ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this article we prove a finiteness result on the number of log minimal models for $3$-folds in char $p>5$. We then use this result to prove a version of Batyrev's conjecture on the structure of nef cone of curves on $3$-folds in characteristic $p>5$. We also give a proof of the same conjecture in full generality in characteristic $0$. We further verify that the duality of movable curves and pseudo-effective divisors hold in arbitrary characteristic. We then give a criterion for the pseudo-effectiveness of the canonical divisor $K_X$ of a smooth projective variety in arbitrary characteristic in terms of the existence of a family of rational curves on $X$.
Divisible design digraphs are constructed from skew balanced generalized weighing matrices and generalized Hadamard matrices. Commutative and non-commutative association schemes are shown to be attached to the constructed divisible design digraphs.
In a large class of models the string excitation and black hole pictures invoked as an explanation of trans-GZK cosmic ray events are equivalent. Single particle inclusive distributions are thermal at the Hagedorn temperature. The hadron multiplicities are reminiscent of multiplicities in heavy nucleus initiated interactions.
Reverberation mapping is now a well-established technique for investigating spatially-unresolved structures in the nuclei of distant galaxies with actively-accreting supermassive black holes. Structural parameters for the broad emission-line region, with angular sizes of microarcseconds, can be constrained through the substitution of time resolution for spatial resolution. Many reverberation experiments over the last 30 years have led to a practical understanding of the requirements necessary for a successful program. With reverberation measurements now in hand for 60 active galaxies, and more on the horizon, we are able to directly constrain black hole masses, derive scaling relationships that allow large numbers of black hole mass estimates throughout the observable Universe, and begin investigating the detailed geometry and kinematics of the broad line region. Reverberation mapping is therefore one of the few techniques available that will allow a deeper understanding of the physical mechanisms involved in AGN feeding and feedback at very small scales, as well as constraints on the growth and evolution of black holes across cosmic time. In this contribution, I will briefly review the background, implementation, and major results derived from this high angular resolution technique.
A natural question is to determine which algebraic stacks are qoutient stacks. In this paper we give some partial answers and relate it to the old question of whether, for a scheme X, the natural map from the Brauer goup (equivalence classes of Azumaya algebras) to the cohomological Brauer group (the torsion subgroup of $H^2(X,{\mathbb G}_m)$ is surjective.
Suppose that $EE$ is a totally real number field which is the composite of all of its subfields $E$ that are relative quadratic extensions of a base field $F$. For each such $E$ with ring of integers $\O_E$, assume the truth of the Birch-Tate conjecture (which is almost fully established) relating the order of the tame kernel $K_2(\O_E)$ to the value of the Dedekind zeta function of $E$ at $s=-1$, and assume the same for $F$ as well. Excluding a certain rare situation, we prove the annihilation of $K_2(\Oc_EE)$ by a generalized Stickelberger element in the group ring of the Galois group of $EE/F$. Annihilation of the odd part of this group is proved unconditionally.
A morphism of nonreduced Gieseker - Maruyama functor (of semistable coherent torsion-free sheaves) on a surface to the nonreduced functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. This leads to the morphism of moduli schemes with possibly nonreduced scheme structures. As usually, we consider subfunctors corresponding to main components of moduli schemes.
In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these generalized polynomials. More precisely, using the Pad\'{e} approximation of the exponential function, we obtain recurrence relations for Apostol-Bernoulli, Euler and also Genocchi polynomials of higher order. As an application we prove lacunary relation for some particular cases.
We derive a consistent 2-loop scaling picture for a Kondo dot in both equilibrium and non-equilibrium situations using the flow equation method. Our analysis incorporates the important decoherence effects from both thermal and non-equilibrium noise in a common setting. We calculate the spin-spin correlation function, the T-matrix, and the magnetization as functions of applied magnetic field, dc-voltage bias and temperature. In all these quantities we observe characteristic non-equilibrium features for a nonvanishing external voltage bias like Kondo splitting and strongly enhanced logarithmic corrections.
We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. We show that critical configurations with positive second variation are local minimizers of the nonlocal area functional and, in fact, satisfy a quantitative isoperimetric inequality with respect to sets that are $L^1$-close. The link with local minimizers for the diffuse-interface Ohta-Kawasaki energy is also discussed. As a byproduct of the quantitative estimate, we get new results concerning periodic local minimizers of the area functional and a proof, via second variation, of the sharp quantitative isoperimetric inequality in the standard Euclidean case. As a further application, we address the global and local minimality of certain lamellar configurations.
We present a framework to analyze various aspects of models for video question answering (VideoQA) using customizable synthetic datasets, which are constructed automatically from gameplay videos. Our work is motivated by the fact that existing models are often tested only on datasets that require excessively high-level reasoning or mostly contain instances accessible through single frame inferences. Hence, it is difficult to measure capacity and flexibility of trained models, and existing techniques often rely on ad-hoc implementations of deep neural networks without clear insight into datasets and models. We are particularly interested in understanding temporal relationships between video events to solve VideoQA problems; this is because reasoning temporal dependency is one of the most distinct components in videos from images. To address this objective, we automatically generate a customized synthetic VideoQA dataset using {\em Super Mario Bros.} gameplay videos so that it contains events with different levels of reasoning complexity. Using the dataset, we show that properly constructed datasets with events in various complexity levels are critical to learn effective models and improve overall performance.
Our single crystal study reveals that PrTr2Al20 (Tr = Ti and V) provides the first examples of a cubic {\Gamma}3 nonmagnetic ground doublet system that shows the Kondo effect including a -ln T dependent resistivity. The {\Gamma}3 quadrupolar moments in PrV2Al20 induce anomalous metallic behavior through hybridization with conduction electrons, such as T^{1/2} dependent resistivity and susceptibility below ~ 20 K down to its ordering temperature T_O = 0.6 K. In PrTi2Al20, however, quadrupoles are well-localized and exhibit an order at T_O = 2.0 K. Stronger Kondo coupling in PrV2Al20 than in PrTi2Al20 suppresses quadrupolar ordering, and instead promotes hybridization between the {\Gamma}3 doublet and conduction electrons, leading to most likely the quadrupolar Kondo effect.
In this paper, a bouncing cosmological scenario is studied in the background of a flat FLRW model with a specific parametrized hyperbolic form of scale factor $ a $ in terms of $ t $, where $ \lambda $ is taken as the model parameter. This model is discussed in $ f(R,G) $ formalism having structured as $ f(R,G)=R+F(G) $, where $ R $ is Ricci scalar and $ G $ is the Gauss-Bonnet invariant. The proposed functional form of the Hubble parameter is considered in such a way that it satisfies the bouncing criteria of the model, which is free from the initial singularity. The physical consequences of the model are discussed. In this model, one can see that the EoS parameter crosses the quintom line $ \omega=-1 $ in the neighborhood of bouncing point $ t\approx0 $, which is a very strong criterion for a successful bouncing cosmological model. Finally, we find that all the essential features of the bouncing model are satisfied successfully.
We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schr\"odinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude. These phase-transitions are robust with respect to Raman noise and scattering losses. We also describe the rich internal quantum noise structure of the solitonic fields in the vicinity of the phase-transition. For optical coherent quantum solitons, this leads to the prediction that eliminating the peak side-band noise due to the electronic nonlinearity of silica fiber by spectral filtering leads to the optimal photon-number noise reduction of a fundamental soliton.
The rich polymorphism exhibited by inorganic/organic interfaces is a major challenge for materials design. In this work we present a method to efficiently explore the potential energy surface and predict the formation energies of polymorphs and defects. This is achieved by training a machine learning model on a list of only 100 candidate structures that are evaluated via dispersion-corrected Density Functional Theory (DFT) calculations. We demonstrate the power of this approach for tetracyanoethylene on Ag(100) and explain the anisotropic ordering that is observed experimentally.
We used deep Gemini-South/GMOS g'r'i'z' images to study the globular cluster (GC) system of the massive elliptical galaxy NGC 1395, located in the Eridanus supergroup. The photometric analysis of the GC candidates reveals a clear colour bimodality distribution, indicating the presence of "blue" and "red" GC subpopulations. While a negative radial colour gradient is detected in the projected spatial distribution of the red GCs, the blue GCs display a shallow colour gradient. The blue GCs also display a remarkable shallow and extended surface density profile, suggesting a significant accretion of low-mass satellites in the outer halo of the galaxy. In addition, the slope of the projected spatial distribution of the blue GCs in the outer regions of the galaxy, is similar to that of the X-ray halo emission. Integrating up to 165 kpc the profile of the projected spatial distribution of the GCs, we estimated a total GC population and specific frequency of 6000$\pm$1100 and $S_N$=7.4$\pm$1.4, respectively. Regarding NGC 1395 itself, the analysis of the deep Gemini/GMOS images shows a low surface brightness umbrella-like structure indicating, at least, one recent merger event. Through relations recently published in the literature, we obtained global parameters, such as $M_\mathrm{stellar}=9.32\times10^{11}$ M$\odot$ and $M_h=6.46\times10^{13}$ M$\odot$. Using public spectroscopic data, we derive stellar population parameters of the central region of the galaxy by the full spectral fitting technique. We have found that, this region, seems to be dominated for an old stellar population, in contrast to findings of young stellar populations from the literature.
The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159--182, 320--334, 486--502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions ($\kappa$-measurability, for some fixed regular cardinal $\kappa$), there is a universal type space (i.e., a terminal object) to which every type space can be mapped in a unique beliefs-preserving way. However, by a probabilistic adaption of the elegant sober-drunk example of Heifetz and Samet [Games Econom. Behav. 22 (1998) 260--273] we show that if all subsets of the spaces are required to be measurable, then there is no universal type space.
We decompose the anomalous diffusive behavior found in a model of aging into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau-Manneville map. The increments can have long-time correlations, fat-tailed distributions and be non-stationary. Each of these properties can cause anomalous diffusion through what is known as the Joseph, Noah and Moses effects, respectively. The model can have either sub- or super-diffusive behavior, which we find is generally due to a combination of the three effects. Scaling exponents quantifying each of the three constitutive effects are calculated using analytic methods and confirmed with numerical simulations. They are then related to the scaling of the distribution of the process through a scaling relation. Finally, the importance of the Moses effect in the anomalous diffusion of experimental systems is discussed.
We are conducting a study on the imprint of the ISM on optical spectra based on two types of ongoing spectroscopic massive-star surveys: on the one hand, intermediate-resolution (R = 2500) green-blue spectra for ~3000 stars obtained with the Galactic O Star Spectroscopic Survey (GOSSS). On the other hand, high-resolution (R = 23 000 - 65 000) optical spectra for 600 stars obtained from three different surveys, OWN, IACOB, and NoMaDS. The R = 2500 data allows us to reach a larger sample with an average larger extinction while the R = 23 000 - 65 000 sample provides access to more diffuse interstellar bands (DIBs) and allows for the resolution in velocity of some ISM features. For each spectrum we are measuring the equivalent widths, FWHMs, and central wavelengths of 10-40 DIBs and interstellar lines (e.g. Ca II H+K, Na I D1+D2) and, in the case of GOSSS, the existence of an H II region around the star. We have also derived from auxiliary data or compiled from the literature values for the reddening, extinction law, H I column density, parallax, and H alpha emission. All of this constitutes the most complete collection ever of optical information on the ISM within 3 kpc of the Sun. We are analyzing the correlations between all of the collected quantities to discriminate between different possible origins of the DIBs.
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As a result, many interesting functions of the joint distribution of graph degrees, such as the distribution of the median degree, become amenable to estimation. Our result is established by proving an asymptotic formula conjectured in 1990 for the number of graphs with given degree sequence. In particular, this gives an asymptotic formula for the number of $d$-regular graphs for all $d$, as $n\to\infty$.
Polariton condensates are investigated in periodical potentials created by surface acoustic waves using both resonant and non-resonant optical excitation. Under resonant pumping condensates are formed due to polariton parametric scattering from the pump. In this case the single particle dispersion in the presence of the condensate shows a strong reduction of the energy gap arising from the acoustic modulation, indicating efficient screening of the surface acoustic wave potential by spatial modulation of the polariton density. The observed results are in good agreement with a model based on generalised Gross-Pitaveskii equations with account taken of the spatial dependence of the exciton energy landscape. In the case of incoherent, non-resonant pumping coexisting non-equilibrium condensates with s- and p- type wavefunctions are observed, which have different energies, symmetry and spatial coherence. The energy splitting between these condensate states is also reduced with respect to the gap of the one particle spectrum below threshold, but the screening effect is less pronounced than in the case of resonantly pumped system due to weaker modulation of the pump state.
We compiled a large sample of Swift-era photometric data on long (Type II) and short (Type I) GRB afterglows. We compare the luminosity and energetics of the different samples to each other and to the afterglows of the pre-Swift era. Here, we present the first results of these studies.
Excitation spectra of square lattice Heisenberg antiferromagnets in magnetic fields are investigated by the spin-wave theory. It is pointed out that a rotonlike structure appears in a narrow range of magnetic fields, as a result of strong nonlinear effects. It is shown that the energy gap and the mass of the "roton" are quite sensitive to the magnetic field: the roton gap softens rapidly and eventually closes as a precursor of a quantum phase transition. The possibility of the experimental observation of the roton and a new ground state after its softening are discussed.
The radio properties of blazars detected by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope have been observed as part of the VLBA Imaging and Polarimetry Survey (VIPS). This large, flux-limited sample of active galactic nuclei (AGN) provides insights into the mechanism that produces strong gamma-ray emission. At lower flux levels, radio flux density does not directly correlate with gamma-ray flux. We find that the LAT-detected BL Lacs tend to be similar to the non-LAT BL Lacs, but that the LAT-detected FSRQs are often significantly different from the non-LAT FSRQs. The differences between the gamma-ray loud and quiet FSRQs can be explained by Doppler boosting; these objects appear to require larger Doppler factors than those of the BL Lacs. It is possible that the gamma-ray loud FSRQs are fundamentally different from the gamma-ray quiet FSRQs. Strong polarization at the base of the jet appears to be a signature for gamma-ray loud AGN.
In this paper, we review the roles of collective modes in nuclear reactions. We emphaize the strong couplings of various collective states with the monopole and quadrupole motions. In inelastic excitation, these couplings can be seen as an important source of anharmonicity in the multiphonon spectrum. In fusion reaction, the breathing and quadrupole motions strongly affects the oscillation of protons against neutrons. Finally, the modification of the collective properties induced by a large amplitude dilution might be the origin of the nuclear multifragmentation, directly related to the nuclear liquid-gas phase transition. In the three cases we derive a coupling matrix element which appears to be in good agreement.
Spin-wave excitations of quarter-filled spin-density-wave state, which coexists with charge ordering, have been studied for one-dimensional extended Hubbard model with the nearest-neighbor repulsive interaction (V) and next-nearest-neighbor one (V_2). We calculate dispersion relations for the acoustic and optical spin-wave within the random phase approximation. Our numerical calculation shows that energy spectrum of the acoustic branch is well described by a simple sine function form. In the states coexisting with charge-density-wave, the spin-wave velocity decreases with increasing V or V_2. Our numerical result, that velocity reduces to zero in the limit of large V or V_2, is analyzed in terms of a spin 1/2 Heisenberg model with effective antiferromagnetic exchange interaction.
The spin-dependent conductance and spin-polarization of a MoS2 quantum dot are studied in presence (absent) of an external electric field perpendicular to the molybdenum plane. It is shown that in absence of the electric field, the deformation of a MoS2 ribbon structure causes spin-splitting in the dot and non-prefect spin filtering is seen. Therefore, the technique could be used for designing spin-dependent devices of MoS2. Also, we show that the device could behave as a prefect spin filter and spin inverter under applying an external electric.
Detailed understanding of solid-solid interface structure-function relations is critical for the improvement and wide deployment of all solid-state batteries. The interfaces between lithium phosphorous oxynitride ("LiPON") solid electrolyte material and lithium metal anode, between LiPON and Li(x)CoO(2) cathode surfaces, have been reported to generate solid electrolyte interphase ("SEI")-like products and/or disordered regions. Using electronic structure calculations and crystalline LiPON models with atomic-layer-deposition-like stoichiometry, we predict LiPON models with purely P-N-P backbones are kinetically inert towards lithium at room temperature. In contrast, transfer of oxygen atoms from low-energy Li(x)CoO(2) (104) surfaces to LiPON is much faster under ambient conditions. The mechanisms of the primary reaction steps, LiPON motifs that readily react with lithium metal, experimental results on amorphous LiPON to partially corroborate these predictions, and possible mitigation strategies to reduce degradations are discussed. LiPON interfaces are found to be useful case studies for highlighting the importance of kinetics-controlled processes during battery assembly at moderate processing temperatures.
We present far-ultraviolet (905 -- 1182 A), time-series spectroscopy of the eclipsing, novalike cataclysmic variable, UX UMa, acquired with FUSE. The time-averaged spectrum is complex and is dominated by overlapping spectral features. The most prominent features are emission lines of CIII, NIII}, NIV, and OVI. They are broad (FWHM >= 1800 km/s) and double-peaked with a central absorption at zero velocity. During eclipse, the spectrum is simpler: the emission lines remain bright, but the absorption components of the lines and the weaker features between the emission lines disappear entirely, leaving a flat continuum. This behavior is also evident in GHRS (1149 -- 1660 A) spectra that we retrieved from the HST archive. The FUV spectra show flickering on time scales of several minutes. The flickering is seen primarily in the continuum and/or the weaker lines rather than in the prominent emission lines. The orbital light curve has a dip in the FUV flux between orbital phases 0.45 -- 0.65, similar to a pre-eclipse dip detected in HST observations. The EWs of the line absorption features decrease during the dip. We have detected a systematic wavelength shift of spectral features on the orbital period, but with a phase lag of ~ 20 degrees, a phenomenon that has been reported at optical wavelengths. We discuss the implications of our results in the context of models of an accretion disk with a chromosphere between the disk and the extended wind. Finally, we note that the observed FUV flux is too low to be consistent with the temperature and radius of the WD derived by Baptista et al. (1995), suggesting that their remaining binary parameters, including a mass ratio of 1, ought to be viewed with skepticism.
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments.