ShantanuT01/DACTYL-Pretraining huggingface dataset:
Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering statistics of discrete density peaks are difficult to evaluate. For this reason, local bias schemes have received considerably more attention in the literature thus far. In this paper, we show that the 2-point correlation function of maxima of a homogeneous and isotropic Gaussian random field can be thought of, up to second order at least, as arising from a local bias expansion formulated in terms of rotationally invariant variables. This expansion relies on a unique smoothing scale, which is the Lagrangian radius of dark matter halos. The great advantage of this local bias approach is that it circumvents the difficult computation of joint probability distributions. We demonstrate that the bias factors associated with these rotational invariants can be computed using a peak-background split argument, in which the background perturbation shifts the corresponding probability distribution functions. Consequently, the bias factors are orthogonal polynomials averaged over those spatial locations that satisfy the peak constraint. In particular, asphericity in the peak profile contributes to the clustering at quadratic and higher order, with bias factors given by generalized Laguerre polynomials. We speculate that our approach remains valid at all orders, and that it can be extended to describe clustering statistics of any point process of a Gaussian random field. Our results will be very useful to model the clustering of discrete tracers with more realistic collapse prescriptions involving the tidal shear for instance.
Superbursts were discovered at the beginning of this millennium. Just like type-I X-ray bursts, they are thought to be due to thermonuclear shell flashes on neutron stars, only igniting much deeper. With respect to type-I bursts, they last 10$^3$ times longer, are 10$^3$ as rare, ignite 10$^3$ times deeper (in column depth) and are thought to be fueled by carbon instead of hydrogen and helium. Observationally, they are sometimes hard to distinguish from intermediate duration bursts which are due to pure helium flashes on cold neutron stars. So far, 26 superbursts have been detected from 15 neutron stars in low-mass X-ray binaries that also exhibit type-I bursts. They are very difficult to catch and only 2 have been measured with highly sensitive instrumentation. Superbursts are sensitive probes of the neutron star crust and the accretion disk. The superburst phenomenon is not fully understood. Questions remain about the nature of the fuel, the collection of that fuel and the ignition conditions. The current state of affairs is reviewed and possible resolutions that lay ahead in the future discussed.
We make a comparison between small scale chromospheric brightenings and energy release processes through examining the temporal evolution of sequential chromospheric brightenings (SCBs), derive propagation velocities, and propose a connection of the small-scale features to solar flares. Our automated routine detects and distinguishes three separate types of brightening regularly observed in the chromosphere: plage, flare ribbon, and point brightenings. By studying their distinct dynamics, we separate out the flare-associated bright points commonly known as SCBs and identify a propagating Moreton wave. Superimposing our detections on complementary off-band images, we extract a Doppler velocity measurement beneath the point brightening locations. Using these dynamic measurements, we put forward a connection between point brightenings, the erupting flare, and overarching magnetic loops. A destabilization of the pre-flare loop topology by the erupting flare directly leads to the SCBs observed.
Hardly any of the observed black hole accretion disks in X-Ray binaries and active galaxies shows constant flux. When the local stochastic variations of the disk occur at specific regions where a resonant behaviour takes place, there appear the Quasi-Periodic Oscillations (QPOs). If the global structure of the flow and its non-linear hydrodynamics affects the fluctuations, the variability is chaotic in the sense of deterministic chaos. Our aim is to solve a problem of the stochastic versus deterministic nature of the black hole binaries vari- ability. We use both observational and analytic methods. We use the recurrence analysis and we study the occurence of long diagonal lines in the recurrence plot of observed data series and compare it to the sur- rogate series. We analyze here the data of two X-Ray binaries - XTE J1550-564, and GX 339-4 observed by Rossi X-ray Timing Explorer. In these sources, the non-linear variability is expected because of the global conditions (such as the mean accretion rate) leading to the pos- sible instability of an accretion disk. The thermal-viscous instability and fluctuations around the fixed-point solution occurs at high accretion rate, when the radiation pressure gives dominant contribution to the stress tensor.
In this paper, we study how small a box contains at least two points from a modular cubic polynomial $y \equiv a x^3 + b x^2 + c x + d \pmod p$ with $(a, p) = 1$. We prove that some square of side length $p^{1/6 + \epsilon}$ contains two such points.
We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations.   Keywords: extremal optimization. flat-histogram algorithm, equal-hit algorithm, spin-glass model, ground state.
This paper predicts the effect of the Dzyaloshinskii-Moriya interaction (DMI) and spin Hall effect in the spin-torque diode response of a Magnetic Tunnel Junction built over a Tantalum strip. Our results indicate that, for a microwave current large enough, the DMI can change qualitatively the resonant response by splitting the ferromagnetic resonance peak. We also find out that the two modes have a non-uniform spatial distribution.
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.
The generation of ac modulated quantized current waveforms using a semiconductor non-adiabatic single electron pump is demonstrated. In standard operation the single electron pump generates a quantized output current of I = ef where e is the charge of the electron and f is the pumping frequency. Suitable frequency modulation of f allows the generation of ac modulated output currents with different characteristics. By sinusoidal and saw tooth like modulation of f accordingly modulated quantized current waveforms with kHz modulation frequencies and peak currents up to 100 pA are obtained. Such ac quantized current sources could find applications ranging from precision ac metrology to on-chip signal generation.
We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In practice, since photons and gravitons are ubiquitous and scatter from massive particles, dynamical collapses of the former will effectively induce collapses of the latter. In non-relativistic models in which particle number is conserved and interactions are modelled by classical potentials, massive systems can be modelled as collections of elementary massive particles bound by potentials, interacting with an environment of photons and gravitons. In this picture, although the photon and/or graviton collapse dynamics effectively localize massive systems, these collapses take the effective form of approximate measurements on the environment whose effect on the massive systems is indirect. We argue that these environmental collapse models, like standard mass-dependent spontaneous localisation models, may be consistent with quantum experiments on microscopic systems while predicting very rapid effective collapse of macroscopic massive systems, and hence a potential solution to the quantum measurement problem. However, the models considered here have different experimental signatures from standard mass-dependent spontaneous localisation models. For example, they predict no deviations from standard quantum interferometry for mesoscopic systems of massive particles isolated from a decohering environment, nor do they predict anomalous spontaneous emission of radiation from isolated matter of the type prediction by standard mass-dependent spontaneous localization models. New experiments and analyses are required to obtain empirical bounds on the decoherence rate in our models.
We have adapted R-matrix theory to calculate phonon scattering across systems of molecular to mesoscopic scale. The key novelty of this work is that the only required information about the scattering region are its normal modes, which are evaluated only once for a system. Thus, R-matrix theory is a computationally efficient and simple approach to calculate phonon scattering in larger systems. To validate and to demonstrate the applicability of the theory, we apply it to two systems: a one dimensional chain of atoms and a graphene nanoribbon. In both cases, we discuss the effect of mass impurities on thermal transport.
Recently, Barraza-Rojas have described the action of the full automorphisms group on the Fermat curve of degree $p$, for $p$ a prime integer, and obtained the group algebra decomposition of the corresponding Jacobian variety. In this short note we observe that the factors in such a decomposition are given by the Jacobian varieties of certain $p$-gonal curves.
Context information plays an indispensable role in the success of semantic segmentation. Recently, non-local self-attention based methods are proved to be effective for context information collection. Since the desired context consists of spatial-wise and channel-wise attentions, 3D representation is an appropriate formulation. However, these non-local methods describe 3D context information based on a 2D similarity matrix, where space compression may lead to channel-wise attention missing. An alternative is to model the contextual information directly without compression. However, this effort confronts a fundamental difficulty, namely the high-rank property of context information. In this paper, we propose a new approach to model the 3D context representations, which not only avoids the space compression but also tackles the high-rank difficulty. Here, inspired by tensor canonical-polyadic decomposition theory (i.e, a high-rank tensor can be expressed as a combination of rank-1 tensors.), we design a low-rank-to-high-rank context reconstruction framework (i.e, RecoNet). Specifically, we first introduce the tensor generation module (TGM), which generates a number of rank-1 tensors to capture fragments of context feature. Then we use these rank-1 tensors to recover the high-rank context features through our proposed tensor reconstruction module (TRM). Extensive experiments show that our method achieves state-of-the-art on various public datasets. Additionally, our proposed method has more than 100 times less computational cost compared with conventional non-local-based methods.
We present a theoretical approach to determine the electronic properties of nanoscale systems exhibiting strong electron-electron and electron-phonon interactions and coupled to metallic electrodes. This approach is based on an interpolative ansatz for the electronic self-energy which becomes exact both in the limit of weak and strong coupling to the electrodes. The method provides a generalization of previous interpolative schemes which have been applied to the purely electronic case extensively. As a test case we consider the single level Anderson-Holstein model. The results obtained with the interpolative ansatz are in good agreement with existing data from Numerical Renormalization Group calculations. We also check our results by considering the case of the electrodes represented by a few discrete levels which can be diagonalized exactly. The approximation describes properly the transition from the Kondo regime where electron-electron interactions dominate to the polaronic case characterized by a strong electron-phonon interaction.
We calculate the hydrodynamic time scales for a spherical ultra-relativistic shell that is decelerated by the ISM and discuss the possible relations between these time scales and the observed temporal structure in $\gamma$-ray bursts. We suggest that the bursts' duration is related to the deceleration time, the variability is related to the ISM inhomogeneities and precursors are related to internal shocks within the shell. Good agreement can be achieved for these quantities with reasonable, not fined tuned, astrophysical parameters. The difference between Newtonian and relativistic reverse shocks may lead to the observed bimodal distribution of bursts' durations.
In this paper we review a number of issues on the security of quantum key distribution (QKD) protocols that bear directly on the relevant physics or mathematical representation of the QKD cryptosystem. It is shown that the cryptosystem representation itself may miss out many possible attacks which are not accounted for in the security analysis and proofs. Hence the final security claims drawn from such analysis are not reliable, apart from foundational issues about the security criteria that are discussed elsewhere. The cases of continuous-variable QKD and multi-photon sources are elaborated upon.
In this third paper of a series on the precision of obtaining ages of stellar populations using the full spectrum fitting technique, we examine the precision of this technique in deriving possible age spreads within a star cluster. We test how well an internal age spread can be resolved as a function of cluster age, population mass fraction, and signal-to-noise (S/N) ratio. For this test, the two ages (Age (SSP1) and Age (SSP2)) are free parameters along with the mass fraction of SSP1. We perform the analysis on 118,800 mock star clusters covering all ages in the range 6.8 < log (age/yr) < 10.2, with mass fractions from 10% to 90% for two age gaps (0.2 dex and 0.5 dex). Random noise is added to the model spectra to achieve S/N ratios between 50 to 100 per wavelength pixel. We find that the mean of the derived Age (SSP1) generally matches the real Age (SSP1) to within 0.1 dex up to ages around log (age/yr) = 9.5. The precision decreases for log (age/yr) > 9.6 for any mass fraction or S/N, due to the similarity of SED shapes for those ages. In terms of the recovery of age spreads, we find that the derived age spreads are often larger than the real ones, especially for log(age/yr) < 8.0 and high mass fractions of SSP1. Increasing the age gap in the mock clusters improves the derived parameters, but Age (SSP2) is still overestimated for the younger ages.
In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtained by tracing out the ancillary system. An example is provided to illustrate the non-Markovian dynamics of the principal system.
We present a study of the extent to which the Sellwood & Binney radial migration of stars is affected by their vertical motion about the midplane. We use both controlled simulations in which only a single spiral mode is excited, as well as slightly more realistic cases with multiple spiral patterns and a bar. We find that rms angular momentum changes are reduced by vertical motion, but rather gradually, and the maximum changes are almost as large for thick disc stars as for those in a thin disc. We find that particles in simulations in which a bar forms suffer slightly larger angular momentum changes than in comparable cases with no bar, but the cumulative effect of multiple spiral events still dominates. We have determined that vertical action, and not vertical energy, is conserved on average during radial migration.
Effects of disorder on the electronic transport properties of graphene are strongly affected by the Dirac nature of the charge carriers in graphene. This is particularly pronounced near the Dirac point, where relativistic charge carriers cannot efficiently screen the impurity potential. We have studied time-dependent conductance fluctuations and magnetoresistance in graphene in the close vicinity of the Dirac point. We show that the fluctuations are due to the quantum interference effects due to scattering on impurities, and find an unusually large reduction of the relative noise power in magnetic field, possibly indicating that an additional symmetry plays an important role in this regime.
We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t < \bar{t}. In this initial time interval classical correlations decay. For t > \bar{t}, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time \bar{t} the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.
In this note we shall review recent work on generalizing rational curve counting to perturbative heterotic theories.
X-ray spectroscopic measurements of the Cygnus Loop supernova remnant indicate that metal abundances throughout most of the remnant's rim are depleted to about 0.2 times the solar value. However, recent X-ray studies have revealed in some narrow regions along the outermost rim anomalously "enhanced" abundances (up to about 1 solar). The reason for these anomalous abundances is not understood. Here, we examine X-ray spectra in annular sectors covering nearly the entire rim of the Cygnus Loop using Suzaku (21 pointings) and XMM-Newton (1 pointing). We find that spectra in the "enhanced" abundance regions commonly show a strong emission feature at about 0.7 keV. This feature is likely a complex of He-like O K(gamma + delta + epsilon), although other possibilities cannot be fully excluded. The intensity of this emission relative to He-like O Kalpha appears to be too high to be explained as thermal emission. This fact, as well as the spatial concentration of the anomalous abundances in the outermost rim, leads us to propose an origin from charge-exchange processes between neutrals and H-like O. We show that the presence of charge-exchange emission could lead to the inference of apparently "enhanced" metal abundances using pure thermal emission models. Accounting for charge-exchange emission, the actual abundances could be uniformly low throughout the rim. The overall abundance depletion remains an open question.
This is an expository article on the adic tropicalization of algebraic varieties. We outline joint work with Sam Payne in which we put a topology and structure sheaf of local topological rings on the exploded tropicalization. The resulting object, which blends polyhedral data of the tropicalization with algebraic data of the associated initial degenerations, is called the adic tropicalization. It satisfies a theorem of the form "Huber analytification is the limit of all adic tropicalizations." We explain this limit theorem in the present article, and illustrate connections between adic tropicalization and the curve complexes of O. Amini and M. Baker.
She et al. (Paper I) assembled a catalog of nearby galaxies observed with the Chandra X-ray observatory, by cross-matching galaxies in the NASA Extragalactic Database (NED) within 50 Mpc and the Chandra archive. That sample has enabled searches of low-mass black holes associated with late-type, bulgeless galaxies and studies of the accretion physics related to low-luminosity active galactic nuclei (LLAGNs). Using a similar approach, here we construct an extended catalog up to 150 Mpc and make a cross-correlation with a catalog of nearby galaxy groups. The new catalog consists of 1,964 galaxies, out of which 1,692 have a redshift independent distance, 1,557 are listed in the galaxy group catalog with group properties available, and 782 are identified to be X-ray AGN candidates. Compared with the AGN sample in Paper I, the new sample is 2.5 times larger in size (782 vs. 314), with ~80% of the new members having an Eddington ratio less than 10^-4. We confirm that the conclusions based on the previous sample remain. With the new sample, we compare AGN fractions between early-type and late-type galaxies, and between central and satellite galaxies in groups, and find no significant difference. This suggests that the secular process is not the dominant mechanism feeding AGNs in the local universe.
We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as gravitational variables, and derive explicit formulas for their Poisson brackets and their time evolution.
The study of local models using finite shared randomness originates from the consideration about the cost of classically simulating entanglement in composite quantum systems. We construct explicitly two families of local-hidden-state (LHS) models for T-states, by mapping the problem to the Werner state. The continuous decreasing of shared randomness along with entanglement, as the anisotropy increases, can be observed in the one from the most economical model for the Werner state. The construction of the one for separable states shows that the separable boundary of T-states can be generated from the one of the Werner state, and the cost is 2 classical bits.
Given $g\ge 1$, the number $n(g)$ of numerical semigroups $S \subset \N$ of genus $|\N \setminus S|$ equal to $g$ is the subject of challenging conjectures of Bras-Amor\'os. In this paper, we focus on the counting function $n(g,2)$ of \textit{two-generator} numerical semigroups of genus $g$, which is known to also count certain special factorizations of $2g$. Further focusing on the case $g=p^k$ for any odd prime $p$ and $k \ge 1$, we show that $n(p^k,2)$ only depends on the class of $p$ modulo a certain explicit modulus $M(k)$. The main ingredient is a reduction of $\gcd(p^\alpha+1, 2p^\beta+1)$ to a simpler form, using the continued fraction of $\alpha/\beta$. We treat the case $k=9$ in detail and show explicitly how $n(p^9,2)$ depends on the class of $p$ mod $M(9)=3 \cdot 5 \cdot 11 \cdot 17 \cdot 43 \cdot 257$.