ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce the concept of a bounded below set in a lattice. This can be used to give a generalization of Rota's broken circuit theorem to any finite lattice. We then show how this result can be used to compute and combinatorially explain the M\"obius function in various examples including non-crossing set partitions, shuffle posets, and integer partitions in dominance order. Next we present a generalization of Stanley's theorem that the characteristic polynomial of a semimodular supersolvable lattice factors over the integers. We also give some applications of this second main theorem, including the Tamari lattices.
We study scaling properties of the model of fully developed turbulence for a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group (RG). The scaling properties in this approach are related to fixed points of the RG equation. Here we study a possible existence of other scaling regimes and an opportunity of a crossover between them. This may take place in some other space dimensions, particularly at $d = 4$. A new regime may there arise and then by continuity moves into $d = 3$. Our calculations have shown that there really exists an additional fixed point, that may govern scaling behaviour.
Existence of a generalized solution to a strongly singular convective elliptic equation in the whole space is established. The differential operator, patterned after the (p,q)-Laplacian, can be non-homogeneous. The result is obtained by solving some regularized problems through fixed point theory, variational methods and compactness results, besides exploiting nonlinear regularity theory and comparison principles.
Upcoming precision measurements of the temperature anisotropy of the cosmic microwave background (CMB) at high multipoles will need to be complemented by a more complete understanding of recombination, which determines the damping of anisotropies on these scales. This is the third in a series of papers describing an accurate theory of HeI and HeII recombination. Here we describe the effect of Thomson scattering, the $^3$He isotope shift, the contribution of rare decays, collisional processes, and peculiar motion. These effects are found to be negligible: Thomson and $^3$He scattering modify the free electron fraction $x_e$ at the level of several $\times 10^{-4}$. The uncertainty in the $2^3P^o-1^1S$ rate is significant, and for conservative estimates gives uncertainties in $x_e$ of order $10^{-3}$. We describe several convergence tests for the atomic level code and its inputs, derive an overall $C_\ell$ error budget, and relate shifts in $x_e(z)$ to the changes in $C_\ell$, which are at the level of 0.5% at $\ell =3000$. Finally, we summarize the main corrections developed thus far. The remaining uncertainty from known effects is $\sim 0.3%$ in $x_e$.
The Cosmic Microwave Background Radiation is the oldest photon radiation that can be observed, having been emitted when the Universe was about 300,000 year old. It is a blackbody at 2.73 K, and is almost perfectly isotropic, the anisotropies being about one part to 100,000. However, these anisotropies, detected by the COBE satellite in 1992, constrain the cosmological parameters such as the curvature of the Universe. Archeops is a balloon-borne experiment designed to map these anisotropies. The instrument is composed of a 1.5 m telescope and bolometers cooled at 85 mK to detect radiation between 150 and 550 GHz. To lower parasitic signals, the instrument is borne by a stratospheric balloon during the arctic night. This instrument is also a preparation for the Planck satellite mission, as its design is similar to HFI. We discuss here the results of the first scientific flight from Esrange (near Kiruna, Sweden) to Russia on January 29th 2001, which led to a 22 % (sub)millimetre sky coverage unprecedented at this resolution. Here, we put some emphasis on interstellar dust foreground emission observations.
We present UV-extended E-MILES stellar population synthesis models covering the spectral range 1680-50000A at moderately high resolution. We employ the NGSL space-based stellar library to compute spectra of single-age, single-metallicity stellar populations in the wavelength range from 1680 to 3540A. These models represent a significant improvement in resolution and age/metallicity coverage over previous studies based on earlier space-based libraries. These model spectra were joined with those we computed in the visible using MILES, and other empirical libraries for redder wavelengths. The models span the metallicity range -1.79<[M/H]<+0.26 and ages above 30 Myr, for a suite of IMF types with varying slopes. We focus on the behaviour of colours, spectra and line-strength indices in the UV range as a function of relevant stellar population parameters. Whereas some indices strengthen with increasing age and metallicity, as most metallicity indicators in the visible, other indices peak around 3 Gyr for metal-rich stellar populations, such as Mg at 2800A. Our models provide reasonably good fits to the integrated colours and most line-strengths of the stellar clusters of the Milky-Way and LMC. Our full-spectrum fits in the UV range for a representative set of ETGs of varying mass yield age and metallicity estimates in very good agreement with those obtained in the optical range. The comparison of UV colours and line-strengths of massive ETGs with our models reveals the presence of young stellar components, with ages in the range 0.1-0.5 Gyr and mass fractions 0.1-0.5%, on the top of an old stellar population.
We present a comparative electronic structure study using DFT and various beyond-DFT (DFT+$U$, $G_0W_0$, DFT+DMFT) methods for ferromagnetic Iron (Fe) to find better approach for describing the spectral properties of correlated magnetic system. The computed value of $U$ ($W$) is $\sim$5.4 ($\sim$0.8) eV. The calculated spectra of all methods are providing good agreement with experimental spectra (ES) for peaks' positions. But, the proper line shape is only found from DFT+DMFT with correct estimation of incoherent states, which depends on $J$ and form of local Coulomb interactions. The estimation of reduced magnetization as function of reduced temperature using DFT+DMFT shows good agreement with the experimental data. The insight of paramagnetic electronic structure of Fe is also explored. This work suggests that even for simple correlated magnetic metal, we need DFT+DMFT method to reproduce the ES with great accuracy.
We estimate the number of templates, computational power, and storage required for a one-step matched filtering search for gravitational waves from inspiraling compact binaries. These estimates should serve as benchmarks for the evaluation of more sophisticated strategies such as hierarchical searches. We use waveform templates based on the second post-Newtonian approximation for binaries composed of nonspinning compact bodies in circular orbits. We present estimates for six noise curves: LIGO (three configurations), VIRGO, GEO600, and TAMA. To search for binaries with components more massive than 0.2M_o while losing no more than 10% of events due to coarseness of template spacing, initial LIGO will require about 1*10^11 flops (floating point operations per second) for data analysis to keep up with data acquisition. This is several times higher than estimated in previous work by Owen, in part because of the improved family of templates and in part because we use more realistic (higher) sampling rates. Enhanced LIGO, GEO600, and TAMA will require computational power similar to initial LIGO. Advanced LIGO will require 8*10^11 flops, and VIRGO will require 5*10^12 flops. If the templates are stored rather than generated as needed, storage requirements range from 1.5*10^11 real numbers for TAMA to 6*10^14 for VIRGO. We also sketch and discuss an algorithm for placing the templates in the parameter space.
The $\eta'$ mass reduction in the nuclear medium is expected from the degeneracy of the pseudoscalar-singlet and octet mesons when chiral symmetry is manifest. In this study, we investigate the $\eta'N$ 2body interaction which is the foundation of the in-medium $\eta'$ properties using the linear sigma model as a chiral effective model. The $\eta'N$ interaction in the linear sigma model comes from the scalar meson exchange with U$_A$(1) symmetry effect and is found to be fairly strong attraction. Moreover, the $\eta N$ transition is included in our calculation, and is important for the imaginary part of the $\eta'$-optical potential. The transition amplitude of $\eta'N$ to the $\eta N$ channel is relatively small compared to that of elastic channel. From the analysis of the $\eta'N$ 2body system, we find a $\eta'N$ bound state with the binding energy $12.3-3.3i$MeV. We expect that this strongly attractive two body interaction leads to a deep and attractive optical potential.
Methods based on local image features have recently shown promise for texture classification tasks, especially in the presence of large intra-class variation due to illumination, scale, and viewpoint changes. Inspired by the theories of image structure analysis, this paper presents a simple, efficient, yet robust descriptor namely local jet pattern (LJP) for texture classification. In this approach, a jet space representation of a texture image is derived from a set of derivatives of Gaussian (DtGs) filter responses up to second order, so called local jet vectors (LJV), which also satisfy the Scale Space properties. The LJP is obtained by utilizing the relationship of center pixel with the local neighborhood information in jet space. Finally, the feature vector of a texture region is formed by concatenating the histogram of LJP for all elements of LJV. All DtGs responses up to second order together preserves the intrinsic local image structure, and achieves invariance to scale, rotation, and reflection. This allows us to develop a texture classification framework which is discriminative and robust. Extensive experiments on five standard texture image databases, employing nearest subspace classifier (NSC), the proposed descriptor achieves 100%, 99.92%, 99.75%, 99.16%, and 99.65% accuracy for Outex_TC-00010 (Outex_TC10), and Outex_TC-00012 (Outex_TC12), KTH-TIPS, Brodatz, CUReT, respectively, which are outperforms the state-of-the-art methods.
A magnetic dynamo experiment is under construction at the New Mexico Institute of Mining and Technology. The experiment is designed to demonstrate in the laboratory the alpha-omega magnetic dynamo, which is believed to operate in many rotating and conducting astrophysical objects. The experiment uses the Couette flow of liquid sodium between two cylinders rotating with different angular velocities to model the omega-effect. The alpha-effect is created by the rising and expanding jets of liquid sodium driven through a pair of orifices in the end plates of the cylindrical vessel, presumably simulating plumes driven by buoyancy in astrophysical objects. The water analog of the dynamo device has been constructed and the flow necessary for the dynamo has been demonstrated. Results of the numerical simulations of the kinematic dynamo are presented. The toroidal field produced by the omega-effect is predicted to be B_{\phi} \simeq (R_m/2\pi) B_{poloidal}\simeq 20 \times B_{poloidal} for the expected magnetic Reynolds number of R_m \sim 120. The critical rate of jets necessary for the dynamo self-excitation is predicted from the calculations to be a pair of plumes every 4 revolutions of the outer cylinder. For reasonable technical limitations on the strength of materials and the power of the drive, the self-excitation of the dynamo appears to be feasible.
In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete interference information about two colors. The conceptual model provides an intuitional picture of the in-phase and out-of-phase photon correlations and a complete quantum understanding about the which-path information of two colored photons.
We present a detailed scanning tunnelling microscopy study which describes the morphological transition from ripple to dome islands during the growth of Ge on the vicinal Si(1 1 10) surface . Our experimental results show that the shape evolution of Ge islands on this surface is markedly different from that on the flat Si(001) substrate and is accomplished by agglomeration and coalescence of several ripples. By combining first principle calculations with continuum elasticity theory, we provide an accurate explanation of our experimental observations.
The formation of compact objects like stars and black holes is strongly constrained by the requirement that nearly all of the initial angular momentum of the diffuse material from which they form must be removed or redistributed during the formation process. The mechanisms that may be involved and their implications are discussed for (1) low-mass stars, most of which probably form in binary or multiple systems; (2) massive stars, which typically form in clusters; and (3) supermassive black holes that form in galactic nuclei. It is suggested that in all cases, gravitational interactions with other stars or mass concentrations in a forming system play an important role in redistributing angular momentum and thereby enabling the formation of a compact object. If this is true, the formation of stars and black holes must be a more complex, dynamic, and chaotic process than in standard models. The gravitational interactions that redistribute angular momentum tend to couple the mass of a forming object to the mass of the system, and this may have important implications for mass ratios in binaries, the upper stellar IMF in clusters, and the masses of supermassive black holes in galaxies.
Soft x-ray linear and circular dichroism (XLD, XMCD) experiments at the Ce M$_{4,5}$ edges are being used to determine the energy scales characterizing the Ce $4f$ degrees of freedom in the ultrathin ordered surface intermetallic CeAg$_x$/Ag(111). We find that all relevant interactions, i. e. Kondo scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study demonstrates the usefulness of combining x-ray absorption experiments probing linear and circular dichroism owing to their strong sensitivity for anisotropies in both charge distribution and paramagnetic response, respectively.
We study the implications of a criterion of naturalness for a simple two Higgs doublet model in the context of the discovery of a Higgs like particle with a mass at 125 GeV. This condition which measures the amount of fine tuning further limits the parameter space of this particular model and together with other phenomenological constraints leads to an allowed range of masses for the other neutral or charged Higgs bosons: H, a^{\pm}, a^0.
KO2 exhibits concomitant antiferromagnetic (AFM) and structural transitions, both of which originate from the open-shell 2p electrons of O$_{2}^{-}$ molecules. The structural transition is accompanied by the coherent tilting of O$_{2}^{-}$ molecular axes. The interplay among the spin-orbital-lattice degrees of freedom in KO2 is investigated by employing the first-principles electronic structure theory and the kinetic-exchange interaction scheme. We have shown that the insulating nature of the high symmetry phase of KO2 at high temperature (T) arises from the combined effect of the spin-orbit coupling and the strong Coulomb correlation of O 2p electrons. In contrast, for the low symmetry phase of KO2 at low T with the tilted O$_{2}^{-}$ molecular axes, the band gap and the orbital ordering are driven by the combined effects of the crystal-field and the strong Coulomb correlation. We have verified that the emergence of the O 2p ferro-orbital ordering is essential to achieve the observed AFM structure for KO2.
We study features of the thermoelectric transport through a Kitaev chain hosting Majorana bound states (MBS) at its ends. We describe the behavior of the Seebeck coefficient and the ZT figure of merit for two different configurations between MBS and normal current leads. We find an important violation of the Wiedemann-Franz law in one of these geometries, leading to sizeable values of the thermoelectric efficiency over a narrow window in chemical potential away from neutrality. These findings could lead to interesting thermoelectric-based MBSs detection devices, via measurements of the Seebeck coefficient and figure of merit.
We discuss some global properties of cosmological spacetimes of de Sitter type, based on results with Lars Andersson obtained in hep-th/0202161. We relate the geometry and topology of conformal infinity to the occurrence of singularities in such spacetimes, thereby extending to a much broader context certain properties of some well-known cosmological models.
We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity system and the Petrovsky system.
Low energy cosmic rays (up to the GeV energy domain) play a crucial role in the physics and chemistry of the densest phase of the interstellar medium. Unlike interstellar ionising radiation, they can penetrate large column densities of gas, and reach molecular cloud cores. By maintaining there a small but not negligible gas ionisation fraction, they dictate the coupling between the plasma and the magnetic field, which in turn affects the dynamical evolution of clouds and impacts on the process of star and planet formation. The cosmic-ray ionisation of molecular hydrogen in interstellar clouds also drives the rich interstellar chemistry revealed by observations of spectral lines in a broad region of the electromagnetic spectrum, spanning from the submillimetre to the visual band. Some recent developments in various branches of astrophysics provide us with an unprecedented view on low energy cosmic rays. Accurate measurements and constraints on the intensity of such particles are now available both for the very local interstellar medium and for distant interstellar clouds. The interpretation of these recent data is currently debated, and the emerging picture calls for a reassessment of the scenario invoked to describe the origin and/or the transport of low energy cosmic rays in the Galaxy.
We prove the equivalence of Kantor's Conjecture and the Sticky Matroid Conjecture due to Poljak und Turz\'ik.
We perform a model independent reconstruction of the cosmic expansion rate based on type Ia supernova data. Using the Union 2.1 data set, we show that the Hubble parameter behaviour allowed by the data without making any hypothesis about cosmological model or underlying gravity theory is consistent with a flat LCDM universe having H_0 = 70.43 +- 0.33 and Omega_m=0.297 +- 0.020, weakly dependent on the choice of initial scatter matrix. This is in closer agreement with the recently released Planck results (H_0 = 67.3 +- 1.2, Omega_m = 0.314 +- 0.020) than other standard analyses based on type Ia supernova data. We argue this might be an indication that, in order to tackle subtle deviations from the standard cosmological model present in type Ia supernova data, it is mandatory to go beyond parametrized approaches.
Equilibrium magnetization states in thin spherical shells of a magnetically soft ferromagnet are determined by the competition between two interactions: (i) The local exchange interaction favours the more homogeneous onion state with magnetization oriented in meridian directions; such a state is realized in relatively small particles. (ii) The nonlocal magnetostatic interaction prefers the double-vortex configuration with the magnetization oriented in the parallels directions, since it minimizes the volume magnetostatic charges. These sates are topologically equivalent, in contrast to the same-name states of magnetic nanoring. As a consequence, a continuous (the second order) phase transition between the vortex and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by micromagnetic simulations.
We define a natural conceptual framework in which a generalization of the Lov\'{a}sz Local Lemma can be established in quantum probability theory.
The quantum algebra of observables postulated in hep-th/9805057 is constructed up to degree five. All independent relations of degree four are given; they involve three as yet undetermined parameters. Definitions and symbols are used as introduced in the above-mentioned article.
Recent advances in semi-supervised object detection (SSOD) are largely driven by consistency-based pseudo-labeling methods for image classification tasks, producing pseudo labels as supervisory signals. However, when using pseudo labels, there is a lack of consideration in localization precision and amplified class imbalance, both of which are critical for detection tasks. In this paper, we introduce certainty-aware pseudo labels tailored for object detection, which can effectively estimate the classification and localization quality of derived pseudo labels. This is achieved by converting conventional localization as a classification task followed by refinement. Conditioned on classification and localization quality scores, we dynamically adjust the thresholds used to generate pseudo labels and reweight loss functions for each category to alleviate the class imbalance problem. Extensive experiments demonstrate that our method improves state-of-the-art SSOD performance by 1-2% AP on COCO and PASCAL VOC while being orthogonal and complementary to most existing methods. In the limited-annotation regime, our approach improves supervised baselines by up to 10% AP using only 1-10% labeled data from COCO.
An unusual Eddington-limited thermonuclear X-ray burst was detected from the accreting neutron star in 2S 0918-549 with the Rossi X-ray Timing Explorer. The burst commenced with a brief (40 ms) precursor and maintained near-Eddington fluxes during the initial 77 s. These characteristics are indicative of a nova-like expulsion of a shell from the neutron star surface. Starting 122 s into the burst, the burst shows strong (87 +/- 1% peak-to-peak amplitude) achromatic fluctuations for 60 s. We speculate that the fluctuations are due to Thompson scattering by fully-ionized inhomogeneities in a resettling accretion disk that was disrupted by the effects of super-Eddington fluxes. An expanding shell may be the necessary prerequisite for the fluctuations.
We studied the changes in the electronic structure of VO2 across the metal-insulator transition. The main technique was cluster model calculations with non-local screening channels. The calculation included a screening from a delocalized state at the Fermi level in the metallic phase, and a screening from the neighboring V site within the V-V dimmer in the insulating phase. Both the coherent and incoherent features in the V 3d band of metallic VO2 are well screened states, whereas the true poorly screened 3d0 state appears deeper in energy due to the relatively large U. The non-local screening state in the insulating phase involves U and consequently appears at higher energies. The change in the non-local screening channel opens the band gap originating the insulating phase.