ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an $\alpha$-stable law, for $0<\alpha<1$, and the other variable has the law defined by polynomially tilting the density of an $\alpha$-stable random variable by a factor $\theta>-\alpha$. When $\theta=0$, these variables equate with the ratio investigated by Lamperti [Trans. Amer. Math. Soc. 88 (1958) 380--387] which, remarkably, was shown to have a simple density. This variable arises in a variety of areas and gains importance from a close connection to the stable laws. This rationale, and connection to the $\operatorname {PD}(\alpha,\theta)$ distribution, motivates the investigations of its generalizations which we refer to as Lamperti-type laws. We identify and exploit links to random variables that commonly appear in a variety of applications. Namely Linnik, generalized Pareto and $z$-distributions. In each case we obtain new results that are of potential interest. As some highlights, we then use these results to (i) obtain integral representations and other identities for a class of generalized Mittag--Leffler functions, (ii) identify explicitly the L\'{e}vy density of the semigroup of stable continuous state branching processes (CSBP) and hence corresponding limiting distributions derived in Slack and in Zolotarev [Z. Wahrsch. Verw. Gebiete 9 (1968) 139--145, Teor. Veroyatn. Primen. 2 (1957) 256--266], which are related to the recent work by Berestycki, Berestycki and Schweinsberg, and Bertoin and LeGall [Ann. Inst. H. Poincar\'{e} Probab. Statist. 44 (2008) 214--238, Illinois J. Math. 50 (2006) 147--181] on beta coalescents. (iii) We obtain explicit results for the occupation time of generalized Bessel bridges and some interesting stochastic equations for $\operatorname {PD}(\alpha,\theta)$-bridges. In particular we obtain the best known results for the density of the time spent positive of a Bessel bridge of dimension $2-2\alpha$.
Let $X=\C^n$. In this paper we present an algorithm that computes the de Rham cohomology groups $H^i_{dR}(U,\C)$ where $U$ is the complement of an arbitrary Zariski-closed set $Y$ in $X$. Our algorithm is a merger of the algorithm given by T.~Oaku and N.~Takayama (\cite{O-T2}), who considered the case where $Y$ is a hypersurface, and our methods from \cite{W-1} for the computation of local cohomology. We further extend the algorithm to compute de Rham cohomology groups with support $H^i_{dR,Z}(U,\C)$ where again $U$ is an arbitrary Zariski-open subset of $X$ and $Z$ is an arbitrary Zariski-closed subset of $U$. Our main tool is the generalization of the restriction process from \cite{O-T1} to complexes of modules over the Weyl algebra. All presented algorithms are based on Gr\"obner basis computations in the Weyl algebra.
Luminous infrared galaxies ($L_{\rm{IR}}>10^{11} L_{\odot}$) are often associated with interacting galactic systems and are thought to be powered by merger--induced starbursts and/or dust--enshrouded AGN. In such systems, the evolution of the dense, star forming molecular gas as a function of merger separation is of particular interest. Here, we present observations of the CO(3-2) emission from a sample of luminous infrared galaxy mergers that span a range of galaxy-galaxy separations. The excitation of the molecular gas is studied by examining the CO(3-2)/CO(1-0) line ratio, $r_{31}$, as a function of merger extent. We find these line ratios, $r_{31}$, to be consistent with kinetic temperatures of $T_k$=(30--50) K and gas densities of $n_{\rm{H}_2}=10^3 \rm{cm}^{-3}$. We also find weak correlations between $r_{31}$ and both merger progression and star formation efficiency ($L_{\rm{fIR}} / L_{\rm{CO(1-0)}}$). These correlations show a tendency for gas excitation to increase as the merger progresses and the star formation efficiency rises. To conclude, we calculate the contributions of the CO(3-2) line to the 850 $\mu$m fluxes measured with SCUBA, which are seen to be significant ($\sim$24%).
Typical device architectures in polymer-based optoelectronic devices, such as field effect transistors organic light emitting diodes and photovoltaic cells include sub-100 nm semiconducting polymer thin-film active layers, whose microstructure is likely to be subject to finite-size effects. The aim of this study was to investigate effect of the two-dimensional spatial confinement on the internal structure of the semiconducting polymer poly(9,9-dioctylfluorene) (PFO). PFO melts were confined inside the cylindrical nanopores of anodic aluminium oxide (AAO) templates and crystallized via two crystallization strategies, namely, in the presence or in the absence of a surface bulk reservoir located at the template surface. We show that highly textured semiconducting nanowires with tuneable crystal orientation can be thus produced. Moreover, our results indicate that employing the appropriate crystallization conditions extended-chain crystals can be formed in confinement. The results presented here demonstrate the simple fabrication and crystal engineering of ordered arrays of PFO nanowires; a system with potential applications in devices where anisotropic optical properties are required, such as polarized electroluminescence, waveguiding, optical switching, lasing, etc.
We report on a matched-filter search for gravitational wave bursts from cosmic string cusps using LIGO data from the fourth science run (S4) which took place in February and March 2005. No gravitational waves were detected in 14.9 days of data from times when all three LIGO detectors were operating. We interpret the result in terms of a frequentist upper limit on the rate of gravitational wave bursts and use the limits on the rate to constrain the parameter space (string tension, reconnection probability, and loop sizes) of cosmic string models.
Recently, several hybrid approaches to quantum information emerged which utilize both continuous- and discrete-variable methods and resources at the same time. In this work, we investigate the bipartite hybrid entanglement between a finite-dimensional, discrete-variable quantum system and an infinite-dimensional, continuous-variable quantum system. A classification scheme is presented leading to a distinction between pure hybrid entangled states, mixed hybrid entangled states (those effectively supported by an overall finite-dimensional Hilbert space), and so-called truly hybrid entangled states (those which cannot be described in an overall finite-dimensional Hilbert space). Examples for states of each regime are given and entanglement witnessing as well as quantification are discussed. In particular, using the channel map of a thermal photon noise channel, we find that true hybrid entanglement naturally occurs in physically important settings. Finally, extensions from bipartite to multipartite hybrid entanglement are considered.
Face frontalization refers to the process of synthesizing the frontal view of a face from a given profile. Due to self-occlusion and appearance distortion in the wild, it is extremely challenging to recover faithful results and preserve texture details in a high-resolution. This paper proposes a High Fidelity Pose Invariant Model (HF-PIM) to produce photographic and identity-preserving results. HF-PIM frontalizes the profiles through a novel texture warping procedure and leverages a dense correspondence field to bind the 2D and 3D surface spaces. We decompose the prerequisite of warping into dense correspondence field estimation and facial texture map recovering, which are both well addressed by deep networks. Different from those reconstruction methods relying on 3D data, we also propose Adversarial Residual Dictionary Learning (ARDL) to supervise facial texture map recovering with only monocular images. Exhaustive experiments on both controlled and uncontrolled environments demonstrate that the proposed method not only boosts the performance of pose-invariant face recognition but also dramatically improves high-resolution frontalization appearances.
Young, intermediate-mass stars are experiencing renewed interest as targets for direct-imaging planet searches. However, these types of stars are part of multiple systems more often than not. Close stellar companions affect the formation and orbital evolution of any planets, and the properties of the companions can help constrain the binary formation mechanism. Unfortunately, close companions are difficult and expensive to detect with imaging techniques. In this paper, we describe the direct spectral detection method wherein a high-resolution spectrum of the primary is cross-correlated against a template for a companion star. Variants of this method have previously been used to search for stellar, brown dwarf, and even planetary companions. We show that the direct spectral detection method can detect companions as late as M-type orbiting A0 or earlier primary stars in a single epoch on small-aperture telescopes. In addition to estimating the detection limits, we determine the sources of uncertainty in characterizing the companion temperature, and find that large systematic biases can exist. After calibrating the systematic biases with synthetic binary star observations, we apply the method to a sample of 34 known binary systems with an A- or B-type primary star. We detect nine total companions, including four of the five known companions with literature temperatures between $4000$ K $ < T < 6000$ K, the temperature range for which our method is optimized. We additionally characterize the companion for the first time in two previously single-lined binary systems and one binary identified with speckle interferometry. This method provides an inexpensive way to use small-aperture telescopes to detect binary companions with moderate mass-ratios, and is competitive with high-resolution imaging techniques inside $\sim 100-200$ mas.
Upcoming surveys such as \LSST{} and \Euclid{} will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics that complement standard weak lensing statistics such as the shear-shear correlation function and peak counts. In this work, we use a recently proposed weak lensing observable -- weak lensing voids -- to make parameter constraint forecasts for an LSST-like survey. We use the \cosmoslics{} $w$CDM simulation suite to measure void statistics as a function of cosmological parameters. The simulation data is used to train a Gaussian process regression emulator that we use to generate likelihood contours and provide parameter constraints from mock observations. We find that the void abundance is more constraining than the tangential shear profiles, though the combination of the two gives additional constraining power. We forecast that without tomographic decomposition, these void statistics can constrain the matter fluctuation amplitude, $S_8$ within 0.3\% (68\% confidence interval), while offering 1.5, 1.5 and 2.7\% precision on the matter density parameter, $\Omega_{\rm m}$, the reduced Hubble constant, $h$, and the dark energy equation of state parameter, $w_0$, respectively. These results are tighter than the constraints from the shear-shear correlation function with the same observational specifications for $\Omega_m$, $S_8$ and $w_0$. The constraints from the WL voids also have complementary parameter degeneracy directions to the shear 2PCF for all combinations of parameters that include $h$, making weak lensing void statistics a promising cosmological probe.
From ROSAT imaging data we have detections and upper limits for a sample of 26 tailed radio sources in clusters of galaxies mostly from the sample of O'Dea \& Owen (1985). All sixteen of the detected sources are unresolved in the ROSAT PSPC images. The sources bright enough to perform X-ray spectral analysis have power-law indices similar to BL~Lacs and Seyfert galaxies. We find that there is a highly significant correlation between the core radio flux density and the X-ray flux but only a weak correlation between the total radio flux density and the X-ray flux. The trend is similar to that found in earlier studies of 3C radio galaxies with {\sl Einstein} and more recently with ROSAT. The result adds an additional constraint on models for the unification of BL~Lac objects with FR~I radio sources. Also this result indicates that the observed enhanced X-ray emission near tailed sources is more likely to be due to nuclear emission rather than substructure in the extended cluster gas.
The two Gamow-Teller (GT) branches connecting the double-beta decay partners (116Cd, 116Sn) and (150Nd, 150Sm) with the intermediate nuclei 116In and 150Pm are studied within a microscopic approach based on a deformed proton-neutron quasiparticle random-phase approximation built on a Skyrme selfconsistent mean field with pairing correlations and spin-isospin residual forces. The results are compared with the experimental GT strength distributions extracted from charge-exchange reactions. Combining the two branches, the nuclear matrix elements for the two-neutrino double-beta decay are evaluated and compared to experimental values derived from the measured half-lives.
Photometric and spectroscopic observations and analysis of the eccentric eclipsing binary V459 Cassiopeiae (e=0.0244) were performed by Lacy et al. (2004). Observations of minimum light show the presence of apsidal motion. In order to find the observed rate of apsidal motion, I followed the procedure described by Guinan & Maloney (1985). A new observed rate of apsidal motion of 15.2/100 yr with a period of 2400 yr is computed which is not in agreement with the one reported earlier. Also the advance of the periastron is calculated theoretically by taking into account the Newtonian (classical) and general-relativistic effects according to the physical and orbital parameters of the system. The theoretical value of 2.64/100 yr is obtained which is 5.75 times smaller than the observed rate of the apsidal motion.
The electrical properties of a two-dimensional packing of metallic beads are studied. Small mechanical perturbations of the packing leads to giant electrical fluctuations. Fluctuations are found to be non-gaussian and seem to belong to Levy stable distributions. Anticorrelations have been also found for the sign of these fluctuations.
We have studied the chemical and electronic properties of LaAlO3/SrVO3 ultrathin films by combining hard x-ray photoemission spectroscopy and transport measurements. We compare single SrVO3 (SVO) ultrathin films and SrVO3 buried below a polar LaAlO3 (LAO) thin layer, both epitaxially grown on SrTiO3. While ultrathin films (4 unit cells) of SVO do show insulating behavior over the entire temperature range, the LAO/SVO interface has a resistivity minimum at 250 K. When increasing the SVO layer thickness, the minimum is observed to shift to higher temperatures, but the resistivity stays always smaller than that of comparable SVO single films. Hard x-ray photoemission spectroscopy reveals a surface or interface related V5+ component in the V 2p spectra for SVO films and LAO/SVO heterostructures, respectively, attributed to a strongly oxidized component. This chemical reconstruction is weaker in LAO/SVO heterostructures compared to single SVO films. We show that this dead layer in SVO ultrathin films has to be considered when the film thickness reaches the few unit-cells limit and propose solutions on how to prevent this detrimental effect.
We show that there exists a non-K\"ahler Calabi-Yau fourfold, constructing an example by smoothing a normal crossing variety.
We present an analysis of the spectral properties of the peculiar X-ray pulsar X Per based on INTEGRAL observations. We show that the source exhibits an unusually hard spectrum and is confidently detected by ISGRI up to more than 100 keV. We find that two distinct components may be identified in the broadband 4-200 keV spectrum of the source. We interpret these components as the result of thermal and bulk Comptonization in the vicinity of the neutron star and describe them with several semi-phenomenological models. The previously reported absorption feature at ~30 keV is not required in the proposed scenario and therefore its physical interpretation must be taken with caution. We also investigated the timing properties of the source in the framework of existing torque theory, concluding that the observed phenomenology can be consistently explained if the magnetic field of the neutron star is ~10^14 G.
We report on reflective electro-optic sampling measurements of TeraHertz emission from nanometer-gate-length InGaAs-based high electron mobility transistors. The room temperature coherent gate-voltage tunable emission is demonstrated. We establish that the physical mechanism of the coherent TeraHertz emission is related to the plasma waves driven by simultaneous current and optical excitation. A significant shift of the plasma frequency and the narrowing of the emission with increasing channel's current are observed and explained as due to the increase of the carriers density and drift velocity.
We perform a foliation of a four dimensional Riemannian space-time with respect to a discrete time which is an integer multiple of the Planck time. We find that the quantum fluctuations of the metric have a discrete energy spectrum. The metric field is expanded in stationary eigenstates, and this leads to the description of a de Sitter-like universe. At the Planck scale the model describes a Planckian Euclidean black hole.
Ultraluminous X-ray sources (ULXs) are some of the most enigmatic X-ray bright sources known to date. It is generally accepted that they cannot host black holes as large as those associated with active galaxies, but they appear to be significantly more luminous than their better understood Galactic X-ray binary (XRB) cousins, while displaying an intriguing combination of differences and similarities with them. Through studying large, representative samples of these sources we may hope to enhance our understanding of them. To this end, we derive a large catalogue of 650 X-ray detections of 470 ULX candidates, located in 238 nearby galaxies, by cross correlating the 2XMM Serendipitous Survey with the Third Reference Catalogue of Bright Galaxies. The presented dedicated catalogue offers a significant improvement over those previously published both in terms of number and the contribution of background contaminants, e.g. distant quasars, which we estimate to be at most 24 per cent, but more likely ~17 per cent. To undertake population studies, we define a `complete' sub-sample of sources compiled from observations of galaxies with sensitivity limits below 10^39 erg/s. The luminosity function of this sample is consistent with a simple power-law. Although we do not find any statistical requirement for a high luminosity cut-off, as has been reported previously, we are not able to rule out its presence. Also, we find that the number of ULXs per unit galaxy mass decreases with increasing galaxy mass for ULXs associated with spiral galaxies, in broad agreement with previous results, but is consistent with being constant with galaxy mass for sources associated with elliptical galaxies.
We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein-Langevin equation. Once the thermal Green's function in a Schwarzschild background becomes available to the required accuracy the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories.
We measure the colour evolution and quenching time-scales of $z=1.0-1.8$ galaxies across the green valley. We derive rest-frame $NUVrK$ colours and select blue-cloud, green-valley and red-sequence galaxies from the spectral energy distribution modelling of CANDELS GOODS-South and UDS multi-band photometry. Separately, we constrain the star-formation history (SFH) parameters (ages, $\tau$) of these galaxies by fitting their deep archival HST grism spectroscopy. We derive the galaxy colour-age relation and show that only rapidly evolving galaxies with characteristic delayed-$\tau$ SFH time-scales of $<0.5$ Gyr reach the red sequence at these redshifts, after a period of accelerated colour evolution across the green valley. These results indicate that the stellar mass build-up of these galaxies stays minimal after leaving the blue cloud and entering the green valley (i.e., it may represent $\lesssim 5\%$ of the galaxies' final, quiescent masses). Visual inspection of age-sensitive features in the stacked spectra also supports the view that these galaxies follow a quenching sequence along the blue-cloud $\rightarrow$ green-valley $\rightarrow$ red-sequence track. For this rapidly evolving population, we measure a green-valley crossing time-scale of $0.99^{+0.42}_{-0.25}$ Gyr and a crossing rate at the bottom of the green valley of $0.82^{+0.27}_{-0.25}$ mag/Gyr. Based on these time-scales, we estimate that the number density of massive ($M_\star>10^{10} M_\odot$) red-sequence galaxies doubles every Gyr at these redshifts, in remarkable agreement with the evolution of the quiescent galaxy stellar mass function. These results offer a new approach to measuring galaxy quenching over time and represent a pathfinder study for future JWST, Euclid, and Roman Space Telescope programs.
The integrals of motion of the tricritical Ising model are obtained by Thermodynamic Bethe Ansatz (TBA) equations derived from the A_4 integrable lattice model. They are compared with those given by the conformal field theory leading to a unique one-to-one lattice-conformal correspondence. They can also be followed along the renormalization group flows generated by the action of the boundary field \phi_{1,3} on conformal boundary conditions in close analogy to the usual TBA description of energies.
In this lecture I make some educated guesses, about the landscape of string theory vacua. Based on the recent work of a number of authors, it seems plausible that the lanscape is unimaginably large and diverse. Whether we like it or not, this is the kind of behavior that gives credence to the Anthropic Principle. I discuss the theoretical and conceptual issues that arise in developing a cosmology based on the diversity of environments implicit in string theory.
Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and back-action of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both, read and record classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where spin polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom.
Hall effect in SN and SNS junctions is considered. It is shown that at small temperature the Hall voltage is significantly suppressed as compared to its normal metal value. The time dependence of the Hall voltage in SNS junctions has a form of narrow pulses with the Josephson frequency.