow to these generalized waves.
In this note we study the moduli space of rank two semistable sheaves on a smooth cubic hypersurface $X\subset\mathbb{P}^{4}$ with $c_{1}=0$, $c_{2}=2$ and $c_{3}=0$. We show that it is isomorphic to the blow-up of the intermediate jacobian $J(X)$ of $X$ along the Fano surface of $X$. We complete previous results of Iliev-Markushevich AG/9910058 and Markushevich-Tikhomirov AG/9910063.
Various statistics on wreath products are defined via canonical words, "colored" right to left minima and "colored" descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type. These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial realizations within the wreath product. The above setting also gives rise to MacMahon type equi-distribution theorem over subsets with prescribed statistics.
$\alpha$-RuCl$_{3}$ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of $\alpha$-RuCl$_{3}$ by a resonant inelastic x-ray scattering study at the Ru $L_{3}$ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized via a quantum "order by disorder" mechanism, leaving ferromagnetism -- along with the Kitaev spin liquid -- as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of $\alpha$-RuCl$_{3}$ in magnetic fields.
A conditioned unitary transformation ($90^o$ polarization rotation) is performed at single-photon level. The transformation is realized by rotating polarization for one of the photons of a polarization-entangled biphoton state (signal photon) by means of a Pockel's cell triggered by the detection of the other (idler) photon after polarization selection. As a result, polarization degree for the signal beam changes from zero to the value given by the idler detector quantum efficiency. This result is relevant to practical realization of various quantum information schemes and can be used for developing a new method of absolute quantum efficiency calibration.
We present the results from a combined study of the average X-ray spectral and timing properties of 14 nearby AGN. For 11 of the sources in the sample, we used all the available data from the RXTE archive, which were taken until the end of 2006. There are 7795 RXTE observations in total for these AGN, obtained over a period of ~7-11 years. We extracted their 3-20 keV spectra and fitted them with a simple power-law model, modified by the presence of a Gaussian line (at 6.4 keV) and cold absorption, when necessary. We used these best-fit slopes to estimate the mean spectral slope for each object, while we used results from the literature to estimate the average spectral slope of the three objects without archival, monitorin RXTE data. Our results show that the AGN average spectral slopes are not correlated either with the black hole mass or the characteristic frequencies that were detected in the power spectra.They are positively correlated, though, with the characteristic frequency when normalised to the sources black hole mass. This is similar to the spectral-timing correlation that has been observed in Cyg X-1, but not the same.The AGN spectral-timing correlation can be explained if we assume that the accretion rate determines both the average spectral slope and the characteristic time scales in AGN. The spectrum should steepen and the characteristic frequency should increase, proportionally, with increasing accretion rate. We also provide a quantitative expression between spectral slope and accretion rate. Thermal Comptonisation models are broadly consistent with our result, but only if the ratio of the soft photons' luminosity to the power injected to the hot corona is proportionally related to the accretion rate.
It is currently understood that high temperature superconductivity (SC) in the transition metal $(M)$ substituted iron arsenides Ba(Fe$_{1-x}$$M$$_{x}$)$_{2}$As$_{2}$ is promoted by magnetic excitations with wave vectors $(\pi,0)$ or $(0,\pi)$. It is known that while a small amount of Co substitution leads to SC, the same does not occur for Mn for any value of $x$. In this work, magnetic excitations in the iron arsenides Ba(Fe$_{1-x}$Mn$_{x}$)$_{2}$As$_{2}$ ($x=0.0$, $0.007$, $0.009$, $0.08$) are investigated by means of Resonant Inelastic X rays Scattering (RIXS) at the Fe $L_{3}$-edge, for momentum transfer $\boldsymbol{q}$ along the high symmetry Brillouin zone $(\pi,0)$ and $(\pi,\pi)$ directions. It is shown that with increasing Mn content ($x$), the excitations become anisotropic both in dispersion and lineshape. Both effects are detected even for small values of $x$, evidencing a cooperative phenomenon between the Mn impurities, that we ascribe to emerging N\'eel order of the Mn spins. Moreover, for $x=0.08$, the excitations along $\boldsymbol{q}\parallel(\pi,0)$ are strongly damped and nearly non dispersive. This result suggests that phases of arsenides containing local moments at the FeAs layers, as in Mn or Cr substituted phases, do not support high temperature SC due to absence of the appropriate magnetic excitations.
Cyclic curves, i.e. curves fixed by a cyclic collineation group, play a central role in the investigation of cyclic arcs in Desarguesian projective planes. In this paper, the genus of a cyclic curve arising from a cyclic k-arc of Singer type is computed.
In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator $g$ and the associated solutions of BSDEs. Moreover, we give a new proof about $g$-convexity.
We establish an analytical link between the level density obtained by means of the Strutinsky averaging method, and the semiclassical level density. This link occurs only in the so-called "asymptotic limit". It turns out that the Strutinsky method amounts to an approximation to the semiclassical method. This approximation contains an unavoidable remainder which constitutes an intrinsic noise in comparison to the semiclassical method. Thus, the "old" problem of the dependency of the Strutinsky procedure on the two free smoothing parameters of the averaging is intimately connected to this noise. On the other hand, we demonstrate that the noise of the method is small in the average density of states and in the average energy, whereas it might be non-negligible in the shell correction itself. In order to improve this method, we give a "rule" which consists simply of minimizing the relative error made on the average energy.
There are observational facts and theoretical arguments for an origin of gamma-ray bursts in molecular clouds in distant galaxies. If this is true, one could detect a significant flux of GRB prompt and early afterglow X-ray radiation scattered into our line of sight by the molecular and atomic matter located within tens of parsecs of the GRB site long after the afterglow has faded away. The scattered flux directly measures the typical density of the GRB ambient medium. Furthemore, if the primary emission is beamed, the scattered X-ray flux will be slowly decreasing for several months to years before falling off rapidly. Therefore, it should be possible to estimate the collimation angle of a burst from the light curve of its X-ray echo and a measured value of the line-of-sight absorption column depth. It is shown that detection of such an echo is for the brightest GRBs just within the reach of the Chandra and XMM-Newton observatories.
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local equations of motion or can be eliminated by appropriate gauge transformations. For a single body at rest these problems are well understood for both the post-Newtonian and the post-Minkowskian cases. However, the situation is still unclear for approximations of higher orders. This paper discusses this problem for a "body" of spherical symmetry to post-linear order. We explicitly demonstrate how the usual Schwarzschild field can be derived directly from the field equations in the post-linear approximation in the harmonic gauge and for an arbitrary spherically symmetric matter distribution. Both external and internal solutions are considered. The case of static incompressible fluid is then compared to the well-known results from the literature. The results of this paper can be applied to generalize the well-known post-Newtonian and post-Minkowskian multipole expansions of the metric in the post-linear approximation.
Scalar-Tensor-Vector Gravity (STVG), also referred as MOdified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to described Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman-Oppenheimer-Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.
Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincar\'e invariance that preserves the Poincar\'e algebra, and only modifies its action on phase space in a Lorentz-invariant way. We show that, in contrast to the case where the Poincar\'e algebra is deformed, the action of boosts on two-particle states is not affected, while the addition law of momenta is to a large extent arbitrary. We give some nontrivial examples of this arising from doubly special relativity and noncommutative geometry and show that Hopf-algebra methods give equivalent results.
In this article, we provide explicit bounds for the prime counting function $\theta(x)$ in all ranges of $x$. The bounds for the error term for $\theta (x)- x$ are of the shape $\epsilon x$ and $\frac{c_k x}{(\log x)^k}$, for $k=1,\ldots,5$. Tables of values for $\epsilon$ and $c_k$ are provided.
In \cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov \cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit constructions are finite quotients of $\tilde{A_d}$-buildings, for $d\geq 2$, over local fields. In this paper, this result is extended to general high rank Bruhat-Tits buildings.
We show that the exactly solved low-temperature branch of the two-dimensional O($n$) model is equivalent with an O($n$) model with vacancies and a different value of $n$. We present analytic results for several universal parameters of the latter model, which is identified as a tricritical point. These results apply to the range $n \leq 3/2$, and include the exact tricritical point, the conformal anomaly and a number of scaling dimensions, among which the thermal and magnetic exponent, the exponent associated with crossover to ordinary critical behavior, and to tricritical behavior with cubic symmetry. We describe the translation of the tricritical model in a Coulomb gas. The results are verified numerically by means of transfer-matrix calculations. We use a generalized ADE model as an intermediary, and present the expression of the one-point distribution function in that language. The analytic calculations are done both for the square and the hexagonal lattice.