ShantanuT01/DACTYL-Pretraining huggingface dataset:
Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using simulation data and a least-$\chi^2$ analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, $f$, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalised constraints on $f$ at $z=0.5$ and $z=1$ than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them.
This is a proof that if the eikonal is, as usually assumed, additive in strong and electro-magnetic interactions then the application of the Bethe Ansatz for the full scattering amplitude leads to the strong interaction scattering amplitude with the ratio ( real/imaginary) independent on the transferred momentum $ t $. Moreover, the unitarity condition makes the strong interaction amplitude vanishing. Thus, the Bethe form for the Coulomb-nuclear scattering amplitude and the same amplitude based on the additive eikonal are incompatible.
In this remark, we give another approach to the local well-posedness of quadratic Schr\"odinger equation with nonlinearity $u\bar u$ in $H^{-1/4}$, which was already proved by Kishimoto \cite{kis}. Our resolution space is $l^1$-analogue of $X^{s,b}$ space with low frequency part in a weaker space $L^{\infty}_{t}L^2_x$. Such type spaces was developed by Guo. \cite{G} to deal the KdV endpoint $H^{-3/4}$ regularity.
We argue that the hour-long neutron transient detected by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) Neutron Spectrometer beginning at 15:45 UT on 2011 June 4 is due to secondary neutrons from energetic protons interacting in the spacecraft. The protons were probably accelerated by a shock that passed the spacecraft about thirty minutes earlier. We reach this conclusion after a study of data from the MESSENGER neutron spectrometer, gamma-ray spectrometer, X-ray Spectrometer, and Energetic Particle Spectrometer, and from the particle spectrometers on STEREO A. Our conclusion differs markedly from that given by Lawrence et al. [2014] who claimed that there is "strong evidence" that the neutrons were produced by the interaction of ions in the solar atmosphere. We identify significant faults with the authors' arguments that led them to that conclusion.
Current-induced spin-orbit torques (SOTs) are of interest for fast and energy-efficient manipulation of magnetic order in spintronic devices. To be deterministic, however, switching of perpendicularly magnetized materials by SOT requires a mechanism for in-plane symmetry breaking. Existing methods to do so involve the application of an in-plane bias magnetic field, or incorporation of in-plane structural asymmetry in the device, both of which can be difficult to implement in practical applications. Here, we reported bias-field-free SOT switching in a single perpendicular CoTb layer with an engineered vertical composition gradient. The vertical structural inversion asymmetry induces strong intrinsic SOTs and a gradient-driven Dzyaloshinskii-Moriya interaction (g-DMI), which breaks the in-plane symmetry during the switching process. Micromagnetic simulations are in agreement with experimental results, and elucidate the role of g-DMI in the deterministic switching. This bias-field-free switching scheme for perpendicular ferrimagnets with g-DMI provides a strategy for efficient and compact SOT device design.
Previous X-ray observations toward the Nuclear Star Cluster (NSC) at the Galactic center have discovered thousands of point sources, most of which were believed to be cataclysmic variables (CVs), i.e., a white dwarf (WD) accreting from a low-mass companion. However, the population properties of these CVs remain unclear, which otherwise contain important information about the evolutionary history of the NSC. In this work we utilize ultradeep archival \textit{Chandra} observations to study the spectral properties of the NSC CVs, in close comparison with those in the Solar vicinity. We find that the NSC CVs have strong Fe XXV and Fe XXVI lines (both of which show equivalent widths $\sim200-300$ eV), indicating metal-rich companions. Moreover, their Fe XXVI to Fe XXV line flux ratio is used to diagnose the characteristic white dwarf mass ($M_{\rm WD}$) of NSC CVs. The results show that the CVs with $L_{\rm 2-10 keV}>6\times10^{31}$ erg s$^{-1}$ have a mean $M_{\rm WD}$ of $\sim0.6/1.0\,M_{\odot}$ if they are magnetic/non-magnetic CVs; while those with $L_{\rm 2-10 keV}$ between $1-6\times10^{31}$ erg s$^{-1}$ have a mean $M_{\rm WD}$ of $\sim0.8/1.2\,M_{\odot}$ if they are magnetic/non-magnetic CVs. All these \textit{Chandra}-detected CVs collectively contribute $\sim$30-50\% of the unresolved 20-40 keV X-ray emission from the NSC. The CV population with massive (i.e., $M_{\rm WD}\sim1.2M_{\odot}$) WDs have not been observed in the Solar vicinity or the Galactic bulge, and they might have been formed via dynamical encounters in the NSC.
The elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure have the form of quotients of minors. Instead of the proof using identities of determinants of \cite{Li}, a direct proof by induction is given.
Let $X$ be a symmetric quasi-Banach function space with Fatou property and let $E$ be an arbitrary symmetric quasi-Banach sequence space. Suppose that $(f_k)_{k\geq0}\subset X$ is a sequence of independent random variables. We present a necessary and sufficient condition on $X$ such that the quantity $$\Big\|\ \Big\|\sum_{k=0}^nf_ke_k\Big\|_{E}\ \Big\|_X$$ admits an equivalent characterization in terms of disjoint copies of $(f_k)_{k=0}^n$ for every $n\ge 0$; in particular, we obtain the deterministic description of $$\Big\|\ \Big\|\sum _{k=0}^nf_ke_k\Big\|_{\ell_q}\ \Big\|_{L_p}$$ for all $0<p,q<\infty,$ which is the ultimate form of Rosenthal's inequality. We also consider the case of a $\Delta$-normed symmetric function space $X$, defined via an Orlicz function $\Phi$ satisfying the $\Delta_2$-condition. That is, we provide a formula for \lq\lq $E$-valued $\Phi$-moments\rq\rq, namely the quantity $\mathbb{E}\big(\Phi\big(\big\|(f_k)_{k\geq0} \big\|_E \big)\big)$, in terms of the sum of disjoint copies of $f_k, k\geq0.$
Recently, it has been observed that {0,1,-1}-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform {-1,1}-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the generated codes indeed could achieve higher retrieval accuracy.
We study the properties of the surface states in three-dimensional topological insulators in the presence of a ferromagnetic exchange field. We demonstrate that for layered materials like Bi$_2$Se$_3$ the surface states on the top surface behave qualitatively different than the surface states at the side surfaces. We show that the group velocity of the surface states can be tuned by the direction and strength of the exchange field. If the exchange field becomes larger than the bulk gap of the material, a phase transition into a topologically nontrivial semimetallic state occurs. In particular, the material becomes a Weyl semimetal, if the exchange field possesses a non-zero component perpendicular to the layers. Associated with the Weyl semimetallic state we show that Fermi arcs appear at the surface. Under certain circumstances either one-dimensional or even two-dimensional surface flat bands can appear. We show that the appearence of these flat bands is related to chiral symmetries of the system and can be understood in terms of topological winding numbers. In contrast to previous systems that have been suggested to possess surface flat bands, the present system has a much larger energy scale, allowing the observation of surface flat bands at room temperature. The flat bands are tunable in the sense that they can be turned on or off by rotation of the ferromagnetic exchange field. Our findings are supported by both numerical results on a finite system as well as approximate analytical results.
We present an algorithm for measurement of the Green's function in the hybridization expansion continuous-time quantum Monte-Carlo based on continuous estimators. Compared to the standard method, the present algorithm has similar or better accuracy with improvement notable especially at low perturbation orders and high frequencies. The resulting statistical noise is weakly correlated so high-accuracy data for the numerical analytical continuation can be produced.
Our Galaxy, the Milky Way, is a benchmark for understanding disk galaxies. It is the only galaxy whose formation history can be studied using the full distribution of stars from white dwarfs to supergiants. The oldest components provide us with unique insight into how galaxies form and evolve over billions of years. The Galaxy is a luminous (L-star) barred spiral with a central box/peanut bulge, a dominant disk, and a diffuse stellar halo. Based on global properties, it falls in the sparsely populated "green valley" region of the galaxy colour-magnitude diagram. Here we review the key integrated, structural and kinematic parameters of the Galaxy, and point to uncertainties as well as directions for future progress. Galactic studies will continue to play a fundamental role far into the future because there are measurements that can only be made in the near field and much of contemporary astrophysics depends on such observations.
We calculated a four-point correlation function G_4(k,r;t) and the corresponding structure factor S_4(k,q;t) for a model glass-forming binary mixture. These functions measure the spatial correlations of the relaxation of different particles. We found that these four-point functions are anisotropic and depend on the angle between vectors k and r (or q). The anisotropy is the strongest for times somewhat longer than the beta relaxation time but it is quite pronounced even for times comparable to the alpha relaxation time, tau_alpha. At the lowest temperatures S_4(k,q;tau_alpha) is strongly anisotropic even for the smallest wavevector q accessible in our simulation.
Loophole-free Bell tests for quantum nonlocality and long-distance secure communication require photodetection efficiencies beyond a threshold eta_{crit} that depends on the Bell inequality and the noise affecting the entangled state received by the distant parties. Most calculations of eta_{crit} assume that the noise is random and can be modeled as white noise. However, most sources suffer from colored noise. Indeed, since entangled states are usually created as a superposition of two possible deexcitation paths, a partial distinguishability between the two processes leads to the appearance of colored noise in the generated state. Recently, there was a proposal for a loophole-free Bell test [A. Cabello and F. Sciarrino, Phys. Rev. X 2, 021010 (2012)], where a specific colored noise appears as a consequence of the precertification of the photon's presence through single-photon spontaneous parametric down-conversion. Here we obtain eta_{crit}, the optimal quantum states, and the local settings for a loophole-free Bell test as a function of the amount of colored noise. We consider three bipartite Bell inequalities with n dichotomic settings: Clauser-Horne-Shimony-Holt (n=2), I_{3322} (n=3), and A_5 (n=4), both for the case of symmetric efficiencies, corresponding to photon-photon Bell tests, and for the totally asymmetric case, corresponding to atom-photon Bell tests. Remarkably, in all these cases, eta_{crit} is robust against the colored noise. The present analysis can find application in any test of Bell inequalities in which the dominant noise is of the colored type.
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments of zeta functions and quadratic L-series. As an application of the theory, in a third section, we obtain the current best known error term for mean values of cubes of central values of Dirichlet L-series. The methods utilized to derive this result are the convexity principle for functions of several complex variables combined with a knowledge of groups of functional equations for certain multiple Dirichlet series.
It has been shown within density-functional theory that in Mn$_{12}$-acetate there are effects due to disorder by solvent molecules and a coupling between vibrational and electronic degrees of freedom. We calculate the in-plane principal axes of the second-order anisotropy caused by the second effect and compare them with those of the fourth-order anisotropy due to the first effect. We find that the two types of the principal axes are not commensurate with each other, which results in a complete quenching of the tunnel-splitting oscillation as a function of an applied transverse field.
We consider models of heavy fermions in the strong coupling or local moment limit and include phonon degrees of freedom on the conduction electrons. Due to the large mass or low coherence temperature of the heavy fermion state, it is shown that such a regime is dominated by vertex corrections which leads to the complete failure of the Migdal theorem. Even at weak electron-phonon couplings, binding of the conduction electrons competes with the Kondo effect and substantially reduces the coherence temperature, ultimately leading to the Kondo breakdown. Those results are obtained using a combination of the slave boson method and Migdal-Eliashberg approximation as well as the dynamical mean-field theory approximation.
The instrumental advances made in this new era of 4-meter class solar telescopes with unmatched spectropolarimetric accuracy and sensitivity, will enable the study of chromospheric magnetic fields and their dynamics with unprecedented detail. In this regard, spectropolarimetric diagnostics can provide invaluable insight into magneto-hydrodynamic (MHD) wave processes. MHD waves and, in particular, Alfv\'enic fluctuations associated to particular wave modes, were recently recognized as important mechanisms not only for the heating of the outer layers of the Sun's atmosphere and the acceleration of the solar wind, but also for the elemental abundance anomaly observed in the corona of the Sun and other Sun-like stars (also known as first ionisation potential; FIP) effect. Here, we take advantage of state-of-the-art and unique spectropolarimetric IBIS observations to investigate the relation between intensity and circular polarisation (CP) fluctuations in a sunspot chromosphere. Our results show a clear link between the intensity and CP fluctuations in a patch which corresponds to a narrow range of magnetic field inclinations. This suggests the presence of Alfv\'enic perturbations in the sunspot.
We consider the inverse problem of recovering the spherically symmetric sound speed, density and attenuation in the Sun from the observations of the acoustic field randomly excited by turbulent convection. We show that observations at two heights above the photosphere and at two frequencies above the acoustic cutoff frequency uniquely determine the solar parameters. We also present numerical simulations which confirm this theoretical result.
In an attempt to clarify the nature of the crossover from a Peierls band insulator to a Mott Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein Hubbard model using exact diagonalization techniques.
Every dXd bipartite system is shown to have a large family of undistillable states with nonpositive partial transpose (NPPT). This family subsumes the family of conjectured NPPT bound entangled Werner states. In particular, all one-copy undistillable NPPT Werner states are shown to be bound entangled.
We present the results of structural and magnetic phase comparisons of the iron oxychalcogenides La$_{2}$O$_{2}$Fe$_{2}$O$M$$_{2}$ ($M$ = S, Se). Elastic neutron scattering reveals that $M$ = S and Se have similar nuclear structures at room and low temperatures. We find that both materials obtain antiferromagnetic ordering at a Neel temperature $T_{N}$ 90.1 $\pm$ 0.16 K and 107.2 $\pm$ 0.06 K for $M$= Se and S, respectively. The magnetic arrangements of $M$ = S, Se are obtained through Rietveld refinement. We find the order parameter exponent $\beta$ to be 0.129 $\pm$ 0.006 for $M$ = Se and 0.133 $\pm$ 0.007 for $M$ = S. Each of these values is near the Ising symmetry value of 1/8. This suggests that although lattice and electronic structural modifications result from chalcogen exchange, the nature of the magnetic interactions is similar in these materials.
We study the homotopy groups of complements to reducible divisors on non-singular projective varieties with ample components and isolated non normal crossings. We prove a vanishing theorem generalizing conditions for commutativity of the fundamental groups. The calculation of supports of non vanishing homotopy groups as modules over the fundamental group in terms of the geometry of the locus of non-normal crossings is discussed. We review previous work on the local study of isolated non-normal crossings and relate the motivic zeta function to the local polytopes of quasiadjunction. As an application, we obtain information about the support loci of homotopy groups of arrangements of hyperplanes
We study the out-of-equilibrium fluctuation-dissipation (FD) relations in the low temperature, finite time, physical aging regime of two simple models with strong glass behaviour, the Fredrickson-Andersen model and the square-plaquette interaction model. We explicitly show the existence of unique, waiting-time independent dynamical FD relations. While in the Fredrickson-Andersen model the FD theorem is obeyed at all times, the plaquette model displays piecewise linear FD relations, similar to what is found in disordered mean-field models and in simulations of supercooled liquids, and despite the fact that its static properties are trivial. We discuss the wider implications of these results.
We explore, employing the renormalization-group theory, the critical scaling behavior of the permutation symmetric three-vector model that obeys non-conserving dynamics and has a relevant anisotropic perturbation which drives the system into a non-equilibrium steady state. We explicitly find the independent critical exponents with corrections up to two loops. They include the static exponents $\nu$ and $\eta$, the off equilibrium exponent $\widetilde{\eta}$, the dynamic exponent $z$ and the strong anisotropy exponent $\Delta$. We also express the other anisotropy exponents in terms of these.
It has been proposed by Ngan [Phys. Rev. E 68, 011301 (2003)] that the granular contact force distribution may be analytically derived by minimizing the analog of a thermodynamic free energy, in this case consisting of the total potential energy stored in the compressed contacts minus a particular form of entropy weighted by a parameter. The parameter is identified as a mechanical temperature. I argue that the particular form of entropy cannot be correct and as a result the proposed method produces increasingly errant results for increasing grain rigidity. This trend is evidenced in Ngan's published results and in other numerical simulations and experiments.
The pathway toward the tailored synthesis of materials starts with precise characterization of the conformational properties and dynamics of individual molecules. Electron spin resonance based scanning tunneling microscopy can potentially address molecular structure with unprecedented resolution. Here, we determine the fine structure and geometry of an individual TiH molecule, utilizing a combination of a newly developed mK ESR-STM in a vector magnetic field and ab initio approaches. We demonstrate a strikingly large anisotropy of the g-tensor unusual for a spin doublet ground state, resulting from a non-trivial orbital angular momentum stemming from the molecular ground state. We quantify the relationship between the resultant fine structure, hindered rotational modes, and orbital excitations. Our model system provides new avenues to determine the structure and dynamics of individual molecules.
We study the Seshadri constants on geometrically ruled surfaces. The unstable case is completely solved. Moreover, we give some bounds for the stable case. We apply these results to compute the Seshadri constant of the rational and elliptic ruled surfaces. Both cases are completely determined. The elliptic case provides an interesting picture of how particular is the behavior of the Seshadri constants.
LDN 1622 has previously been identified as a possible strong source of dust-correlated Anomalous Microwave Emission (AME). Previous observations were limited by resolution meaning that the radio emission could not be compared with current generation high-resolution infrared data from Herschel, Spitzer or WISE. This Paper presents arcminute resolution mapping observations of LDN 1622 at 4.85 GHz and 13.7 GHz using the 100 m Robert C. Byrd Green Bank Telescope. The 4.85 GHz map reveals a corona of free-free emission enclosing LDN 1622 that traces the photo-dissociation region of the cloud. The brightest peaks of the 4.85 GHz map are found to be within 10% agreement with the expected free-free predicted by SHASSA H{\alpha} data of LDN 1622. At 13.7 GHz the AME flux density was found to be 7.0 $\pm$ 1.4 mJy and evidence is presented for a rising spectrum between 13.7 GHz and 31 GHz. The spinning dust model of AME is found to naturally account for the flux seen at 13.7 GHz. Correlations between the diffuse 13.7 GHz emission and the diffuse mid-infrared emission are used to further demonstrate that the emission originating from LDN 1622 at 13.7 GHz is described by the spinning dust model.