ShantanuT01/DACTYL-Pretraining huggingface dataset:
This article investigates an extension of General Relativity based upon a class of lifted metrics on the cotangent bundle of space-time. The dynamics of the theory is determined by a fixed section of the cotangent bundle, representing the momentum of a fluid flow, and Einstein's equations for the fluid applied to the induced space-time metric on the submanifold of the cotangent bundle defined by the image of the section. This construction is formally analogous to the extension of Galilean Relativity by Special Relativity, and is shown to reduce to General Relativity as the gravitational constant approaches zero. By examining the consequences of the model for homogeneous cosmologies, it is demonstrated that this construction globalizes the equivalence principle, in that, the perfect fluid model of Special Relativity is sufficient to predict both the inflationary and the current era.
We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold expansion are associated with subgraphs of a given graph and are explicitly written through Taylor expansions of the corresponding integrands in certain sets of parameters. They are manifestly homogeneous in the threshold expansion parameter, so that the calculation of the given Feynman integral near the threshold reduces to the calculation of integrals of a much simpler type. The general method is illustrated by two-loop two-point and three-point diagrams. We discuss the use of the threshold expansion for problems of physical interest, such as the next-to-next-to-leading order heavy quark production cross sections close to threshold and matching calculations and power counting in non-relativistic effective theories.
Because several observing programs are underway in various spectral regimes to explore the Chandra Deep Field South (CDF-S), the value of local photometric standards is obvious. As part of an NOAO Surveys Program to establish u'g'r'i'z' standard stars in the southern hemisphere, we have observed the central region of the CDF-S to create local standards for use by other investigators using these filters. As a courtesy, we present the CDF-S standards to the public now, although the main program will not finish until mid-2005.
Let $\Gamma_{n,q}$ be the point-hyperplane incidence graph of the projective space $\operatorname{PG}(n,q)$, where $n \ge 2$ is an integer and $q$ a prime power. We determine the order of magnitude of $1-i_V(\Gamma_{n,q})$, where $i_V(\Gamma_{n,q})$ is the vertex-isoperimetric number of $\Gamma_{n,q}$. We also obtain the exact values of $i_V(\Gamma_{2,q})$ and the related incidence-free number of $\Gamma_{2,q}$ for $q \le 16$.
The past 15 years have seen an explosion in the number of redshifts recovered via wide area spectroscopic surveys. At the current time there are approximately 2million spectroscopic galaxy redshifts known (and rising) which represents an extraordinary growth since the pioneering work of Marc Davis and John Huchra. Similarly there has been a parallel explosion in wavelength coverage with imaging surveys progressing from single band, to multi-band, to truly multiwavelength or pan-chromatic involving the coordination of multiple facilities. With these empirically motivated studies has come a wealth of new discoveries impacting almost all areas of astrophysics. Today individual surveys, as best demonstrated by the Sloan Digital Sky Survey, now rank shoulder-to-shoulder alongside major facilities. In the coming years this trend is set to continue as we being the process of designing and conducting the next generation of spectroscopic surveys supported by multi-facility wavelength coverage.
Effectiveness of using laser field to produce entanglement between two dipole-interacting identical two-level atoms is considered in detail. The entanglement is achieved by driving the system with a carefully designed laser pulse transferring the system's population to one of the maximally entangled Dicke states in a way analogous to population inversion by a resonant $\pi$-pulse in a two-level atom. It is shown that for the optimally chosen pulse frequency, power and duration, the fidelity of generating a maximally entangled state approaches unity as the distance between the atoms goes to zero.
This text is a mostly self-contained textbook-like introduction to classical and modern Iwasawa Theory in Spanish language. It grew out of notes for a course that the authors gave at the annual conference of the Mexican Mathematical Society (SMM) in 2018. It covers some preliminaries from algebraic number theory and profinite algebra, the theory of the Iwasawa algebra and its modules, results about class groups in $\mathbb{Z}_p$-extensions, $p$-adic $L$-functions for Dirichlet characters and their various constructions (along with some complex theory of $L$-functions), the cyclotomic main conjecture in different formulations together with its most important implications, and a chapter about generalizations outlining logarithmic Iwasawa theory and generalizations of the Main conjecture to elliptic curves, motives and the ETNC. The text includes references and detailed proofs, some of which are not available in the standard literature, and is accessible for anyone with basic knowledge of algebra and some algebraic number theory.
The commuting graph of a semigroup is the set of non-central elements; the edges are defined as pairs $(u,v)$ satisfying $uv=vu$. We provide an example of a field $F$ and an integer $n$ such that the commuting graph of $\operatorname{Mat}_n(F)$ has maximal possible diameter, equal to six.
Let $g>1$ be an integer and $f(X)\in{\mathbb Z}[X]$ a polynomial of positive degree with no multiple roots, and put $u(n)=f(g^n)$. In this note, we study the sequence of quadratic fields ${\mathbb Q}(\sqrt{u(n)}\,)$ as $n$ varies over the consecutive integers $M+1,\ldots,M+N$. Fields of this type include Shanks fields and their generalizations. Using the square sieve together with new bounds on character sums, we improve an upper bound of Luca and Shparlinski (2009) on the number of $n \in \{M+1,\ldots,M+N\}$ with ${\mathbb Q}(\sqrt{u(n)}\,) = {\mathbb Q}(\sqrt{s}\,)$ for a given squarefree integer $s$.
This paper has been withdrawn. The contents of this paper can now be found in 0907.3000, which combines the erstwhile 0901.2981 and 0901.2982 in a somewhat compact form.
In the framework of nonrelativistic QCD, we compute the leading double-logarithmic corrections of order alpha_s^3 ln^2(1/alpha_s) to the heavy-quark-antiquark bound-state wave function at the origin, which determines the production and annihilation rates of heavy quarkonia. The phenomenological implications for the top-antitop and Upsilon systems are discussed.
We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This method uses the correction vector to obtain precise Green's functions on the real frequency axis at zero temperature. By using a self-consistent bath configuration with very low entanglement, we take full advantage of the DMRG to calculate dynamical response functions paving the way to treat large effective impurities such as those corresponding to multi-orbital interacting models and multi-site or multi-momenta clusters. This method leads to reliable calculations of non-local self energies at arbitrary dopings and interactions and at any energy scale.
We study the properties of Lyman-alpha emitters (LAEs) and Lyman-break galaxies (LBGs) at z=3-6 using cosmological SPH simulations. We investigate two simple scenarios for explaining the observed Ly-a and rest-frame UV luminosity functions (LFs) of LAEs: (i) the "escape fraction" scenario, in which the "effective" escape fraction (including the IGM attenuation) of Ly-a photons is f_Lya ~0.1 (0.15) at z=3 (6), and (ii) the "stochastic" scenario, in which the fraction of LAEs that are turned on at z=3 (6) is \Cstoc ~0.07 (0.2) after correcting for the IGM attenuation. Our comparisons with a number of different observations suggest that the stochastic scenario is preferred over the escape fraction scenario. We find that the mean values of stellar mass, metallicity and black hole mass hosted by LAEs are all smaller in the stochastic scenario than in the escape fraction scenario. In our simulations, the galaxy stellar mass function evolves rapidly, as expected in hierarchical structure formation. However, its evolution is largely compensated by a beginning decline in the specific star formation rate, resulting in little evolution of the rest-frame UV LF from z=6 to 3. The rest-frame UV LF of both LAEs and LBGs at z=3 & 6 can be described well by the stochastic scenario provided the extinction is moderate, E(B-V) ~0.15, for both populations, although our simulation might be overpredicting the number of bright LBGs at z=6. We also discuss the correlation function and bias of LAEs. The Ly-a LFs at z=6 in a field-of-view of 0.2 deg^2 show a significantly larger scatter owing to cosmic variance relative to that in a 1 deg^2 field, and the scatter seen in the current observational estimates of the Ly-a LF can be accounted for by cosmic variance.
Scene classification, aiming at classifying a scene image to one of the predefined scene categories by comprehending the entire image, is a longstanding, fundamental and challenging problem in computer vision. The rise of large-scale datasets, which constitute the corresponding dense sampling of diverse real-world scenes, and the renaissance of deep learning techniques, which learn powerful feature representations directly from big raw data, have been bringing remarkable progress in the field of scene representation and classification. To help researchers master needed advances in this field, the goal of this paper is to provide a comprehensive survey of recent achievements in scene classification using deep learning. More than 200 major publications are included in this survey covering different aspects of scene classification, including challenges, benchmark datasets, taxonomy, and quantitative performance comparisons of the reviewed methods. In retrospect of what has been achieved so far, this paper is also concluded with a list of promising research opportunities.
The variation of the dark energy field is found under the assumption that the dark energy is parametric and interacts with the cold dark matter. Considering that the variation of the field could not exceed the Planck mass, we obtain bounds on the coupling and adiabatic coefficients. Three parameterizations of the adiabatic coefficients are considered and two coupling terms where the energy flows from dark energy to dark matter, or the other way around.
Let K(X) be the collection of all non-zero finite dimensional subspaces of rational functions on an n-dimensional irreducible variety X. For any n-tuple L_1,..., L_n in K(X), we define an intersection index [L_1,..., L_n] as the number of solutions in X of a system of equations f_1 = ... = f_n = 0 where each f_i is a generic function from the space L_i. In counting the solutions, we neglect the solutions x at which all the functions in some space L_i vanish as well as the solutions at which at least one function from some subspace L_i has a pole. The collection K(X) is a commutative semigroup with respect to a natural multiplication. The intersection index [L_1,..., L_n] can be extended to the Grothendieck group of K(X). This gives an extension of the intersection theory of divisors. The extended theory is applicable even to non-complete varieties. We show that this intersection index enjoys all the main properties of the mixed volume of convex bodies. Our paper is inspired by the Bernstein-Kushnirenko theorem from the Newton polytope theory.
In this paper we measure the merger fraction and rate, both minor and major, of massive early-type galaxies (M_star >= 10^11 M_Sun) in the COSMOS field, and study their role in mass and size evolution. We use the 30-band photometric catalogue in COSMOS, complemented with the spectroscopy of the zCOSMOS survey, to define close pairs with a separation 10h^-1 kpc <= r_p <= 30h-1 kpc and a relative velocity Delta v <= 500 km s^-1. We measure both major (stellar mass ratio mu = M_star,2/M_star,1 >= 1/4) and minor (1/10 <= mu < 1/4) merger fractions of massive galaxies, and study their dependence on redshift and on morphology. The merger fraction and rate of massive galaxies evolves as a power-law (1+z)^n, with major mergers increasing with redshift, n_MM = 1.4, and minor mergers showing little evolution, n_mm ~ 0. When split by their morphology, the minor merger fraction for early types is higher by a factor of three than that for spirals, and both are nearly constant with redshift. Our results show that massive early-type galaxies have undergone 0.89 mergers (0.43 major and 0.46 minor) since z ~ 1, leading to a mass growth of ~30%. We find that mu >= 1/10 mergers can explain ~55% of the observed size evolution of these galaxies since z ~ 1. Another ~20% is due to the progenitor bias (younger galaxies are more extended) and we estimate that very minor mergers (mu < 1/10) could contribute with an extra ~20%. The remaining ~5% should come from other processes (e.g., adiabatic expansion or observational effects). This picture also reproduces the mass growth and velocity dispersion evolution of these galaxies. We conclude from these results that merging is the main contributor to the size evolution of massive ETGs at z <= 1, accounting for ~50-75% of that evolution in the last 8 Gyr. Nearly half of the evolution due to mergers is related to minor (mu < 1/4) events.
We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.
We give an Ore-Type condition sufficient for a graph G to have a spanning tree with a specified degree sequence.
We review recent developments in determining the evolution of magnetic massive OB stars. One of the important scientific questions is the completeness and the detection limits of contemporaneous spectropolarimetric surveys across the HR diagram. We present the characteristics of the MiMeS survey of O-type stars, and how the limits of the current available observations warrant the design of new high-precision surveys that target the older O-type star population. Another important question is whether the presence of the magnetic fields changes stellar evolutionary tracks in a significant way, hence leading to a wrong determination of stellar parameters. We review new evolution models that include the effect of magnetic wind quenching, and suppression of convection in the iron opacity peak zone.
We are concerned with nonnegative solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term $u^p$ with $p>1$. The density decays {\it fast} at infinity, in the sense that $\rho(x)\sim |x|^{-q}$ as $|x|\to +\infty$ with $q\ge 2.$ In the case when $q=2$, if $p$ is bigger than $m$, we show that, for large enough initial data, solutions blow-up in finite time and for small initial datum, solutions globally exist. On the other hand, in the case when $q>2$, we show that existence of global in time solutions always prevails. The case of {\it slowly} decaying density at infinity, i.e. $q\in [0,2)$, is examined in [41].
We present the first 3D observations of a diffuse elliptical galaxy (dE). The good quality data (S/N up to 40) reveal the kinematical signature of an embedded stellar disc, reminiscent of what is commonly observed in elliptical galaxies, though similarity of their origins is questionable. Colour map built from HST ACS images confirms the presence of this disc. Its characteristic scale (about 3 arcsec = 250 pc) is about a half of galaxy's effective radius, and its metallicity is 0.1-0.2 dex larger than the underlying population. Fitting the spectra with synthetic single stellar populations (SSP) we found an SSP-equivalent age of 5 Gyr and nearly solar metallicity [Fe/H]=-0.06 dex. We checked that these determinations are consistent with those based on Lick indices, but have smaller error bars. The kinematical discovery of a stellar disc in dE gives additional support to an evolutionary link from dwarf irregular galaxies due to stripping of the gas against the intra-cluster medium.
Weyl invariant gravity has been investigated as the fundamental theory of the vector inflation. Accordingly, we consider a Weyl invariant extension of Dirac-Born-Infeld type gravity. We find that an appropriate choice of the metric removes the scalar degree of freedom which is at the first sight required by the local scale invariance of the action, and then a vector field acquires mass. Then nonminimal couplings of the vector field and curvatures are induced. We find that the Dirac-Born-Infeld type gravity is a suitable theory to the vector inflation scenario.
Unsupervised point cloud completion aims to infer the whole geometry of a partial object observation without requiring partial-complete correspondence. Differing from existing deterministic approaches, we advocate generative modeling based unsupervised point cloud completion to explore the missing correspondence. Specifically, we propose a novel framework that performs completion by transforming a partial shape encoding into a complete one using a latent transport module, and it is designed as a latent-space energy-based model (EBM) in an encoder-decoder architecture, aiming to learn a probability distribution conditioned on the partial shape encoding. To train the latent code transport module and the encoder-decoder network jointly, we introduce a residual sampling strategy, where the residual captures the domain gap between partial and complete shape latent spaces. As a generative model-based framework, our method can produce uncertainty maps consistent with human perception, leading to explainable unsupervised point cloud completion. We experimentally show that the proposed method produces high-fidelity completion results, outperforming state-of-the-art models by a significant margin.
We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on $G$-bundles with $G$ a constant reductive group. The conjectures concern the set of connected components, the uniformization by affine flag varieties of twisted loop groups, the Picard groups, and the space of global sections of a dominant line bundle. Since a first version of this paper was circulated, Heinloth [arXiv:0711.4450] has proved a good part of these conjectures.
By adopting empirical estimates of the Helium enhancement (Delta Y) between consecutive stellar generations for a sample of Galactic globular clusters (GGC), we uniquely constraint the star formation efficiency of each stellar generation in these stellar systems. In our approach, the star formation efficiency is the central factor that links stellar generations as it defines both their stellar mass and the remaining mass available for further star formation, fixing also the amount of matter required to contaminate the next stellar generation. In this way, the star formation efficiency is here shown to be fully defined by the He enhancement between successive stellar generations in a GC.   Our approach has also an impact on the evolution of clusters and thus considers the possible loss of stars through evaporation, tidal interactions and stellar evolution. We focus on the present mass ratio between consecutive stellar generations and the present total mass of Galactic globular clusters. Such considerations suffice to determine the relative proportion of stars of consecutive generations that remain today in globular clusters. The latter is also shown to directly depend on the values of Delta Y and thus the He enhancement between consecutive stellar generations in GGC places major constraints on models of star formation and evolution of GC.
Semi-Detached binary stars are very important systems for the precise determination of astrophysical parameters and the analysis of mass transfer and loss mechanisms between the components. In this study, the light curve analysis of some semi-detached systems (RV Pic and AS Eri), which light changes are obtained by the Transiting Exoplanet Survey Satellite (TESS), was performed. The astrophysical parameters of the systems were obtained. In addition, oscillational properties of the systems were investigated, and the mass transfer and the loss amount of such stars are discussed and compared with observational data.
We study the single- and many-particle properties of a two-leg ladder model threaded by a flux with the legs coupled by a spatially varying term. Although a priori unrelated to twisted bilayer graphene (TBG), the model is found to have striking similarities: a quasi-flat low-energy band emerges with characteristics similar to that of magic angle TBG. We study the effect of interparticle interaction in our model using the density matrix renormalization group and find that when the band is quasi-flat, the ground state is a ferromagnetic Mott insulator. As the band becomes more dispersive, the system undergoes a ferromagnetic to antiferromagnetic transition. We discuss how our model is relevant not only to magic-angle physics in TBG, but also in the larger context of one-dimensional correlations and magnetism.
We introduce and study a new partial order on Dyck paths. We prove that these posets are meet-semilattices. We show that their numbers of intervals are the same as the number of bicubic planar maps. We describe an unexpected connection with the Hochschild polytopes of Saneblidze.
A new class of high-mass X-ray binaries (HMXBs) --- supergiant fast X-ray transients (SFXTs) --- are discovered by INTEGRAL, which are associated with OB supergiants and present long spin periods. Observational evidence indicates that some accreting neutron stars in HMXBs display accretion reversals. It has been suggested that the inverted torque can lead to a very slow rotator. According to three characteristic radii in wind-fed accretion, we developed a retrograde accretion scenario and divided the accretion phase into three regimes, to interpret the formation of the long spin period of SFXTs. The accretion regime in some SFXT systems can be determined by their spin and orbital periods.
It was first shown by Cameron and Ku that the group $G=Sym(n)$ has the strict EKR property. Then Godsil and Meagher presented an entirely different proof of this fact using some algebraic properties of the symmetric group. A similar method was employed to prove that the projective general linear group $PGL(2,q)$, with its natural action on the projective line $\mathbb{P}_q$, has the strict EKR property. The main objective in this thesis is to formally introduce this method, which we call the module method, and show that this provides a standard way to prove Erdos-Ko-Rado theorems for other permutation groups. We then, along with proving Erdos-Ko-Rado theorems for various groups, use this method to prove some permutation groups have the strict EKR property. We will also show that this method can be useful in characterizing the maximum independent sets of some Cayley graphs. To explain the module method, we need some facts from representation theory of groups, in particular, the symmetric group. We will provide the reader with a sufficient level of background from representation theory as well as graph theory and linear algebraic facts about graphs.