ShantanuT01/DACTYL-Pretraining huggingface dataset:
In thermal leptogenesis, the cosmic matter-antimatter asymmetry is produced by CP violation in the decays N --> l + \Phi of heavy right-handed Majorana neutrinos N into ordinary leptons l and Higgs particles \Phi. If some charged-lepton Yukawa couplings are in equilibrium during the leptogenesis epoch, the l interactions with the background medium are flavor sensitive and the coherence of their flavor content defined by N --> l+\Phi is destroyed, modifying the efficiency of the inverse decays. We point out, however, that it is not enough that the flavor-sensitive processes are fast on the cosmic expansion time scale, they must be fast relative to the N <--> l +\Phi reactions lest the flavor amplitudes of l remain frozen by the repeated N <--> l+\Phi ``measurements''. Our more restrictive requirement is significant in the most interesting ``strong wash-out case'' where N <--> l +\Phi is fast relative to the cosmic expansion rate. We derive conditions for the unflavored treatment to be adequate and for flavor effects to be maximal. In this ``fully flavored regime'' a neutrino mass bound survives. To decide if this bound can be circumvented in the intermediate case, a full quantum kinetic treatment is required.
Entanglement renormalization techniques are applied to numerically investigate the ground state of the spin-1/2 Heisenberg model on a kagome lattice. Lattices of N={36,144,inf} sites with periodic boundary conditions are considered. For the infinite lattice, the best approximation to the ground state is found to be a valence bond crystal (VBC) with a 36-site unit cell, compatible with a previous proposal. Its energy per site, E=-0.43221, is an exact upper bound and is lower than the energy of any previous (gapped or algebraic) spin liquid candidate for the ground state.
The weak value of a variable O is a description of an effective interaction with that variable in the limit of weak coupling. It is particularly important for a pre- and post-selected quantum system.
One of the main problems for extracting the Cosmic Microwave Background (CMB) from submm/mm observations is to correct for the Galactic components, mainly synchrotron, free - free and thermal dust emission with the required accuracy. Through a series of papers, it has been demonstrated that this task can be fulfilled by means of simple neural networks with high confidence. The main purpose of this paper is to demonstrate that the CMB BB power spectrum detected in the Planck 2015 polarization maps is present in the improved Planck 2017 maps with higher signal-to-noise ratio. Two features have been detected in the EB power spectrum in the new data set, both with S/N $\sim$4 . The origin of these features is most likely leakage from E to B with a level of about 1 per cent. This leakage gives no significant contribution to the detected BB power spectrum. The TB power spectrum is consistent with a zero signal. Altogether, the BB power spectrum is not consistent with the 'canonical' tensor-to-scalar models combined with gravitational lensing spectra. These results will give additional strong arguments for support to the proposed polarization satellite projects to follow up on the Planck mission .
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these show that the quantum mechanical extension of the classical method, for which trajectories are plotted as expectation values of the corresponding quantum operators, appears to work well, providing results consistent with the corresponding classical problems. The results appear to provide a new contribution to the subject of quantum chaos.
In order to understand the dynamical and chemical evolution of our Galaxy it is of fundamental importance to study the local neighborhood. White dwarf stars are ideal candidates to probe the history of the solar neighborhood, since these ``fossil'' stars have very long evolutionary time-scales and, at the same time, their evolution is relatively well understood. In fact, the white dwarf luminosity function has been used for this purpose by several authors. However, a long standing problem arises from the relatively poor statistics of the samples, especially at low luminosities. In this paper we assess the statistical reliability of the white dwarf luminosity function by using a Monte Carlo approach.
In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A $k$-assignment, $L$, for a graph $G$ assigns a list, $L(v)$, of $k$ available colors to each $v \in V(G)$, and an equitable $L$-coloring of $G$ is a proper coloring, $f$, of $G$ such that $f(v) \in L(v)$ for each $v \in V(G)$ and each color class of $f$ has size at most $\lceil |V(G)|/k \rceil$. In 2018, Kaul, Mudrock, and Pelsmajer subsequently introduced the List Equitable Total Coloring Conjecture which states that if $T$ is a total graph of some simple graph, then $T$ is equitably $k$-choosable for each $k \geq \max \{\chi_\ell(T), \Delta(T)/2 + 2 \}$ where $\Delta(T)$ is the maximum degree of a vertex in $T$ and $\chi_\ell(T)$ is the list chromatic number of $T$. In this paper we verify the List Equitable Total Coloring Conjecture for subdivisions of stars and the generalized theta graph.
A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST system first-order, are given modified evolution equations designed to drive constraint violations toward zero. The algebraic structure of the new system is investigated, showing that the modifications preserve the hyperbolicity of the fundamental and constraint evolution equations. The evolution of the constraints for pertubations of flat spacetime is completely analyzed, and all finite-wavelength constraint modes are shown to decay exponentially when certain adjustable parameters satisfy appropriate inequalities. Numerical simulations of a single Schwarzschild black hole are presented, demonstrating the effectiveness of the new constraint-damping modifications.
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach extends existing constructions of rational varieties with torus action of complexity one and delivers all Mori dream spaces with torus action. We exhibit the example class of general arrangement varieties and obtain classification results in the case of complexity two and Picard number at most two, extending former work in complexity one.
We present one of the most precise measurement to date of the spatial clustering of X-ray selected AGNs using a sample derived from the Chandra X-ray Observatory survey in the Bootes field. The real-space two-point correlation function over a redshift interval from z=0.17 to z~3 is well described by the power law, xi(r)=(r/r0)^-gamma, for comoving separations r<~20h^-1 Mpc. We find gamma=1.84+-0.12 and r0 consistent with no redshift trend within the sample (varying between r0=5.5+-0.6 h^-1 Mpc for <z>=0.37 and r0=6.9+-1.0 h^-1 Mpc for <z>=1.28). Further, we are able to measure the projections of the two-point correlation function both on the sky plane and in the line of sight. We use these measurements to show that the Chandra/Bootes AGNs are predominantly located at the centers of dark matter halos with the circular velocity Vmax>320 km/s or M_200 > 4.1e12 h^-1 Msun, and tend to avoid satellite galaxies in halos of this or higher mass. The halo occupation properties inferred from the clustering properties of Chandra/Bootes AGNs --- the mass scale of the parent dark matter halos, the lack of significant redshift evolution of the clustering length, and the low satellite fraction --- are broadly consistent with the Hopkins et al. scenario of quasar activity triggered by mergers of similarly-sized galaxies.
This paper was withdrawn due to a misidentification of the source.
We extend a recent chiral approach to nuclear matter of Lutz et al. [Phys. Lett. B474 (2000) 7] by calculating the underlying (complex-valued) single-particle potential U(p,k_f) + i W(p,k_f). The potential for a nucleon at the bottom of the Fermi-sea, U(0,k_{f0})= - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi-surface. Also, the imaginary single-particle potential, W(0,k_{f0}) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear matter equation of state can be obtained if the short range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1pi-exchange). We also consider the equation of state of pure neutron matter $bar E_n(k_n)$ and the asymmetry energy A(k_f) in that approach. The downward bending of these quantities above nuclear matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics.
We develop a formalism for relative Gromov-Witten invariants of Li that is analogous to the Symplectic Field Theory of Eliashberg, Givental, and Hofer. This formalism allows us to express natural degeneration formulae in terms of generating functions and re-derive the formulae of Caporaso-Harris, Ran, and Vakil. In addition, our framework gives a homology theory analogous to SFT Homology.
Let $n \in \mathbb{Z}_{\geq 3}$ be given. We prove Lebesgue-almost everywhere pointwise inversion formulae for the Siegel transforms in the geometry of numbers. These inversion formulae are quite general; for instance, they are valid for the Siegel transforms of any even and compactly supported Borel measurable function $f : \mathbb{R}^n \to \mathbb{R}$ that belongs to $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n).$
We show that the linearization of all exact solutions of classical chiral gravity around the AdS3 vacuum have positive energy. Non-chiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity-- the theory with logarithmically relaxed boundary conditions --has finite asymptotic symmetry generators but is not chiral and hence may be dual at the quantum level to a logarithmic CFT. Moreover we show that log gravity contains chiral gravity within it as a decoupled charge superselection sector. We normally evaluate the Euclidean sum over geometries of chiral gravity and show that it gives precisely the holomorphic extremal CFT partition function. The modular invariance and integrality of the expansion coefficients of this partition function are consistent with the existence of an exact quantum theory of chiral gravity. We argue that the problem of quantizing chiral gravity is the holographic dual of the problem of constructing an extremal CFT, while quantizing log gravity is dual to the problem of constructing a logarithmic extremal CFT.
We show that every Fricke invariant meromorphic modular form for $\Gamma_0(N)$ whose divisor on $X_0(N)$ is defined over $\mathbb{Q}$ and supported on Heegner divisors and the cusps is a generalized Borcherds product associated to a harmonic Maass form of weight $1/2$. Further, we derive a criterion for the finiteness of the multiplier systems of generalized Borcherds products in terms of the vanishing of the central derivatives of $L$-function of certain weight $2$ newforms. We also prove similar results for twisted Borcherds products.
Magnetic susceptibility anisotropy and high sensitivity magnetostriction measurements are used to investigate the symmetry of CeB6 ordered states. The antiferromagnetic state is confirmed as tetragonal, but no deviation from the cubic symmetry is observed in the so-called antiferroquadrupolar phase, where only volume effects are detected. In this phase, the temperature dependence of the strain field-susceptibilities is typical of non-ordered quadrupoles. Moreover, while an antiferroquadruplar order should be cubic, this symmetry is incompatible with the <1/2 1/2 1/2> ordering wave-vector. The antiferroquadrupolar description of CeB6 phase II is clearly inconsistent and an alternative model, based on a unidimensional representation of the cube, has to be sought for.
This is a survey article on developments in modularity since the proof of Fermat's Last Theorem, with an emphasis on the historical development of the subject rather than any technical details.
In this note, we investigate J.-C. Liu's work on truncated Gauss' square exponent theorem and obtain more truncations. We also discuss some possible multiple summation extensions of Liu's results.
Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately normalized, converges as $n\to\infty$ to the Gumbel distribution. In some sense, the the random variable $L_n$, being the maximum of $n(n+1)/2$ dependent standard gaussian variables, behaves like the maximum of $Hn \log n$ independent standard gaussian variables. Here, $H\in (0,\infty)$ is some constant. We also prove a version of the above result for the Brownian motion.
The crossover between two different conduction mechanisms (variable range and small polaron hoppings) is probed utilizing a conjunction of thermally varying conductivity and impedance in polycrystalline Pr2NiTiO6 (PNT). A combination of X-ray diffraction (XRD) and Raman spectroscopic investigations authenticates the lower symmetric monoclinic structure for PNT. The conductivity, impedance and relaxation spectra highlight the combined contributions of the electrodes, grain-boundaries and grain microstructures to the carrier dynamics in PNT. The relaxation mechanism has a non-ideal nature with distribution of relaxation times as observed from the dielectric and impedance spectroscopic data. The dc resistivity investigation points towards a transition in the conduction mechanism showing a gradual crossover at temperature 490 K, from small polaron hopping to Mott s variable range hopping due to reduced activation energy.
IGR J17361-4441 was discovered by INTEGRAL undergoing its first detectable X-ray outburst in 2011 and initially classified as an accreting X-ray binary in the globular cluster NGC 6388. A reanalysis of the outburst data collected with INTEGRAL and Swift suggested that the enhanced X-ray emission from IGR J17361-4441 could have been due to a rare tidal disruption event of a terrestrial- icy planet by a white dwarf. In this letter we report on the analysis of XMM-Newton data collected in 2011 during the outburst from IGR J17361-4441. Our analysis revealed the presence of a $\sim$100 mHz quasi-periodic oscillation in the X-ray emission from the source and confirmed the presence of a soft thermal component (kT$\sim$0.08 keV) in its spectrum. We discuss these findings in the context of the different possibilities proposed to explain the nature of IGR J17361-4441.
An Impulsive Heating Multiple Strand (IHMS) Model is able to reproduce the observational characteristics of EUV (~ 1 MK) active region loops. This model implies that some of the loops must reach temperatures where X-ray filters are sensitive (> 2.5 MK) before they cool to EUV temperatures. Hence, some bright EUV loops must be preceded by bright X-ray loops. Previous analysis of X-ray and EUV active region observations, however, have concluded that EUV loops are not preceded by X-ray loops. In this paper, we examine two active regions observed in both X-ray and EUV filters and analyze the evolution of five loops over several hours. These loops first appear bright in the X-ray images and later appear bright in the EUV images. The delay between the appearance of the loops in the X-ray and EUV filters is as little as 1 hour and as much as 3 hours. All five loops appear as single ``monolithic'' structures in the X-ray images, but are resolved into many smaller structures in the (higher resolution) EUV images. The positions of the loops appear to shift during cooling implying that the magnetic field is changing as the loops evolve. There is no correlation between the brightness of the loop in the X-ray and EUV filters meaning a bright X-ray loop does not necessarily cool to a bright EUV loop and vice versa. The progression of the loops from X-ray images to EUV images and the observed substructure is qualitatively consistent with the IMHS model.
The asymptotic behavior of the micromagnetic free energy governing a ferromagnetic film is studied as its thickness gets smaller and smaller compared to its cross section. Here the static Maxwell equations are treated as a Murat's constant-rank PDE constraint on the energy functional. In contrast to previous work this approach allows to keep track of the induced magnetic field without solving the magnetostatic equations. In particular, the mathematical results of Gioia and James [Proc. R. Soc. Lond. A 453 (1997), pp. 213-223] regarding convergence of minimizers are recovered by giving a characterization of the corresponding Gamma-limit.
Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.
We prove a part of Shokurov's conjecture on characterization of toric varieties modulo the minimal model program and adjunction conjecture.
In the present paper we find a simple algorithm for counting Jacobian group of the generalized Petersen graph GP(n,k). Also, we obtain a closed formula for the number of spanning trees of this graph in terms of Chebyshev polynomials.
We comment on the ubiquity of the so-called warped anti-de Sitter spacetimes in three-dimensional (2,0) supergravity theory. By using isometry-invariant tensors and simple counting, we prove their existence for arbitrary $(2,0)$ supergravity models suitably defined close to a minimal model. We also analyze their offshell supersymmetry and the supersymmetry of two geometric orbifolds.
We study super-Eddington accretion flows onto black holes using a global three dimensional radiation magneto-hydrodynamical simulation. We solve the time dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220L_edd/c^2 and forms a radiation driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10L_edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.
We present a theoretical investigation of magnetostatic interaction effects in geometrically frustrated arrays of anisotropic multilayer ferromagnetic nanoparticles arranged in different spatially configured systems with triangular symmetry. We show that the interlayer magnetostatic interaction significantly expands the opportunities to create magnetically frustrated systems. The effects of the magnetostatic interaction in magnetization reversal processes and the possibility to control the ferromagnetic resonance spectrum in such systems are discussed.
To identify and fit geometric primitives (e.g., planes, spheres, cylinders, cones) in a noisy point cloud is a challenging yet beneficial task for fields such as robotics and reverse engineering. As a multi-model multi-instance fitting problem, it has been tackled with different approaches including RANSAC, which however often fit inferior models in practice with noisy inputs of cluttered scenes. Inspired by the corresponding human recognition process, and benefiting from the recent advancements in image semantic segmentation using deep neural networks, we propose BAGSFit as a new framework addressing this problem. Firstly, through a fully convolutional neural network, the input point cloud is point-wisely segmented into multiple classes divided by jointly detected instance boundaries without any geometric fitting. Thus, segments can serve as primitive hypotheses with a probability estimation of associating primitive classes. Finally, all hypotheses are sent through a geometric verification to correct any misclassification by fitting primitives respectively. We performed training using simulated range images and tested it with both simulated and real-world point clouds. Quantitative and qualitative experiments demonstrated the superiority of BAGSFit.