ShantanuT01/DACTYL-Pretraining huggingface dataset:
The spin angular momentum $S$ of an isolated Kerr black hole is bounded by the surface area $A$ of its apparent horizon: $8\pi S \le A$, with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses $M$ and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to $S/M^2 = 0.994$. We measure the area and (using approximate Killing vectors) the spin on the individual and common apparent horizons, finding that the inequality $8\pi S < A$ is satisfied in all cases but is very close to equality on the common apparent horizon at the instant it first appears. We also introduce a gauge-invariant lower bound on the extremality by computing the smallest value that Booth and Fairhurst's extremality parameter can take for any scaling. Using this lower bound, we conclude that the common horizons are at least moderately close to extremal just after they appear. Finally, following Lovelace et al. (2008), we construct quasiequilibrium binary-black-hole initial data with "overspun" marginally trapped surfaces with $8\pi S > A$ and for which our lower bound on their Booth-Fairhurst extremality exceeds unity. These superextremal surfaces are always surrounded by marginally outer trapped surfaces (i.e., by apparent horizons) with $8\pi S<A$. The extremality lower bound on the enclosing apparent horizon is always less than unity but can exceed the value for an extremal Kerr black hole. (Abstract abbreviated.)
The WL-rank of a digraph $\Gamma$ is defined to be the rank of the coherent configuration of $\Gamma$. We construct a new infinite family of strictly Deza Cayley graphs for which the WL-rank is equal to the number of vertices. The graphs from this family are divisible design and integral.
Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the upper half plane generalising the iterated Shimura integrals of Manin. In this paper, some first properties of the underlying theory are established in the case of the full modular group: in particular, the relationship with special values of L-functions of modular forms at all positive integers; and the action of the conjectural motivic Galois group via a certain group of automorphisms.
We study the shifted convolution sum of the divisor function $d_3$ and the Ramanujan $\tau$ function.
We consider the p-Zassenhaus filtration (G_n) of a profinite group G. Suppose that G=S/N for a free profinite group S and a normal subgroup N of S contained in S_n. Under a cohomological assumption on the n-fold Massey products (which holds e.g., if the p-cohomological dimension of G is at most 1), we prove that G_{n+1} is the intersection of all kernels of upper-triangular unipotent (n+1)-dimensional representations of G over \mathbb F_p. This extends earlier results by Minac, Spira, and the author on the structure of absolute Galois groups of fields.
Microquasars, the local siblings of extragalactic quasars, are binary systems comprising a compact object and a companion star. By accreting matter from their companions, microquasars launch powerful winds and jets, influencing the interstellar environment around them. Steady gamma-ray emission is expected to rise from their central objects, or from interactions between their outflows and the surrounding medium. The latter prediction was recently confirmed with the detection of SS 433 at high (TeV) energies. In this report, we analyze more than ten years of GeV gamma-ray data from the Fermi Gamma-ray Space Telescope on this source. Detailed scrutiny of the data reveal emission in the SS 433 vicinity, co-spatial with a gas enhancement, and hints for emission possibly associated with a terminal lobe of one of the jets. Both gamma-ray excesses are relatively far from the central binary, and the former shows evidence for a periodic variation at the precessional period of SS 433, linking it with the microquasar. This result challenges obvious interpretations and is unexpected from any previously published theoretical models. It provides us with a chance to unveil the particle transport from SS 433 and to probe the structure of the local magnetic field in its vicinity.
We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian.The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.
GRB 090709A is a long gamma-ray burst (GRB) discovered by Swift, featuring a bright X-ray afterglow as well as a faint infrared transient with very red and peculiar colors. The burst attracted a large interest because of a possible quasi-periodicity at P=8.1 s in the prompt emission, suggesting that it could have a different origin with respect to standard, long GRBs. In order to understand the nature of this burst, we obtained a target of opportunity observation with XMM-Newton. X-ray spectroscopy, based on XMM-Newton and Swift data, allowed us to model the significant excess in photoelectric absorption with respect to the Galactic value as due to a large column density (about 6.5E+22 cm^-2) in the GRB host, located at z=4.2. Such a picture is also consistent with the infrared transient's properties. Re-analysis of the prompt emission, based on INTEGRAL and on Swift data, excludes any significant modulation at P=8.1 s. Thus, we conclude that GRB 090709A is a distant, standard, long GRB.
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in several variables over complex numbers. The exposition is aimed for a general audience in mathematics and we hope to be accessible to undergraduate as well as advance high school students. The topics discussed belong to relatively new, and closely related branches of algebraic geometry which are usually referred to as tropical geometry and toric geometry. These areas make connections between the study of algebra and geometry of polynomials and the combinatorial and convex geometric study of piecewise linear functions. The main results discussed in this note are descriptions of the so-called "ring of conditions" of algebraic torus.
Dissipative coupling of resonators arising from their cooperative dampings to a common reservoir induces intriguingly new physics such as energy level attraction. In this study, we report the nonlinear properties in a dissipatively coupled cavity magnonic system. A magnetic material YIG (yttrium iron garnet) is placed at the magnetic field node of a Fabry-Perot-like microwave cavity such that the magnons and cavity photons are dissipatively coupled. Under high power excitation, a nonlinear effect is observed in the transmission spectra, showing bistable behaviors. The observed bistabilities are manifested as clockwise, counterclockwise, and butterfly-like hysteresis loops with different frequency detuning. The experimental results are well explained as a Duffing oscillator dissipatively coupled with a harmonic one and the required trigger condition for bistability could be determined quantitatively by the coupled oscillator model. Our results demonstrate that the magnon damping has been suppressed by the dissipative interaction, which thereby reduces the threshold for conventional magnon Kerr bistability. This work sheds light upon potential applications in developing low power nonlinearity devices, enhanced anharmonicity sensors and for exploring the non-Hermitian physics of cavity magnonics in the nonlinear regime.
In this paper, according to CA duality, we study the complexity growth of dyonic RN-type black holes with quartic field strength corrections ($F^4$ corrections) to the matter action in general $D\geq4$-dimensions and find the behavior of action growth, similar to the case of the normal RN black holes, is different between electric and magnetic black holes which is unexpected since violates the electromagnetic duality. For restoring this duality, we add the Maxwell boundary term (at order 3-derivative) to the action and discuss the outcomes of the addition. Also, we have used another method that introduces UV finite cut off at AdS boundary to evaluate the complexity growth rate of dyonic black holes with and without $F^4$ corrections. In this method, without adding a surface term, late time growth rate of complexity exhibits expected behavior.
We develop the general relativity of extended spacetime-property for describing events including their properties. The anticommuting nature of property coordinates, augmenting space-time $({\bf x},t)$, allows for the natural emergence of generations and for the simple incorporation of gauge fields in the spacetime-property sector. With one electric property this results in a geometrical unification of gravity and electromagnetism, leading to a Maxwell-Einstein Lagrangian plus a cosmological term. Addition of one neutrinic and three chromic properties should lead to unification of gravity with electroweak and strong interactions.
Let $(W,H,\mu)$ be the classical Wiener space, assume that $U_\la=I_W+u_\la$ is an adapted perturbation of identity where the perturbation $u_\la$ is an $H$-valued map, defined up to $\mu$-equivalence classes, such that its Lebesgue density $s\to \dot{u}_\la(s)$ is almost surely adapted to the canonical filtration of the Wiener space and depending measurably on a real parameter $\la$. Assuming some regularity for $u_\la$, its Sobolev derivative and integrability of the divergence of the resolvent operator of its Sobolev derivative, we prove the almost sure and $L^p$-regularity w.r. to $\la$ of the estimation $E[\dot{u}_\la(s)|\calU_\la(s)]$ and more generally of the conditional expectations of the type $E[F\mid\calU_\la(s)]$ for nice Wiener functionals, where   $(\calU_\la(s),s\in [0,1])$ is the the filtration which is generated by $U_\la$. These results are applied to prove the invertibility of the adapted perturbations of identity, hence to prove the strong existence and uniqueness of functional SDE's; convexity of the entropy and the quadratic estimation error and finally to the information theory.
The application of handwritten text recognition to historical works is highly dependant on accurate text line retrieval. A number of systems utilizing a robust baseline detection paradigm have emerged recently but the advancement of layout analysis methods for challenging scripts is held back by the lack of well-established datasets including works in non-Latin scripts. We present a dataset of 400 annotated document images from different domains and time periods. A short elaboration on the particular challenges posed by handwriting in Arabic script for layout analysis and subsequent processing steps is given. Lastly, we propose a method based on a fully convolutional encoder-decoder network to extract arbitrarily shaped text line images from manuscripts.
Studies of the halo gas in the Milky Way and in nearby spiral galaxies show the presence of gas complexes that cannot be reconciled with an internal (galactic fountain) origin and are direct evidence of gas accretion. Estimating gas accretion rates from these features consistently gives values, which are one order of magnitude lower than what is needed to feed the star formation. I show that this problem can be overcome if most of the accretion is in fact "hidden" as it mixes with the galactic fountain material coming from the disk. This model not only provides an explanation for the missing gas accretion but also reproduces the peculiar kinematics of the halo gas in particular the vertical rotation gradient. In this view this gradient becomes indirect evidence for gas accretion.
We show that relativistic mean fields theories with scalar, $S$, and vector, $V$, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry {\it and positive energy bound states} when $S=-V$. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.
Using the collective variables theory, we study the effect of competition between Coulomb and dispersion forces on the gas-liquid phase behaviour of a model ionic fluid, i.e. a charge-asymmetric primitive model with additional short-range attractive interactions. Both the critical parameters and the coexistence envelope are calculated in a one-loop approximation as a function of the parameter $\alpha$ measuring the relative strength of the Coulomb to short-range interactions. We found the very narrow region of $\alpha$ bounded from the both sides by tricritical points which separates the models with "nonionic" and "Coulombic" phase behaviour. This is at variance with the result of available computer simulations where no tricritical point is found for the finely-discretized lattice version of the model.
On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous results in which the symplectic manifold was compact. The main tool is a finiteness theorem for R-constructible sheaves on a real analytic manifold in a non proper situation.
In the mapping of the local ISM it is of some interest to know where the first indications of the boundary of the Local Bubble can be measured. The Hipparcos distances combined to B-V photometry and some sort of spectral classification permit mapping of the spatial extinction distribution. Photometry is available for almost the complete Hipparcos sample and Michigan Classification is available for brighter stars south of delta = +5 deg (1900). For the northern and fainter stars spectral types, e.g. the HD types, are given but a luminosity class is often missing. The B-V photometry and the parallax do, however, permit a dwarf/giant separation due to the value of the slope of the reddening vector compared to the gradient of the main sequence in a color magnitude diagram, in the form: B-V vs. M_V+A_V = V+5(1+log(pi)), together with the rather shallow extinction present in the Hipparcos sample. We present the distribution of median A_V(l, b) for stars with Hipparcos 2 distances less than 55 pc. The northern part of the first and second quadrant has most extinction, up to 0.2 mag and the southern part of the third and fourth quadrant the slightest extinction, 0.05 mag. The boundary of the extinction minimum appears rather coherent on an angular resolution of a few degrees
We present the design of the Fabry-Perot system of the Robert Stobie Spectrograph on the 10-meter class Southern African Large Telescope and its characterization as measured in the laboratory. This system provides spectroscopic imaging at any desired wavelength spanning a bandpass 430 - 860 nm, at four different spectral resolving powers ranging from 300 to 9000. Our laboratory tests revealed a wavelength dependence of the etalon gap and parallelism with a maximum variation between 600 - 720 nm that arises because of the complex structure of the broadband multi-layer dielectric coatings. We also report an unanticipated optical effect of this multi-layer coating structure that produces a significant, and wavelength dependent, change in the apparent shape of the etalon plates. This change is caused by two effects: the physical non-uniformities or thickness variations in the coating layers, and the wavelength dependence of the phase change upon refection that can amplify these non-uniformities. We discuss the impact of these coating effects on the resolving power, finesse, and throughput of the system. This Fabry-Perot system will provide a powerful tool for imaging spectroscopy on one of the world's largest telescopes.
A generation procedure, based on the 5-dimensional covariance of the Kaluza-Klein theory, is developed. The procedure allows one to obtain exact solutions of the 4-dimensional Einstein equations with electromagnetic and scalar fields from vacuum 5-dimensional solutions using special 5-dimensional coordinate transformations. Relations between the physical properties of the resulting solutions and invariant geometrical properties of the generating Killing vectors are found out.
Thin films of the ferromagnet Fe$_2$Ge were grown via molecular beam epitaxy, and their electrical and magneto-transport properties measured for the first time. X-ray diffraction and vibrating sample magnetometry measurements confirmed the crystalline ferromagnetic Fe$_2$Ge phase. The observed high temperature maximum in the longitudinal resistivity, as well as the observed suppression of electron-magnon scattering at low temperatures, point to the presence of strong spin polarization in this material. Measurements of the Hall resistivity, $\rho_{xy}$, show contributions from both the ordinary Hall effect and anomalous Hall effect, $\rho_{xy}^{AH}$, from which we determined the charge carrier concentration and mobility. Measurements also show a small negative magnetoresistance in both the longitudinal and transverse geometries. Fe$_2$Ge holds promise as a useful spintronic material, especially for its semiconductor compatibility.
Based on magnetization, specific heat, magnetostriction, and neutron diffraction studies on single-crystal TbCo2B2C, it is found out that the paramagnetic properties, down to liquid nitrogen temperatures, are well described by a Curie-Weiss behavior of the Tb+3 moments. Furthermore, below Tc= 6.3 K, the Tb-sublattice undergoes a ferromagnetic (FM) phase transition with the easy axis being along the (100) direction and, concomitantly, the unit cell undergoes a tetragonal-to-orthorhhombic distortion. For fields up to 90 kOe, no field-induced splitting of the Co 3d orbitals was observed; as such the internal field must be well below the critical value needed to polarize the Co 3d subsystem. The manifestation of a FM state in TbCo2B2C is unique among all other isomorphous borocarbides, in particular TbNi2B2C (Tn=15 K, incommensurate modulated magnetic state) even though the Tb-ions in both isomorphs have almost the same crystalline electric field properties. The difference in the magnetic modes of these Tb-based isomorphs is attributed to a difference in their exchange couplings caused by a variation in their lattice parameters and in the position of their Fermi levels.
A low-energy non-unitary leptonic mixing matrix is a generic effect of a large class of theories accounting for neutrino masses. It is shown how the extra CP-odd phases of a general non-unitary matrix allow for sizeable CP-asymmetries in channels other than those dominant in the standard unitary case. The $\nu_\mu\to \nu_\tau$ channel turns out to be an excellent tool to further constrain moduli and phases. Furthermore, we clarify the relationship between our approach and the so-called "non-standard neutrino interactions" schemes: the sensitivities explored here apply as well to such constructions.
Graffiti is a common phenomenon in urban scenarios. Differently from urban art, graffiti tagging is a vandalism act and many local governments are putting great effort to combat it. The graffiti map of a region can be a very useful resource because it may allow one to potentially combat vandalism in locations with high level of graffiti and also to cleanup saturated regions to discourage future acts. There is currently no automatic way of obtaining a graffiti map of a region and it is obtained by manual inspection by the police or by popular participation. In this sense, we describe an ongoing work where we propose an automatic way of obtaining a graffiti map of a neighbourhood. It consists of the systematic collection of street view images followed by the identification of graffiti tags in the collected dataset and finally, in the calculation of the proposed graffiti level of that location. We validate the proposed method by evaluating the geographical distribution of graffiti in a city known to have high concentration of graffiti -- Sao Paulo, Brazil.
The Palomar Cosmic Web Imager (PCWI), an integral field spectrograph designed to detect and map low surface brightness emission, has obtained imaging spectroscopic maps of Ly-alpha from the circum-QSO medium (CQM) of QSO HS1549+19 at redshift of 2.843. Extensive extended emission is detected from the CQM, consistent with fluorescent and pumped Ly-alpha produced by the ionizing and Ly-alpha continuum of the QSO. Many features present in PCWI spectral images match those detected in narrow-band images. Filamentary structures with narrow line profiles are detected in several cases as long as 250-400 kpc. One of these is centered at a velocity redshifted with respect to the systemic velocity, and displays a spatially collimated and kinematically cold line profile increasing in velocity width approaching the QSO. This suggests that the filament gas is infalling onto the QSO, perhaps in a cold accretion flow. Because of the strong ionizing flux, the neutral column density is low, typically N(HI) is roughly 10E12-10E15/square-cm, and the line center optical depth is also low (typically tau0 is less than 10), insufficient to display well-separated double peak emission characteristic of higher line optical depths. With a simple ionization and cloud model we can very roughly estimate the total gas mass (log M(gas) equal to 12.5 +/- 0.5) and the total mass (log M(tot) equal to 13.3+/- 0.5). We can also calculate a kinematic mass from the total line profile (2x10E13 M(sun)), which agrees with the mass estimated from the gas emission. The intensity-binned spectrum of the CQM shows a progression in kinematic properties consistent with heirarchical structure formation.
The purpose in this paper is to determine the global behavior of solutions to the initial-boundary value problems for energy-subcritical and critical semilinear heat equations by initial data with lower energy than the mountain pass level in energy spaces associated with self-adjoint operators satisfying Gaussian upper bounds. Our self-adjoint operators include the Dirichlet Laplacian on an open set, Robin Laplacian on an exterior domain, and Schr\"odinger operators, etc.
Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.