ShantanuT01/DACTYL-Pretraining huggingface dataset:
Future galaxy surveys require one percent precision in the theoretical knowledge of the power spectrum over a large range including very nonlinear scales. While this level of accuracy is easily obtained in the linear regime with perturbation theory, it represents a serious challenge for small scales where numerical simulations are required. In this paper we quantify the precision of present-day $N$-body methods, identifying main potential error sources from the set-up of initial conditions to the measurement of the final power spectrum. We directly compare three widely used $N$-body codes, Ramses, Pkdgrav3, and Gadget3 which represent three main discretisation techniques: the particle-mesh method, the tree method, and a hybrid combination of the two. For standard run parameters, the codes agree to within one percent at $k\leq1$ $h\,\rm Mpc^{-1}$ and to within three percent at $k\leq10$ $h\,\rm Mpc^{-1}$. We also consider the bispectrum and show that the reduced bispectra agree at the sub-percent level for $k\leq 2$ $h\,\rm Mpc^{-1}$. In a second step, we quantify potential errors due to initial conditions, box size, and resolution using an extended suite of simulations performed with our fastest code Pkdgrav3. We demonstrate that the simulation box size should not be smaller than $L=0.5$ $h^{-1}\rm Gpc$ to avoid systematic finite-volume effects (while much larger boxes are required to beat down the statistical sample variance). Furthermore, a maximum particle mass of $M_{\rm p}=10^{9}$ $h^{-1}\rm M_{\odot}$ is required to conservatively obtain one percent precision of the matter power spectrum. As a consequence, numerical simulations covering large survey volumes of upcoming missions such as DES, LSST, and Euclid will need more than a trillion particles to reproduce clustering properties at the targeted accuracy.
We consider the origins of Higher Tannaka duality, as well as it consequences. In a first time we review the work of J. Wallbridge on that subject, which shows in particular that Hopf algebras are essential to generating Tannakian infinity-categories. While doing so we provide an analysis of what it means for Higher Tannaka to be a reconstruction program for stacks. Putting Wallbridge's work in perspective paves the way for causal models in Higher Category Theory. We introduce two interesting concepts that we deem to be instrumental within this framework; that of blow-ups of categories as well as that of fractal infinity-categories.
We demonstrate a simple method for testing the significance of peaks in the periodogram of red noise data. The procedure was designed to test for spurious periodicities in X-ray light curves of active galaxies, but can be used quite generally to test for periodic components against a background noise spectrum assumed to have a power law shape. The method provides a simple and fast test of the significance of candidate periodic signals in short, well-sampled time series such as those obtained from XMM-Newton observations of Seyfert galaxies, without the need for Monte Carlo simulations. A full account is made of the number of trials and the uncertainties inherent to the model fitting. Ignoring these subtle effects can lead to substantially overestimated significances. These difficulties motivate us to demand high standards of detection (minimum >99.9 per cent confidence) for periodicities in sources that normally show red noise spectra. The method also provides a simple means to estimate the power spectral index, which may be an interesting parameter itself, regardless of the presence/absence of periodicities.
We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.
We report benchmark calculations of electroabsorption in semiconducting single-walled carbon nanotubes to provide motivation to experimentalists to perform electroabsorption measurement on these systems. We show that electroabsorption can detect continuum bands in different energy manifolds, even as other nonlinear absorption measurements have failed to detect them. Direct determination of the binding energies of excitons in higher manifolds thereby becomes possible. We also find that electroabsorption can provide evidence for Fano-type coupling between the second exciton and the lowest continuum band states.
We present long-duration numerical simulations of the tidal disruption of stars modelled with accurate stellar structures and spanning a range of pericentre distances, corresponding to cases where the stars are partially and completely disrupted. We substantiate the prediction that the late-time power-law index of the fallback rate $n_{\infty} \simeq -5/3$ for full disruptions, while for partial disruptions---in which the central part of the star survives the tidal encounter intact---we show that $n_{\infty} \simeq -9/4$. For the subset of simulations where the pericenter distance is close to that which delineates full from partial disruption, we find that a stellar core can reform after the star has been completely destroyed; for these events the energy of the zombie core is slightly positive, which results in late-time evolution from $n \simeq -9/4$ to $n \simeq -5/3$. We find that self-gravity can generate an $n(t)$ that deviates from $n_{\infty}$ by a small but significant amount for several years post-disruption. In one specific case with the stellar pericenter near the critical value, we find self-gravity also drives the re-collapse of the central regions of the debris stream into a collection of several cores while the rest of the stream remains relatively smooth. We also show that it is possible for the surviving stellar core in a partial disruption to acquire a circumstellar disc that is shed from the rapidly rotating core. Finally, we provide a novel analytical fitting function for the fallback rates that may also be useful in a range of contexts beyond TDEs.
We perform classical molecular dynamics to investigate the effects of mechanical strain on single-layer black phosphorus nanoresonators at different temperatures. We find that the resonant frequency is highly anisotropic in black phosphorus due to its intrinsic puckered configuration, and that the quality factor in the armchair direction is higher than in the zigzag direction at room temperature. The quality factors are also found to be intrinsically larger than graphene and MoS2 nanoresonators. The quality factors can be increased by more than a factor of two by applying tensile strain, with uniaxial strain in the armchair direction being most effective. However, there is an upper bound for the quality factor increase due to nonlinear effects at large strains, after which the quality factor decreases. The tension induced nonlinear effect is stronger along the zigzag direction, resulting in a smaller maximum strain for quality factor enhancement.
We study the estimation of a stable Cox-Ingersoll-Ross model, which is a special subcritical continuous-state branching process with immigration. The process is characterized in terms of some stochastic equations. The exponential ergodicity and strong mixing property of the process and the heavy tail behavior of some related random sequences are studied. We also establish the convergence of some point processes and partial sums associated with the model. From those results, we derive the consistency and central limit theorems of the conditional least squares estimators and the weighted conditional least squares estimators of the drift parameters based on low frequency observations. A weakly consistent estimator is also proposed for the volatility coefficient based on high frequency observations.
We construct thin shell wormholes in the magnetic Melvin universe. It is shown that in order to make a TSW in the Melvin spacetime the radius of the throat can not be larger than $\frac{2}{B_{0}}$ in which $B_{0}$ is the magnetic field constant. We also analyze the stability of the constructed wormhole in terms of a linear perturbation around the equilibrium point. In our stability analysis we scan a full set of the Equation of States such as Linear Gas, Chaplygin Gas, Generalized Chaplygin Gas, Modified Generalized Chaplygin Gas and Logarithmic Gas. Finally we extend our study to the wormhole solution in the unified Melvin and Bertotti-Robinson spacetime. In this extension we show that for some specific cases, the local energy density is partially positive but the total energy which supports the wormhole is positive.
The TEDI (TripleSpec - Exoplanet Discovery Instrument) will be the first instrument fielded specifically for finding low-mass stellar companions. The instrument is a near infra-red interferometric spectrometer used as a radial velocimeter. TEDI joins Externally Dispersed Interferometery (EDI) with an efficient, medium-resolution, near IR (0.9 - 2.4 micron) echelle spectrometer, TripleSpec, at the Palomar 200" telescope. We describe the instrument and its radial velocimetry demonstration program to observe cool stars.
This is a manuscript to be published as a book chapter. The text summarizes some of my critics concerning Everett's theory as seen from the perspective of a Bohmian. This is the second draft and comments are still welcome.
I gamely try to disentangle ideas that have been confused with one another.
The global structure of solutions of the Einstein equations coupled to the Vlasov equation is investigated in the presence of a two-dimensional symmetry group. It is shown that there exist global CMC and areal time foliations. The proof is based on long-time existence theorems for the partial differential equations resulting from the Einstein-Vlasov system when conformal or areal coordinates are introduced.
[Abridged] We assemble a sample of 45 intermediate X-ray luminosity galaxy clusters at low redshifts using SDSS data to conduct a comprehensive investigation into the photometric variation of red sequence modal galaxy colours with environment. The clusters span a range of Bautz-Morgan types and evolutionary stages and are representative of the global underlying intermediate L_X cluster sample. We define cluster membership using SDSS spectroscopic data and characterize the clusters by deriving new recession velocities, velocity dispersions and other parameters for each. We construct colour-magnitude diagrams for each of these clusters and obtain the position of the red sequence using a robust line fitting algorithm with a Lorentzian merit function. In doing so, we describe a population of discordant points on the colour-magnitude plane which are the result of photometric blending, dust and other causes. By fitting the clusters with Schechter functions to derive M* values in each SDSS passband, we combine the red sequence of the galaxy clusters together to form a composite sample. We detail how the modal colour value of the red sequence varies with radius from the centre of this composite cluster and local galaxy density for all SDSS colours. In agreement with previous studies, these colours are shown to systematically move blueward with increasing distance from the cluster centres, or equivalently lower local galaxy density, whilst the width of the red sequence increases. This supports the idea that the galaxies at the outskirts of these clusters have younger luminosity-weighted ages than those at the core indicating their star formation has been quenched more recently than in the core. A comparison of our derived gradients in (g-r) with earlier works tentatively suggests that these gradients vary with redshift which would reflect the hierarchical build-up of the red sequence over time.
We introduce a stochastic model of two-dimensional Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other (plasma case) and at negative temperatures, like-sign vortices attract each other (gravity case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N-body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N, where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for $N\to +\infty$. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-H\"uckel approximation valid at the order O(1/N). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-H\"uckel model of electrolytes.
Recent work about synthetic indoor datasets from perspective views has shown significant improvements of object detection results with Convolutional Neural Networks(CNNs). In this paper, we introduce THEODORE: a novel, large-scale indoor dataset containing 100,000 high-resolution diversified fisheye images with 14 classes. To this end, we create 3D virtual environments of living rooms, different human characters and interior textures. Beside capturing fisheye images from virtual environments we create annotations for semantic segmentation, instance masks and bounding boxes for object detection tasks. We compare our synthetic dataset to state of the art real-world datasets for omnidirectional images. Based on MS COCO weights, we show that our dataset is well suited for fine-tuning CNNs for object detection. Through a high generalization of our models by means of image synthesis and domain randomization, we reach an AP up to 0.84 for class person on High-Definition Analytics dataset.
We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion formula of Caron-Huot and the integral (Mellin) representation of conformal blocks, we show that the contribution from individual exchanges to anomalous dimensions and corrections to the OPE coefficients for "double-twist" operators $[\mathcal{O}_1\mathcal{O}_2]_{\Delta,J}$ in $s-$channel can be written at finite conformal spin in terms of generalized Wilson polynomials. This approach is democratic {\it wrt} space-time dimensions, thus generalizing the earlier findings to cases where closed form expressions of the conformal blocks are not available.
We show that infinite variety of Poincar\'{e} bialgebras with nontrivial classical r-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincar\'{e} bialgebras to quantum Poincar\'{e} groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition law in any order of dimensionfull deformation parmeter $\lambda$ (from physical reasons we can put $\lambda = \lambda_{p}$ where $\lambda_{p}$ is the Planck lenght). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of basis in Poincar\'{e} algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct. In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can help to resolve the problem of consistent passage to macroscopic classical limit.
In gravitational microlensing, interference visibility is established when the spectral resolution of the observation is less than the reciprocal of the time delay difference. Using high resolutionspectroscopy fringes will be visible at large path differences, even when the source emission is incoherent. This is possible because coherence can be established after interference has already occurred. Results of a laboratory test are presented which demonstrate this retroactive establishment of coherence.
Fifty years ago, in 1952, the first significant paper on accretion flows was written by Bondi. The subject has grown exponentially since then. In fact, today many of the satellites engaged in space physics research look for signatures of accretion processes in whatever objects are studied. In this review, I will touch upon the significant developments in these years in this subject, emphasizing mainly on accretion onto black holes. Since winds and accretions are generally studied under similar framework, some references of the winds/outflows studies will also be made.
We explore the evolution of the internal gas kinematics of star-forming galaxies from the peak of cosmic star-formation at $z\sim2$ to today. Measurements of galaxy rotation velocity $V_{rot}$, which quantify ordered motions, and gas velocity dispersion $\sigma_g$, which quantify disordered motions, are adopted from the DEEP2 and SIGMA surveys. This sample covers a continuous baseline in redshift from $z=2.5$ to $z=0.1$, spanning 10 Gyrs. At low redshift, nearly all sufficiently massive star-forming galaxies are rotationally supported ($V_{rot}>\sigma_g$). By $z=2$, the percentage of galaxies with rotational support has declined to 50$\%$ at low stellar mass ($10^{9}-10^{10}\,M_{\odot}$) and 70$\%$ at high stellar mass ($10^{10}-10^{11}M_{\odot}$). For $V_{rot}\,>\,3\,\sigma_g$, the percentage drops below 35$\%$ for all masses. From $z\,=\,2$ to now, galaxies exhibit remarkably smooth kinematic evolution on average. All galaxies tend towards rotational support with time, and it is reached earlier in higher mass systems. This is mostly due to an average decline in $\sigma_g$ by a factor of 3 since a redshift of 2, which is independent of mass. Over the same time period, $V_{rot}$ increases by a factor of 1.5 for low mass systems, but does not evolve for high mass systems. These trends in $V_{rot}$ and $\sigma_g$ with time are at a fixed stellar mass and should not be interpreted as evolutionary tracks for galaxy populations. When galaxy populations are linked in time with abundance matching, not only does $\sigma_g$ decline with time as before, but $V_{rot}$ strongly increases with time for all galaxy masses. This enhances the evolution in $V_{rot}/\sigma_g$. These results indicate that $z\,=\,2$ is a period of disk assembly, during which the strong rotational support present in today's massive disk galaxies is only just beginning to emerge.
At low energy, electrons in doped graphene sheets behave like massless Dirac fermions with a Fermi velocity which does not depend on carrier density. Here we show that modulating a two-dimensional electron gas with a long-wavelength periodic potential with honeycomb symmetry can lead to the creation of isolated massless Dirac points with tunable Fermi velocity. We provide detailed theoretical estimates to realize such artificial graphene-like system and discuss an experimental realization in a modulation-doped GaAs quantum well. Ultra high-mobility electrons with linearly-dispersing bands might open new venues for the studies of Dirac-fermion physics in semiconductors.
The ternary Golay code -- one of the first and most beautiful classical error-correcting codes discovered -- naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distill the "most magic" qutrit state -- an eigenstate of the qutrit Fourier transform known as the strange state -- with cubic error-suppression and a remarkably high threshold. It also distills the "second-most magic" qutrit state, the Norell state, with quadratic error-suppression and an equally high threshold to depolarizing noise.
The close theoretical analogy between the physics of rapidly rotating atomic Bose condensates and the quantum Hall effect (i.e., a two dimensional electron gas in a strong magnetic field) was first pointed out ten years ago. As a consequence of this analogy, a large number of strongly correlated quantum Hall-type states have been predicted to occur in rotating Bose systems, and suggestions have been made how to manipulate and observe their fractional quasiparticle excitations. Due to a very rapid development in experimental techniques over the past years, experiments on BEC now appear to be close to reaching the quantum Hall regime. This paper reviews the theoretical and experimental work done to date in exploring quantum Hall physics in cold bosonic gases. Future perspectives are discussed briefly, in particular the idea of exploiting some of these strongly correlated states in the context of topological quantum computing.
We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.
The problem of appearance invariant subject recognition for Entry-Exit surveillance applications is addressed. A novel Semantic Entry-Exit matching model that makes use of ancillary information about subjects such as height, build, complexion and clothing color to endorse exit of every subject who had entered private area is proposed in this paper. The proposed method is robust to variations in clothing. Each describing attribute is given equal weight while computing the matching score and hence the proposed model achieves high rank-k accuracy on benchmark datasets. The soft biometric traits used as a combination though cannot achieve high rank-1 accuracy, it helps to narrow down the search to match using reliable biometric traits such as gait and face whose learning and matching time is costlier when compared to the visual soft biometrics.
Boundary states that preserve supersymmetry are constructed for fractional D-strings with travelling waves on a ${\bf C}^3/ {{\bf Z}_2\times {\bf Z}_2}$ orbifold. The gravitational radiation emitted between two D-strings with antiparallel travelling waves is calculated.
We present a pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.
We establish a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of M\"{o}bius and divisor functions. Specifically, we prove that the ratios conjecture and an arithmetic correlations conjecture imply the same result. This provides new support for the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. Our main theorem generalises a recent calculation pertaining to the special case of two-over-two ratios.