ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study cosmology on a BPS D3-brane evolving in the 10D SUGRA background describing a non-BPS brane. Initially the BPS brane is taken to be a probe whose dynamics we determine in the non-compact non-BPS background. The cosmology observed on the brane is of the FRW type with a scale factor $S(\tau)$. In this mirage cosmology approach, there is no self-gravity on the brane which cannot inflate. Self-gravity is then included by compactifying the background space-time. The low energy effective theory below the compactification scale is shown to be bi-metric, with matter coupling to a different metric than the geometrically induced metric on the brane. The geometrical scale factor on the brane is now $S(\tau) a(\tau)$ where $a(\tau)$ arises from brane self-gravity. In this non-BPS scenario the brane generically inflates. We study the resulting inflationary scenario taking into account the fact that the non-BPS brane eventually decays on a time-scale much larger than the typical inflationary time-scale. After the decay, the theory ceases to be bi-metric and COBE normalization is used to estimate the string scale which is found to be of order $10^{14}$ GeV.
We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's category of motives. We prove that this motive can be written as a homotopy colimit of motives of smooth projective Quot schemes of torsion quotients of sums of line bundles on the curve. When working with rational coefficients, we prove that the motive of the stack of bundles lies in the localising tensor subcategory generated by the motive of the curve, using Bialynicki-Birula decompositions of these Quot schemes. We conjecture a formula for the motive of this stack, and we prove this conjecture modulo a conjecture on the intersection theory of the Quot schemes.
We investigate star formation at very early evolutionary phases in five massive clouds in the inner 500 pc of the Galaxy, the Central Molecular Zone. Using interferometer observations of H$_2$O masers and ultra-compact H II regions, we find evidence of ongoing star formation embedded in cores of 0.2 pc scales and $\gtrsim$10$^5$ cm$^{-3}$ densities. Among the five clouds, Sgr C possesses a high (9%) fraction of gas mass in gravitationally bound and/or protostellar cores, and follows the dense ($\gtrsim$10$^4$ cm$^{-3}$) gas star formation relation that is extrapolated from nearby clouds. The other four clouds have less than 1% of their cloud masses in gravitationally bound and/or protostellar cores, and star formation rates 10 times lower than predicted by the dense gas star formation relation. At the spatial scale of these cores, the star formation efficiency is comparable to that in Galactic disk sources. We suggest that the overall inactive star formation in these Central Molecular Zone clouds could be because there is much less gas confined in gravitationally bound cores, which may be a result of the strong turbulence in this region and/or the very early evolutionary stage of the clouds when collapse has only recently started.
Aims: We used 12,530 photometrically-selected blue horizontal branch (BHB) stars from the Sloan Digital Sky Survey (SDSS) to estimate the total extinction of the Milky Way at the high Galactic latitudes, $R_V$ and $A_V$ in each line of sight. Methods: A Bayesian method was developed to estimate the reddening values in the given lines of sight. Based on the most likely values of reddening in multiple colors, we were able to derive the values of $R_V$ and $A_V$.   Results: We selected 94 zero-reddened BHB stars from seven globular clusters as the template. The reddening in the four SDSS colors for the northern Galactic cap were estimated by comparing the field BHB stars with the template stars. The accuracy of this estimation is around 0.01\,mag for most lines of sight. We also obtained $<R_V>$ to be around 2.40$\pm1.05$ and $A_V$ map within an uncertainty of 0.1\,mag. The results, including reddening values in the four SDSS colors, $A_V$, and $R_V$ in each line of sight, are released on line. In this work, we employ an up-to-date parallel technique on GPU card to overcome time-consuming computations. We plan to release online the C++ CUDA code used for this analysis.   Conclusions: The extinction map derived from BHB stars is highly consistent with that from Schlegel, Finkbeiner & Davis(1998). The derived $R_V$ is around 2.40$\pm1.05$. The contamination probably makes the $R_V$ be larger.
After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $su_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $su_q(2)$ algebra .
We present the rest-1500\AA\ UV luminosity functions (LF) for star-forming galaxies during the cosmic \textit{high noon} -- the peak of cosmic star formation rate at $1.5<z<3$. We use deep NUV imaging data obtained as part of the \textit{Hubble} Ultra-Violet Ultra Deep Field (UVUDF) program, along with existing deep optical and NIR coverage on the HUDF. We select F225W, F275W and F336W dropout samples using the Lyman break technique, along with samples in the corresponding redshift ranges selected using photometric redshifts and measure the rest-frame UV LF at $z\sim1.7,2.2,3.0$ respectively, using the modified maximum likelihood estimator. We perform simulations to quantify the survey and sample incompleteness for the UVUDF samples to correct the effective volume calculations for the LF. We select galaxies down to $M_{UV}=-15.9,-16.3,-16.8$ and fit a faint-end slope of $\alpha=-1.20^{+0.10}_{-0.13}, -1.32^{+0.10}_{-0.14}, -1.39^{+0.08}_{-0.12}$ at $1.4<z<1.9$, $1.8<z<2.6$, and $2.4<z<3.6$, respectively. We compare the star formation properties of $z\sim2$ galaxies from these UV observations with results from H\alpha\ and UV$+$IR observations. We find a lack of high SFR sources in the UV LF compared to the H\alpha\ and UV$+$IR, likely due to dusty SFGs not being properly accounted for by the generic $IRX-\beta$ relation used to correct for dust. We compute a volume-averaged UV-to-H\alpha\ ratio by \textit{abundance matching} the rest-frame UV LF and H\alpha\ LF. We find an increasing UV-to-H\alpha\ ratio towards low mass galaxies ($M_\star \lesssim 5\times10^9$ M$_\odot$). We conclude that this could be due to a larger contribution from starbursting galaxies compared to the high-mass end.
Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial distribution takes only two values, the Lynden-Bell distribution is similar to the Fermi-Dirac statistics. Such distributions have recently been observed in direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve corresponding to the Lynden-Bell statistics in relation with the HMF model and analyze the dynamical and thermodynamical stability of spatially homogeneous solutions by using two general criteria previously introduced in the literature. We express the critical energy and the critical temperature as a function of a degeneracy parameter fixed by the initial condition. Below these critical values, the homogeneous Lynden-Bell distribution is not a maximum entropy state but an unstable saddle point. We apply these results to the situation considered by Antoniazzi et al. For a given energy, we find a critical initial magnetization above which the homogeneous Lynden-Bell distribution ceases to be a maximum entropy state, contrary to the claim of these authors. For an energy U=0.69, this transition occurs above an initial magnetization M_{x}=0.897. In that case, the system should reach an inhomogeneous Lynden-Bell distribution (most mixed) or an incompletely mixed state (possibly fitted by a Tsallis distribution). Thus, our theoretical study proves that the dynamics is different for small and large initial magnetizations, in agreement with numerical results of Pluchino et al. (2004). This new dynamical phase transition may reconcile the two communities.
The 3D radial escape-velocity profile of galaxy clusters has been suggested to be a promising and competitive tool for constraining mass profiles and cosmological parameters in an accelerating universe. However, the observed line-of-sight escape profile is known to be suppressed compared to the underlying 3D radial (or tangential) escape profile. Past work has suggested that velocity anisotropy in the phase-space data is the root cause. Instead, we find that the observed suppression is from the statistical undersampling of the phase spaces and that the 3D radial escape edge can be accurately inferred from projected data. We build an analytical model for this suppression that only requires the number of observed galaxies $N$ in the phase-space data within the sky-projected range $0.3 \le r_\perp/R_{200, \text{critical}} \le 1$. The radially averaged suppression function is an inverse power law $\langle Z_\text{v} \rangle = 1 + (N_0/N)^\lambda$ with $N_0 = 17.818$ and $\lambda= 0.362$. We test our model with $N$-body simulations, using dark matter particles, subhalos, and semianalytic galaxies as the phase-space tracers, and find excellent agreement. We also assess the model for systematic biases from cosmology ($\Omega_{\Lambda}$, $H_0$), cluster mass ($M_{200, \text{critical}}$), and velocity anisotropy ($\beta$). We find that varying these parameters over large ranges can impart a maximal additional fractional change in $\langle Z_\text{v} \rangle$ of $2.7\%$. These systematics are highly subdominant (by at least a factor of 13.7) to the suppression from $N$.
We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random trees, we show that random trees conditioned to have large functional values always converge locally to immortal trees. We also derive a very general ratio limit property for functionals of random trees satisfying the monotonicity property. Then we move on to study the local convergence of critical continuous-state branching processes, and prove a similar result. Finally we give a definition of continuum condensation trees, which should be the correct local limits for certain subcritical Levy trees under suitable conditionings.
The Sydney University Stellar Interferometer (SUSI) has been used to make a new determination of the angular diameter of Sirius A. The observations were made at an effective wavelength of 694.1 nm and the new value for the limb-darkened angular diameter is 6.048 +/- 0.040mas (+/-0.66%). This new result is compared with previous measurements and is found to be in excellent agreement with a conventionally calibrated measurement made with the European Southern Observatory's Very Large Telescope Interferometer (VLTI) at 2.176 microns (but not with a second globally calibrated VLTI measurement). A weighted mean of the SUSI and first VLTI results gives the limb-darkened angular diameter of Sirius A as 6.041 +/- 0.017mas (+/-0.28%). Combination with the Hipparcos parallax gives the radius equal to 1.713 +/- 0.009R_sun. The bolometric flux has been determined from published photometry and spectrophotometry and, combined with the angular diameter, yields the emergent flux at the stellar surface equal to (5.32+/- 0.14)x10^8 Wm^-2 and the effective temperature equal to 9845 +/- 64 K. The luminosity is 24.7 +/- 0.7 L_sun.
We present high signal-to-noise echelle spectra of the compact high surface brightness, low ionization planetary nebula IC 418. These reveal 807 emission lines down to intensities less than 10$^{-5}$ that of H$\beta$ for which we determine widths and relative intensities. We show that line profiles are a valuable parameter for making line identifications and in constraining the excitation mechanism of the lines. We present evidence that indicates that many supposed high-level recombination lines may in fact be excited by a process other than recombination. We contend from the detection of dielectronic recombination lines that their relatively low intensities argue against their making a significant contribution to level populations of the heavy ions in this object. Following similar analyses of other PNe we find that IC 418 shows a small discrepancy in ion abundances derived from forbidden vs. recombination lines of the heavy elements.
Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that radiation damping causes a 3.5PN order, spin-spin induced precession of the individual spins. This contrasts with the case of spin-orbit coupling, where there is no effect on the spins at 3.5PN order. Employing the equations of motion and of spin precession, we verify that the loss of total energy and total angular momentum induced by spin-spin effects precisely balances the radiative flux of those quantities calculated by Kidder et al.
InAs-AlSb quantum wells are investigated by transport experiments in magnetic fields tilted with respect to the sample normal. Using the coincidence method we find for magnetic fields up to 28 T that the spin splitting can be as large as 5 times the Landau splitting. We find a value of the g-factor of about 13. For small even-integer filling factors the corresponding minima in the Shubnikov-de Haas oscillations cannot be tuned into maxima for arbitrary tilt angles. This indicates the anti-crossing of neighboring Landau and spin levels. Furthermore we find for particular tilt angles a crossover from even-integer dominated Shubnikov-de Haas minima to odd-integer minima as a function of magnetic field.
The quenched scalar Yukawa theory is solved in the light-front Tamm-Dancoff approach including up to four constituents (one scalar nucleon, three scalar pions). The Fock sector dependent renormalization is implemented. By studying the Fock sector norms, we find that the lowest two Fock sectors dominate the state even in the large-coupling region. The one-body sector shows convergence with respect to the Fock sector truncation. However, the four-body norm exceeds the three-body norm at the coupling $\alpha \approx 1.7$.
Z. Rudnick and P. Sarnak have proved that the pair correlation for the fractional parts of $n^2 \alpha$ is Poissonian for almost all $\alpha$. However, they were not able to find a specific $\alpha$ for which it holds. We show that the problem is related to the problem of determining the number of $(a,b,r) \in \N^3$ such that $a \le M$, $b \le N$, $r \le K$ and $p ab \equiv r (q)$ for $p$ and $q$ coprime. With suitable assumptions on the relative size of $K$, $M$, $N$ and $q$ one should expect there to be $KMN/q$ such triples asymptotically and we will show that this holds on average.
We study the running vacuum model in which the vaccum energy density depends on square of Hubble parameter in comparison with the $\Lambda$CDM model. In this work, the Bayesian inference method is employed to test against the standard $\Lambda$CDM model to appraise the relative significance of our model, using the combined data sets, Pantheon+CMB+BAO and Pantheon+CMB+BAO+Hubble data. The model parameters and the corresponding errors are estimated from the marginal likelihood function of the model parameters. Marginalizing over all model parameters with suitable prior, we have obtained the Bayes factor as the ratio of Bayesian evidence of our model and the $\Lambda$CDM model. The analysis based on Jeffrey's scale of bayesian inference shows that the evidence of our model against the $\Lambda$CDM model is weak for both data combinations. Even though the running vacuum model gives a good account of the evolution of the universe, it is not superior to the $\Lambda$CDM model.
Automatic data abstraction is an important capability for both benchmarking machine intelligence and supporting summarization applications. In the former one asks whether a machine can `understand' enough about the meaning of input data to produce a meaningful but more compact abstraction. In the latter this capability is exploited for saving space or human time by summarizing the essence of input data. In this paper we study a general reinforcement learning based framework for learning to abstract sequential data in a goal-driven way. The ability to define different abstraction goals uniquely allows different aspects of the input data to be preserved according to the ultimate purpose of the abstraction. Our reinforcement learning objective does not require human-defined examples of ideal abstraction. Importantly our model processes the input sequence holistically without being constrained by the original input order. Our framework is also domain agnostic -- we demonstrate applications to sketch, video and text data and achieve promising results in all domains.
After a short report of results on infinite servers queues systems, focusing on its busy period, using networks of queues with infinite servers nodes a model is constructed to study a two echelons repair system. These repair systems may be useful, for instance, in the operation of a fleet of aircraft, of shipping or of trucks. Additionally, it is shown how this model may be used in the evaluation of differential costs.
We study the nonlinear stochastic heat equation driven by space-time white noise in the case that the initial datum $u_0$ is a (possibly signed) measure. In this case, one cannot obtain a mild random-field solution in the usual sense. We prove instead that it is possible to establish the existence and uniqueness of a weak solution with values in a suitable function space. Our approach is based on a construction of a generalized definition of a stochastic convolution via Young-type inequalities.
The variety of all smooth hypersurfaces of given degree and dimension has the Fermat hypersurface as a natural base point. In order to study the period map for such varieties, we first determine the integral polarized Hodge structure of the primitive cohomology of a Fermat hypersurface (as a module over the automorphism group of the hypersurface). We then focus on the degree 3 case and show that the period map for cubic fourfolds as analyzed by R. Laza and the author gives complete information about the period map for cubic hypersurfaces of lower dimension dimension. In particular, we thus recover the results of Allcock-Carlson-Toledo on the cubic surface case.
Embedding nanostructures within a bulk matrix is an important practical approach towards the electronic engineering of high performance thermoelectric systems. For power generation applications, it ideally combines the efficiency benefit offered by low dimensional systems along with the high power output advantage offered by bulk systems. In this work, we uncover a few crucial details about how to embed nanowires and nanoflakes in a bulk matrix so that an overall advantage over pure bulk may be achieved. First and foremost, we point out that a performance degradation with respect to bulk is inevitable as the nanostructure transitions to being multi moded. It is then shown that a nano embedded system of suitable cross-section offers a power density advantage over a wide range of efficiencies at higher packing fractions, and this range gradually narrows down to the high efficiency regime, as the packing fraction is reduced. Finally, we introduce a metric - \emph{the advantage factor}, to elucidate quantitatively, the enhancement in the power density offered via nano-embedding at a given efficiency. In the end, we explore the maximum effective width of nano-embedding which serves as a reference in designing generators in the efficiency range of interest.
We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.
The effect of projectile shape on cross sections and momentum distributions of fragments from heavy ion reactions is studied. We propose a new approach that implements the underlying symmetries of each isotope with a few parameters directly in the density. Various densities and their nuclear structure are then analyzed in the reactions of $^{12}$C and $^{11}$Li, $^{11}$Be, and $^{11}$C on a carbon target.
We have observationally quantified the effect of gravitational torques on stars in disk galaxies due to the stellar distribution itself and explored whether these torques are efficient at transporting angular momentum within a Hubble Time. We derive instantaneous torque maps for a sample of 24 spiral galaxies, based on stellar mass maps that were derived using the pixel-by-pixel mass-to-light estimator by Zibetti, Rix and Charlot. In conjunction with an estimate of the rotation velocity, the mass maps allow us to determine the torque-induced instantaneous angular momentum flow across different radii, resulting from the overall stellar distributions for each galaxy in the sample. By stacking the sample, which effectively replaces a time average by an ensemble average, we find that the torques due to the stellar disk act to transport angular momentum outward over much of the disk (within 3 disk scale lengths). The strength of the ensemble-averaged gravitational torques within one disk scale length have a timescale of ~ 4 Gyr for angular momentum redistribution. This study is the first to observationally determine the strength of torque-driven angular momentum flow of stars for a sample of spiral galaxies, providing an important empirical constraint on secular evolution. (abridged)
In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observational data. This measure is most often given in terms of a density with respect to a reference measure in a high-dimensional (or infinite-dimensional) Banach space. Although Monte Carlo sampling methods provide a way of querying the posterior, the necessity of evaluating the forward operator many times (which will often be a costly PDE solver) prohibits this in practice. For this reason, many practitioners choose a suitable Gaussian approximation of the posterior measure, in a procedure called Laplace's method. Once generated, this Gaussian measure is a lot easier to sample from and properties like moments are immediately acquired. This paper derives Laplace's approximation of the posterior measure attributed to the inverse problem explicitly as the posterior measure of a second-order approximation of the data-misfit functional, specifically in the infinite-dimensional setting. By use of a reverse Cauchy-Schwarz inequality we are able to explicitly bound the Hellinger distance between the posterior and its approximation.