ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, where the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine tuned exception) must have one and only one dark energy phase, either occurring in the contracting era or in the expanding era. Hence,these bounce solutions are necessarily asymmetric. We calculate the spectral indexes and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation or using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model where the presence of dark energy behavior in the Universe does not turn problematic the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine tunings, to yield the observed amplitude for scalar perturbations, and also for the ratio between tensor and scalar amplitudes, $r = T/S \lesssim 0.1$. The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model where a single field induces not only an expanding background dark energy phase, but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order.
In our first paper we described three regions of the 9C survey of radio sources with the Ryle telescope at 15.2 GHz, constituting a total area of 520 deg^2 to a completeness limit of approximately 25 mJy. Here we report on a series of deeper regions, amounting to an area of 115 deg^2 complete to approximately 10 mJy and of 29 deg^2 complete to approximately 5.5 mJy. We have investigated the source counts and the distributions of the 1.4 to 15.2 GHz spectral index (alpha) for these deeper samples. The whole catalogue of 643 sources is available online.   Down to our lower limit of 5.5 mJy we detect no evidence for any change in the differential source count from the earlier fitted count above 25 mJy.   We have matched both our new and earlier catalogues with the NRAO VLA Sky Survey (NVSS) catalogue at 1.4 GHz. For samples of sources selected at 15.2 GHz, in three flux density ranges, we detect a significant shift in the median value of alpha; samples with higher flux densities have higher proportions of sources with flat and rising spectra. We suggest that this observed shift is consistent with a model containing two distinct source populations having differently sloped source counts. Samples selected at 1.4 GHz contain significantly smaller proportions of sources with flat and rising spectra. Also, in our area complete to approximately 10 mJy, we find 5 sources between 10 to 15 mJy, amounting to 4.3 per cent of sources in this range, with no counterpart in the NVSS catalogue. These results illustrate the problems inherent in using a low frequency catalogue to characterise the source population at a much higher frequency and emphasise the value of our blind 15.2 GHz survey.
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables, probability measures, expectation, distributions, characteristic function, independence of random variables, types of convergence and limit theorems. The first part is separated into two different chapters. The first chapter is about combinatorial aspects of probability theory and the second chapter is the actual introduction to probability theory, which contains the modern probability language. The second part covers conditional expectations, martingales and Markov chains, which are easily accessible after reading the first part. The chapters are exactly covered in this order and go into some more details of the respective topic.
Determining the number of singular fibers in a family of varieties over a curve is a generalization of Shafarevich's Conjecture and has implications for the types of subvarieties that can appear in the corresponding moduli stack. We consider families of log canonically polarized varieties over $\P^1$, i.e. families $g:(Y,D)\to \P^1$ where $D$ is an effective snc divisor and the sheaf $\omega_{Y/\P^1}(D)$ is $g$-ample. After first defining what it means for fibers of such a family to be singular, we show that with the addition of certain mild hypotheses (the fibers have finite automorphism group, $\sO_Y(D)$ is semi-ample, and the components of $D$ must avoid the singular locus of the fibers and intersect the fibers transversely), such a family must either be isotrivial or contain at least 3 singular fibers.
We present an updated theoretical prediction of $\epse$, using the next-to-leading $\DSone$ effective hamiltonian and lattice QCD matrix elements. The CP violating phase is costrained by using both the experimental values of $\ep$ and $x_d$, assuming the theoretical determination of $f_B$. Predictions of $\cos\delta$ and $\sin 2\beta$ are also obtained in this way. For $\epse$, our estimate is $\epse=(2.8 \pm 2.4)\times 10^{-4}$.}
Recent hard X-ray surveys have proven to be effective in discovering large numbers of X-ray sources that, despite the likely association with active nuclei, appear to be characterized by "peculiar" properties. Among these "exotic" source populations, we will focus on the nature of two classes of hard X-ray sources: those characterized by high X-ray-to-optical flux ratios -- a fraction of these are associated with the rather elusive Type 2 quasars -- and the X-ray bright optically normal galaxies, also known as XBONGs.
The post-merger product of the first binary neutron star merger event detected in gravitational waves, GW170817, depends on neutron star equation of state (EoS) and is not well determined. We generally discuss the constraints one may pose on the maximum mass of a non-spinning neutron star, $M_{\rm TOV}$, based on the observations and some EoS-independent universal relations of rapidly-spinning neutron stars. If the merger product is a black hole after a brief hypermassive neutron star (HMNS) phase, we derive $M_{\rm TOV} < 2.09^{+0.11}_{-0.09}(^{+0.06}_{-0.04}) M_{\odot}$ at the 2$\sigma$ (1$\sigma$) level. The cases for a massive neutron star (MNS), either a supra-massive neutron star (SMNS) or even a stable neutron star (SNS), are also allowed by the data. We derive $2.09^{+0.11}_{-0.09}(^{+0.06}_{-0.04} M_{\odot}) \leq M_{\rm TOV}< 2.43^{+0.10}_{-0.08}(^{+0.06}_{-0.04}) M_{\odot}$ for the SMNS case and $M_{\rm TOV} \geq 2.43^{+0.10}_{-0.08}(^{+0.06}_{-0.04})M_{\odot}$ for the SNS case, at the $2\sigma$ ($1\sigma$) confidence level. In the MNS cases, we also discuss the constraints on the neutron star parameters (the dipolar magnetic field strength at the surface $B_p$ and the ellipticity $\epsilon$) that affect the spindown history, by considering different MNS survival times, e.g. 300 s, 1 d, and 155 d after the merger, as suggested by various observational arguments. We find that once an SMNS is formed, without violating the EM observational constraints, there always exist a set of ($B_p, \epsilon$) parameters that allow the SMNS to survive for 300s, 1 d, 155 d, or even longer.
We study a special Teichmueller curve in the moduli space of curves of genus 3 that is intersected by infinitely many other Teichmueller curves. The Veech group of the underlying translation surface is SL_2(Z). All occurring Teichmueller curves are induced by origamis, i.e. unramified coverings of the once punctured torus.
Geometric features (including convexity properties) of an exact interior gravitational field due to a self-gravitating axisymmetric body of perfect fluid in stationary, rigid rotation are studied. In spite of the seemingly non-Newtonian features of the bounding surface for some rotation rates, we show, by means of a detailed analysis of the three-dimensional spatial geodesics, that the standard Newtonian convexity properties do hold. A central role is played by a family of geodesics that are introduced here, and provide a generalization of the Newtonian straight lines parallel to the axis of rotation.
X-ray binary Cygnus X-1 is microquasar containing historically first candidate to black hole. Paradigm of magnetic disc accretion dominates in theoretical models describing processes taking place in objects containing black holes such as microquasars and active galactic nuclei. Nevertheless up to now there were no reliable measurements of magnetic fields in these systems. The first prediction of the Cyg X-1 magnetic field was done by V.F.Shvartsman. He wrote that Cyg X-1 X-ray emission millisecond flickering evidences the presence of a black hole and points to the magnetic field role in accretion onto a black hole. From that times there were many of attempts to search for the Cyg X-1 magnetic field but all of these efforts indicated upper limits only. Our VLT FORS1 2007 and 2008 observations revealed a presence of a magnetic field in the system. For the first time we obtained on the level of 6 standard deviations a magnetic field of the order of 130 G on the surface of the Cyg X-1 optical component (O-supergiant) and observational estimation on a 4 sigma level of a magnetic field on a outer part of accretion structure (about 600 G) in accordance with theoretical prediction. Scaling this field value to black hole vicinity we showed that the field is strong enough to explain the X-ray millisecond flickering and can explain it. Our result presents the first direct determination of magnetic field in accreting disk around a black hole.
In the present work we consider energy accumulation mechanism in relativistic electron-positron plasma in the magnetosphere of pulsars. Waves propagating almost across the magnetic field lines are generated that accumulate the energy of plasma particles, as the waves stay significantly long in the resonance region. The accumulated energy is transmitted in the parallel direction of the magnetic field lines as soon as the non-linear plasma processes start to operate. It is suggested that exit of the accumulated energy via waves propagating along the magnetic field lines matching the viewing angle of the observer produces giant pulses. It is shown that these waves come in the radio domain, explaining the Giant Radio Pulse phenomenon.
In this paper we study the initial boundary value problem for the system $\Delta v= u_{x_1},\ u_t-\mbox{div}\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathbf{q}|}\right)\nabla u\right)=-\nabla u\cdot\mathbf{q}$, where $\mathbf{q}=(-v_{x_2}, v_{x_1})^T$, $\mathbf{q}\otimes\mathbf{q}=\mathbf{q}\mathbf{q}^T$. This problem has been proposed as a model for a fluid flowing through a porous medium under the influence of gravity and hydrodynamic dispersion. For each $T>0$ we obtain a so-called strong solution $(v, u)$ in the function space $L^\infty(0,T; \left(W^{1,\infty}(\Omega)\right)^2)$, where $\Omega$ is a bounded domain in $\mathbb{R}^2$. The key ingredient in our approach is the decomposition $A^2=\mbox{tr} (A)A-\mbox{det}(A) I$ for any $2\times 2$ symmetric matrix $A$. By exploring this decomposition, we are able to derive an equation of parabolic type for the function $\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathbf{q}|}\right)\nabla u\cdot\nabla u\right)^j, j\geq 1$. With the aid of this equation we obtain a uniform bound for $\nabla u$.
In the presence of the Hubbard interaction, graphene zigzag nanoribbons have spontaneous edge magnetism with anti-parallel configuration, whose amplitude can be tuned by a transversal electric field. As the electric field increases or decreases across a critical value, the edges are demagnetized or re-magnetized, respectively. A magnetic field at each edge determines the orientation of the re-magnetization. Thus, a combination of slowly varying transversal electric field and magnetic field in monolayer graphene zigzag nanoribbon could drive the quantum system into a bistability loop. The same phenomenon can be induced in a bilayer/monolayer zigzag nanoribbon without the magnetic field, because the non-symmetry superexchange interaction controls the orientation of the re-magnetization. By this way, the quantum system is switched between ground state and quasi-stable excited state with different magnetism, band structures and conductance. This feature could be used to develop graphene-based spintronic nano-devices without magnetic field.
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.
We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order $1 / \sqrt{N}$, where $N$ is the sample size, is achieved, the last being in sharp contrast to the slower non-parametric rates achieved by kernel smoothing of cumulative distribution functions.
We show that there is no real conflict between the two determinations of the strange sea density from the opposite--sign dimuon production and from the difference of the $F_2$ structure functions measured in neutrino and muon deep inelastic scattering. Once non universal sea parton densities are introduced, which take into account the effects of different mass thresholds and different longitudinal contributions, the discrepancy is shown to disappear and both sets of data are simultaneously well reproduced. No need for a large strange sea content of the nucleon emerges.
Recently, increasing attention has been drawn to the internal mechanisms of convolutional neural networks, and the reason why the network makes specific decisions. In this paper, we develop a novel post-hoc visual explanation method called Score-CAM based on class activation mapping. Unlike previous class activation mapping based approaches, Score-CAM gets rid of the dependence on gradients by obtaining the weight of each activation map through its forward passing score on target class, the final result is obtained by a linear combination of weights and activation maps. We demonstrate that Score-CAM achieves better visual performance and fairness for interpreting the decision making process. Our approach outperforms previous methods on both recognition and localization tasks, it also passes the sanity check. We also indicate its application as debugging tools. Official code has been released.
Averaging over imaginary quadratic fields, we prove, quantitatively, the equidistribution of CM points associated to 3-torsion classes in the class group. We conjecture that this equidistribution holds for points associated to ideals of any fixed odd order. We prove a partial equidistribution result in this direction and present empirical evidence.
The ESR response from highly metal-semiconductor(M-SC) separated SWCNTs for temperatures T between 0.39 and 200 K is characteristically different for the two systems. The signal originates from defect spins but interaction with free electrons leads to a larger line width for M tubes. The latter decreases with increasing T whereas it increases with T for SC tubes. The spins undergo a ferromagnetic phase transition below around 10 K. Indirect exchange is suggested to be responsible for the spin-spin interaction, supported by RKKY interaction in the case of M tubes. For SC tubes spin-lattice relaxation via an Orbach process is suggested to determine the line width.
The transient X-ray source GS 1826-238 was monitored during five different observing periods between August 1996 and October 1998 with the BeppoSAX Wide Field Camera instrument in the framework of a deep observation of the Galactic Center region. A first detection of X-ray bursts from this source occurred, ruling out its previously suggested black hole candidacy and strongly suggesting the compact object to be a weakly magnetized neutron star. During the 2.5 years of monitoring, corresponding to ~2.0 Ms observing time, 70 bursts were detected from the source. We here report a quasi-periodicity of 5.76 h in the burst occurrence time which is present during all observations. This is the first example of quasi-periodic bursting over a period of years. It is in line with the history of a rather constant flux since the turn on in 1988 and points to a very stable accretion.
In the present paper we prove lower bounds for L-functions from the Selberg class, by this means improving earlier results obtained by the second author together with J\"orn Steuding. We formulate two theorems which use slightly different technical assumptions, and give two totally different proofs. The first proof uses the "resonance method", which was introduced by Soundararajan, while the second proof uses methods from Diophantine approximation which resemble those used by Montgomery. Interestingly, both methods lead to roughly the same lower bounds, which fall short of those known for the Riemann zeta function and seem to be difficult to be improved. Additionally to these results, we also prove upper bounds for L-functions in the Selberg class and present a further application of a theorem of Chen which is used in the Diophantine approximation method mentioned above.
People increasingly share personal information, including their photos and photo collections, on social media. This information, however, can compromise individual privacy, particularly as social media platforms use it to infer detailed models of user behavior, including tracking their location. We consider the specific issue of location privacy as potentially revealed by posting photo collections, which facilitate accurate geolocation with the help of deep learning methods even in the absence of geotags. One means to limit associated inadvertent geolocation privacy disclosure is by carefully pruning select photos from photo collections before these are posted publicly. We study this problem formally as a combinatorial optimization problem in the context of geolocation prediction facilitated by deep learning. We first demonstrate the complexity both by showing that a natural greedy algorithm can be arbitrarily bad and by proving that the problem is NP-Hard. We then exhibit an important tractable special case, as well as a more general approach based on mixed-integer linear programming. Through extensive experiments on real photo collections, we demonstrate that our approaches are indeed highly effective at preserving geolocation privacy.
Extremely luminous, red eruptive variables like RV in M31 are being suggested as exemplars of a new class of astrophysical object. Our greatly extended series of nova simulations shows that classical nova models can produce very red, luminous eruptions. In a poorly studied corner of 3-D nova parameter space (very cold, low-mass white dwarfs, accreting at very low rates) we find bona fide classical novae that are very luminous and red because they eject very slowly moving, massive envelopes. A crucial prediction of these nova models - in contrast to the predictions of merging star ("mergeburst") models - is that a hot remnant, the underlying white dwarf, will emerge after the massive ejected envelope has expanded enough to become optically thin. This blue remnant must fade on a timescale of decades - much faster than a "mergeburst", which must fade on timescales of millennia or longer. Furthermore, the cooling nova white dwarf and its expanding ejecta must become redder in the years after eruption, while a contracting mergeburst must become hotter and bluer. We predict that red novae will always brighten to L~1000 Lsun for about 1 year before rising to maximum luminosity at L~10^6 - 10^7 Lsun. The maximum luminosity attainable by a nova is likely to be L~10^7 Lsun, corresponding to M-12. In an accompanying paper we describe a fading, luminous blue candidate for the remnant of M31-RV; it is observed with HST to be compatible only with the nova model.
We show the dominance of the restriction map from a moduli space of stable sheaves on the projective plane to the Coble quartic. With the dominance and the interpretation of a stable sheaf on the plane in terms of the hyperplane arrangements, we expect to investigate the geometry of the Coble quartic.
Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which is based on the Hasse Derivative and is referred to as negacyclic Hasse derivative. Finite field Taylor series and alpha-adic expansions over GF(p), p prime, are then considered. Applications to exponential and trigonometric functions are presented. Theses tools can be useful in areas such as coding theory and digital signal processing.
We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators.
We will study the least square estimator $\hat{\theta}_{T,S}$ for the drift parameter $\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation X_{t,s}= -\theta \int^{t}_{0} \int^{s}_{0} X_{v,u}dvdu + B^{\alpha, \beta}_{t,s}, \qquad (t,s) \in [0,T]\times [0,S] driven by the fractional Brownian sheet $B^{\alpha ,\beta}$ with Hurst parameters $\alpha, \beta$ in $(1/2, 5/8)$. Using the properties of multiple Wiener-It\^o integrals we prove that the estimator is strongly consistent for the parameter $\theta$. In contrast to the one-dimensional case, the estimator $\hat{\theta}_{T,S}$ is not asymptotically normal.
A seed layer-free growth of HfO$_2$ on commercially available CVD graphene from various suppliers is investigated. It is revealed that the samples of monolayer graphene transferred from Cu to SiO$_2$/Si substrates have different coverage with bi- and multi-layer graphene islands. We find that the distribution and number of such islands impact the nucleation and growth of HfO$_2$ by CVD. In particular, we show that the edges and surface of densely distributed bi-layer graphene islands provide good nucleation sites for conformal CVD HfO$_2$ layers. Dielectric constant of 16 is extracted from measurements on graphene- HfO$_2$-TiN capacitors.