ShantanuT01/DACTYL-Pretraining huggingface dataset:
The goal of this investigation is to reconstruct the cosmic star formation rate density history from local observations and in doing so to gain insight into how galaxies might have formed and evolved. A new chemical evolution model is described which accounts for the formation of globular clusters as well as the accompanying field stars. When this model is used in conjunction with the observed age metallicity relations for the clusters and with input which allows for the formation of the nearly universally observed bimodal distribution of globular clusters, star formation rates are obtained. By confining attention to a representative volume of the local universe, these rates allow a successful reconstruction of the Madau plot while complementary results similtaneously satisfy many local cosmological constraints. A physical framework for galaxy formation is presented which incorporates the results from this chemical evolution model and assumes an anisotropic collapse. In addition to providing the `classical' halo, bulge and disk components, the model also predicts a new stellar halo component with peak [Fe/H] ~ -0.8 and disk-like angular momentum and allows for the formation of a thick disk as outlined by the group of metal rich globular clusters. Milky Way counterparts of the latter two components are identified.
We report on the first joint search for gravitational waves by the TAMA and LIGO collaborations. We looked for millisecond-duration unmodelled gravitational-wave bursts in 473 hr of coincident data collected during early 2003. No candidate signals were found. We set an upper limit of 0.12 events per day on the rate of detectable gravitational-wave bursts, at 90% confidence level. From simulations, we estimate that our detector network was sensitive to bursts with root-sum-square strain amplitude above approximately 1-3x10^{-19} Hz^{-1/2} in the frequency band 700-2000 Hz. We describe the details of this collaborative search, with particular emphasis on its advantages and disadvantages compared to searches by LIGO and TAMA separately using the same data. Benefits include a lower background and longer observation time, at some cost in sensitivity and bandwidth. We also demonstrate techniques for performing coincidence searches with a heterogeneous network of detectors with different noise spectra and orientations. These techniques include using coordinated signal injections to estimate the network sensitivity, and tuning the analysis to maximize the sensitivity and the livetime, subject to constraints on the background.
The problem of the event horizon in relativistic gravity is discussed. Singular solutions in general relativity are well known. The Schwarschild metric of a spherical mass is singular at zero ($r = 0$) and at the event horizon ($r = r_g$). Both features reflect the existence of the phenomenon of collapse in general relativity for compact masses exceeding $3M_{\odot }$. A material particle crossing the event horizon falls into a central singularity according to the classical theory of general relativity. In the quantum theory of gravity, there may be no central singularity. The physics of the event horizon is currently being refined. A promising technique is the study of gravitational waves (GW) accompanying the merger of binary black holes at the ringdown stage. GW observations of quasi-normal modes of the newly formed super dense remnant will help clarify the physics of the event horizon.
In this paper we consider a family of active scalars with a velocity field given by $u = \Lambda^{-1+\alpha}\nabla^{\perp} \theta$, for $\alpha \in (0,1)$. This family of equations is a more singular version of the two-dimensional Surface Quasi-Geostrophic (SQG) equation, which would correspond to $\alpha=0$.   We consider the evolution of sharp fronts by studying families of almost-sharp fronts. These are smooth solutions with simple geometry in which a sharp transition in the solution occurs in a tubular neighbourhood (of size $\delta$). We study their evolution and that of compatible curves, and introduce the notion of a spine for which we obtain improved evolution results, gaining a full power (of $\delta$) compared to other compatible curves.
We investigate a processor sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue, or renege, before completing service. The corresponding stochastic processes are represented by measure valued Markov processes on R^2\_+. A scaling procedure that gives rise to a fluid model with a nontrivial, yet tractable steady state behavior, is presented. This fluid model model captures many essential features of the underlying stochastic model, and it is used to analyze the impact of impatience in processor sharing queues.
According to the Schwarz symmetry principle, every harmonic function vanishing on a real analytic curve has an odd continuation, while a harmonic function satisfying homogeneous Neumann condition has the even continuation. There are different generalizations of the Schwarz symmetry principle. Most of them are dealing with homogeneous conditions and the Dirichlet case. Using a technique of Dirichlet to Neumann and Robin to Neumann operators, we derive reflection formulae for nonhomogeneous Neumann and Robin conditions from a reflection formula subject to a nonhomogeneous Dirichlet condition.
(Ga,Mn)As in wurtzite crystal structure, is coherently grown by molecular beam epitaxy on the {1100} side facets of wurtizte (Ga,In)As nanowires and further encapsulated by (Ga,Al)As and low temperature GaAs. For the first time a true long-range ferromagnetic magnetic order is observed in non-planar (Ga,Mn)As, which is attributed to a more effective hole confinement in the shell containing Mn by a proper selection/choice of both the core and outer shell materials.
We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length $y$ around $x$, where $y\ll (\log x)^2$. In particular we conjecture that the maximum grows surprisingly slowly as $y$ ranges from $\log x$ to $(\log x)^2$. We will show that our conjectures are somewhat supported by available data, though not so well that there may not be room for some modification.
Proton radii of nuclei in the $sd$ shell depart appreciably from the asymptotic law, $\rho_{\pi}=\rho_0A^{1/3}$. The departure exhibits systematic trends fairly well described by a single phenomenological term in the Duflo-Zuker formulation, which also happens to explain the sudden increase in slope in the isotope shifts of several chains at neutron number $N=28$. It was recently shown that this term is associated with the abnormally large size of the $s_{1/2}$ and $p$ orbits in the $sd$ and $pf$ shells respectively. Further to explore the problem, we propose to calculate microscopically radii in the former. Since the (square) radius is basically a one body operator, its evolution is dictated by single particle occupancies determined by shell model calculations. Assuming that the departure from the asymptotic form is entirely due to the $s_{1/2}$ orbit, the expectation value $\langle s_{1/2}|r^2|s_{1/2}\rangle$ is determined by demanding that its evolution be such as to describe well nuclear radii. It does, for an orbit that remains very large (about 1.6 fm bigger than its $d$ counterparts) up to $N,\,Z=14$ then drops abruptly but remains some 0.6 fm larger than the $d$ orbits. An unexpected behavior bound to challenge our understanding of shell formation.
Let $C$ be a real-valued $M\times M$ matrix with singular values $\lambda_1\ge...\ge\lambda_M$ and $E$ a random matrix of centered i.i.d. entries with finite fourth moment. In this paper we give a universal upper bound on the expectation of $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$, where $X:=C+E$ and $\hat\pi_r$ (resp. $\pi_r$) is a rank-$r$ projection maximizing the Hilbert-Schmidt norm $||\tilde\pi_rX||_{S_2}$ (resp. $||\tilde\pi_rC||_{S_2}$) over the set $\S_{M,r}$ of all orthogonal rank-$r$ projections. This result is a generalization of a theorem for Gaussian matrices due to Rohde (2012). Our approach differs substantially from the techniques of the mentioned article. We analyze $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$ from a rather deterministic point of view by an upper bound on $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$, whose randomness is totally determined by the largest singular value of $E$.
Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that $M_n$ is singular is at most $(1/\sqrt{2} + o(1))^n$, improving on the previous best upper bound of $(3/4 + o(1))^n$ proven by Tao and Vu in arXiv:math/0501313v2. This paper follows a similar approach to the Tao and Vu result, including using a variant of their structure theorem. We also extend this type of exponential upper bound on the probability that a random matrix is singular to a large class of discrete random matrices taking values in the complex numbers, where the entries are independent but are not necessarily identically distributed.
Treating the quark and diquark as elementary particles, the Bethe-Salpeter equation for the nucleon is solved numerically. The dependence of the mass on the diquark mass and on the coupling constants is investigated. The resulting relativistic quark-diquark-nucleon vertex is presented and discussed.
In this paper, we build the equivalence between rough differential equations driven by the lifted $G$-Brownian motion and the corresponding Stratonovich type SDE through the Wong-Zakai approximation. The quasi-surely convergence rate of Wong-Zakai approximation to $G-$SDEs with mesh-size $\frac{1}{n}$ in the $\alpha$-H\"older norm is estimated as $(\frac{1}{n})^{\frac12-}.$ As corollary, we obtain the quasi-surely continuity of the above RDEs with respect to uniform norm.
The fast variability observed in the X-ray emission from black-hole binaries has a very complex phenomenology, but offers the possibility to investigate directly the properties of the inner accretion flow. In particular, type-B oscillations in the 2-8 Hz range, observed in the Soft-Intermediate state, have been associated to the emission from a relativistic jet. We present the results of the timing and spectral analysis of a set of observations of the bright transient MAXI J1348-630 made with the NICER telescope. The observations are in the brightest part of the outburst and all feature a strong type-B QPO at ~4.5 Hz. We compute the energy dependence of the fractional rms and the phase lags at the QPO frequency, obtaining high signal-to-noise data and sampling for the first time at energies below 2 keV. The fractional rms decreases from more than 10% at 9 keV to 0.6% at 1.5 keV, and is constant below that energy. Taking the 2-3 keV band as reference, photons at all energies show a hard lag, increasing with the distance from the reference band. The behaviour below 2 keV has never been observed before, due to the higher energy bandpass of previous timing instruments. The energy spectrum can be fitted with a standard model for this state, consisting of a thin disc component and a harder power law, plus an emission line between 6 and 7 keV. We discuss the results, concentrating on the phase lags, and show that they can be interpreted within a Comptonization model.
N66/NGC346 is the largest and brightest HII region in the Small Magellanic Cloud and contains at least one known supernova remnant SNR0057-7226. Optical emission from the remnant is overwhelmed by the bright photoionized emission from the nebula, but the remnant has been detected by way of far ultraviolet absorption lines. Here we present data from the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite showing strong OVI and CIII emission from a position at the edge of SNR0057-7226. We also present high-resolution, long-slit Halpha spectra across N66 showing high- and low-velocity emission corresponding closely to the X-ray boundaries of the supernova remnant. We use these FUV and optical data to determine the physical parameters of the shock and interaction geometry with N66. We find that ionizing photons from the many massive cluster stars nearby likely affect the ionization balance in the post-shock gas, hindering the production of lower-ionization and neutral species. We discuss the importance and inherent difficulty of searching for supernova remnants in or near bright HII regions and suggest that the far ultraviolet provides a viable means to discover and study such remnants.
Classical light field rendering for novel view synthesis can accurately reproduce view-dependent effects such as reflection, refraction, and translucency, but requires a dense view sampling of the scene. Methods based on geometric reconstruction need only sparse views, but cannot accurately model non-Lambertian effects. We introduce a model that combines the strengths and mitigates the limitations of these two directions. By operating on a four-dimensional representation of the light field, our model learns to represent view-dependent effects accurately. By enforcing geometric constraints during training and inference, the scene geometry is implicitly learned from a sparse set of views. Concretely, we introduce a two-stage transformer-based model that first aggregates features along epipolar lines, then aggregates features along reference views to produce the color of a target ray. Our model outperforms the state-of-the-art on multiple forward-facing and 360{\deg} datasets, with larger margins on scenes with severe view-dependent variations.
Classical vorticity solution branches of the three dimensional incompressible Euler equation are constructed where a velocity component can blow up at some point after finite time for regular data in H2. Furthermore, vorticity can blow up after finite time for data in H2, and there are classical solution branches with regular data which develop weak singularities at some point of space time after finite time. The construction of these time-local solution branches is by viscosity limits of viscosity extensions of time-reversed Euler-type equations. The short time (weak) singularities are then initial values of local solution branches of the time-reversed Euler type equations, which are constructed via (not time-reversible) viscosity extensions. These solutions of the 3-D Euler equation have a straightforward interpretation as solution of incompressible Navier Stokes equation with time dependent force terms with restricted regularity or blow up of a velocity component at some point, as the time-dependent force term can be chosen such that it cancels the viscosity term of the incompressible Navier Stokes equation.
The earliest stars to form in the Universe were the first sources of light, heat and metals after the Big Bang. The products of their evolution will have had a profound impact on subsequent generations of stars. Recent studies of primordial star formation have shown that, in the absence of metals (elements heavier than helium), the formation of stars with masses 100 times that of the Sun would have been strongly favoured, and that low-mass stars could not have formed before a minimum level of metal enrichment had been reached. The value of this minimum level is very uncertain, but is likely to be between 10^{-6} and 10^{-4} that of the Sun. Here we show that the recent discovery of the most iron-poor star known indicates the presence of dust in extremely low-metallicity gas, and that this dust is crucial for the formation of lower-mass second-generation stars that could survive until today. The dust provides a pathway for cooling the gas that leads to fragmentation of the precursor molecular cloud into smaller clumps, which become the lower-mass stars.
We present the discovery of a powerful candidate microquasar in NGC 300, associated with the S 10 optical nebula (previously classified as a supernova remnant). Chandra images show four discrete X-ray knots aligned in the plane of the sky over a length of $\approx$150 pc. The X-ray emission from the knots is well fitted with a thermal plasma model at a temperature of $\approx$0.6 keV and a combined 0.3-8 keV luminosity of $\approx$10$^{37}$ erg s$^{-1}$. The X-ray core, if present at all, does not stand out above the thermal emission of the knots: this suggests that the accreting compact object is either currently in a dim state or occulted from our view. We interpret the emission from the knots as the result of shocks from the interaction of a jet with the interstellar medium (possibly over different epochs of enhanced activity). Cooler shock-heated gas is likely the origin also of the optical bubble and lobes near the X-ray structure, detected in images from the Hubble Space Telescope and the Very Large Telescope. In the radio bands, we observed the region with the Australia Telescope Compact Array, and discovered an elongated radio nebula (about 170 $\times$ 55 pc in size) with its major axis aligned with the chain of Chandra sources. The radio nebula has an integrated 5.5 GHz radio luminosity of $\approx$10$^{34}$ erg s$^{-1}$ for a distance of 1.88 Mpc. The morphology, size and luminosity of the extended X-ray, optical and radio structure suggest that NGC 300-S 10 belongs to the same class of powerful ($P_{\rm jet} > 10^{39}$ erg s$^{-1}$) microquasars as SS 433, Ho II X-1 and NGC 7793-S 26.
We update the experimental moments for the charm quark as computed in arXiv:hep-ph/0702103. and used in arXiv:0907.2110 and arXiv:1010.6157 for the determination of the charm-quark mass. The new value for the MSbar charm-quark mass reads mc(3GeV)=0.993+/-0.008 GeV.
We study the zero-temperature ground-state (GS) properties of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore, using the coupled cluster method (CCM) implemented to high orders of approximation. The system comprises a $J_{1}$--$J_{2}$ model on the checkerboard lattice, with isotropic Heisenberg interactions of strength $J_{1}$ between all nearest-neighbour pairs of spins on the square lattice, and of strength $J_{2}$ between half of the next-nearest-neighbour pairs (in the checkerboard pattern). We calculate results for the GS energy and average local GS on-site magnetization, using various antiferromagnetic classical ground states as CCM model states. We also give results for the susceptibility of one of these states against the formation of crossed-dimer valence-bond crystalline (CDVBC) ordering. The complete GS phase diagram is presented for arbitrary values of the frustration parameter $\kappa \equiv J_{2}/J_{1}$, and when each of the exchange couplings can take either sign.
An antichain of subsets is a set of subsets such that no subset in the antichain is a proper subset of any other subset in the antichain. The Dedekind number counts the total number of antichains of subsets of an n-element set. This paper investigates the interval structure of the lattice of antichains. Several partitioning theorems and counting formulas for the size of intervals are derived.
We consider minisuperspace models constituted of Bianchi I geometries with a free massless scalar field. The classical solutions are always singular (with the trivial exception of flat space-time), and always anisotropic once they begin anisotropic. When quantizing the system, we obtain the Wheeler-DeWitt equation as a four-dimensional massless Klein-Gordon equation. We show that there are plenty of quantum states whose corresponding bohmian trajectories may be non-singular and/or presenting large isotropic phases, even if they begin anisotropic, due to quantum gravitational effects. As a specific example, we exhibit field plots of bohmian trajectories for the case of gaussian superpositions of plane wave solutions of the Wheeler-DeWitt equation which have those properties. These conclusions are valid even in the absence of the scalar field.
We study analytically the general features of electroweak symmetry breaking in the context of the Minimal Supersymmetric Standard Model extended by one Higgs singlet. The exact analytical forms of the renormalization group evolutions of the Yukawa couplings and of the soft supersymmetry breaking parameters are derived to one-loop order. They allow on one hand controllable approximations in closed analytical form, and on the other a precise study of the behaviour of infrared quasi fixed point regimes which we carry out. Some of these regimes are shown to be phenomenologically inconsistent, leading to too small an effective $\mu$-parameter. The remaining ones serve as a suitable benchmark to understand analytically some salient aspects, often noticed numerically in the literature, in relation to the electroweak symmetry breaking in this model. The study does not need any specific assumption on $\tan \beta$ or on boundary conditions for the soft supersymmetry breaking parameters, thus allowing a general insight into the sensitivity of the low energy physics to high energy assumptions.
We discuss the new model expression $\bar{\alpha}_{an}(Q^2)$ recently obtained for the QCD running coupling with a regular ghost-free behavior in the "low $Q^2$" region. Being deduced from the standard "asymptotic-freedom" expression by imposing the $Q^2$-analyticity -- without any adjustable parameters -- it obeys nice features: (i) The universal limiting value $\bar{\alpha}_{an}(0)=4\pi /\beta_0 \simeq 1.4$ expressed only via group symmetry factors and independent of experimental estimates on the running coupling $\bar{\alpha}_s(Q^2)$ (of QCD scale parameter $\Lambda$). This value turns out to be stable with respect to higher order corrections; (ii) Stability of IR behavior with respect to higher-loop effects; (iii) Coherence between the experimental $\bar{\alpha}_{an}(M_{\tau}^2)$ value and integral information on IR $\bar{\alpha}_s(Q^2)$ behavior as extracted from jet physics data.
We give a new proof of the theorem of Boesch-Tindell and Farzad-Mahdian-Mahmoodian-Saberi-Sadri that a directed graph extends to a strongly connected digraph on the same vertex set if and only if it has no complete directed cut. Our proof bounds the number of edges needed for such an extension; we give examples to demonstrate sharpness. We apply the characterization to a problem on non-transitive dice.
We compute the back-reaction of pairs of codimension-two branes within an explicit flux-stabilized compactification, to trace how its properties depend on the parameters that define the brane-bulk couplings. Both brane tension and magnetic couplings to the stabilizing flux play an important role in the resulting dynamics, with the magnetic coupling allowing some of the flux to be localized on the branes (thus changing the flux-quantization conditions). We find that back-reaction lifts the classical flat directions of the bulk supergravity, and we calculate both the scalar potential and changes to the extra-dimensional and on-brane geometries that result, as functions of the assumed brane couplings. When linearized about simple rugby-ball geometries the resulting solutions allow a systematic exploration of the system's response. Several of the systems we explore have remarkable properties. Among these are a propensity for the extra dimensions to stabilize at exponentially large sizes, providing a mechanism for generating extremely large volumes. In some circumstances the brane-dilaton coupling allows the bulk dilaton to adjust to suppress the on-brane curvature parametrically below the change in brane tension, potentially providing a mechanism for reducing the vacuum energy. We explore the stability of this suppression to quantum effects in the case where their strength is controlled by the value of the field along the classical flat direction, and find it can (but need not) be stable.