ShantanuT01/DACTYL-Pretraining huggingface dataset:
For given simple graphs $G_1$ and $G_2$, the size Ramsey number $\hat{R}(G_1,G_2)$ is the smallest positive integer $m$, where there exists a graph $G$ with $m$ edges such that in any edge coloring of $G$ with two colors red and blue, there is either a red copy of $G_1$ or a blue copy of $G_2$. In 1981, Erd\H{o}s and Faudree investigated the size Ramsey number $\hat{R}(K_n,tK_2)$, where $K_n$ is a complete graph on $n$ vertices and $tK_2$ is a matching of size $t$. They obtained the value of $\hat{R}(K_n,tK_2)$ when $n\geq 4t-1$ as well as for $t=2$ and asked for the behavior of these numbers when $ t $ is much larger than $ n $. In this regard, they posed the following interesting question: For every positive integer $n$, is it true that $$\lim_{t\to \infty} \frac{\hat{R}(K_n,tK_2)} {t\, \hat{R}(K_n,K_2)} = \min\left\{\dfrac{\binom{n+2t-2}{2}} {t\binom{n}{2}}\mid t\in \mathbb{N}\right\} ? $$ In this paper, we obtain the exact value of $ \hat{R}(K_n,tK_2) $ for every positive integers $ n,t $ and as a byproduct, we give an affirmative answer to the question of Erd\H{o}s and Faudree.
Point cloud has drawn more and more research attention as well as real-world applications. However, many of these applications (e.g. autonomous driving and robotic manipulation) are actually based on sequential point clouds (i.e. four dimensions) because the information of the static point cloud data could provide is still limited. Recently, researchers put more and more effort into sequential point clouds. This paper presents an extensive review of the deep learning-based methods for sequential point cloud research including dynamic flow estimation, object detection \& tracking, point cloud segmentation, and point cloud forecasting. This paper further summarizes and compares the quantitative results of the reviewed methods over the public benchmark datasets. Finally, this paper is concluded by discussing the challenges in the current sequential point cloud research and pointing out insightful potential future research directions.
In the Standard Model, the Higgs potential allows only one minimum at tree-level. But the open possibility that there might be two scalar doublets enriches the vacuum structure, allowing for the risk that we might now be in a metastable state, which we dub the panic vacuum. Current experiments at the LHC are probing the Higgs particle predicted as a result of the spontaneous symmetry breaking. Remarkably, in the two Higgs model with a softly broken U(1) symmetry, the LHC experiments already preclude panic vacuum solutions.
We consider simple models of tunneling of an object with intrinsic degrees of freedom. This important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. We show possibilities of enhancement for the probability of tunneling due to the presence of intrinsic degrees of freedom split by weak external fields or by polarizability of the slow composite object.
We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of $\mathbb P^3$ branched along stable hyperplane arrangements.
Haldane's geometrical description of fractional quantum Hall states is generalized to compressible states. It is shown that anisotropy in the composite fermion Fermi surface is a direct reflection of this intrinsic geometry. A simple model is introduced in which the geometric parameter can be obtained exactly from other parameters including electron mass anisotropy. Our results compare favorably with recent measurements of anisotropy in composite fermion Fermi surface [D. Kamburov, Y. Liu, M. Shayegan, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Phys. Rev. Lett. 110, 206801 (2013)]. Broader implications of our results are discussed.
Let $\{X_i(t):\, t\in S\subset \R^d \}_{i=1,2,\ldots,n}$ be independent copies of a stationary centered Gaussian field with almost surely smooth sample paths. In this paper, we are interested in the conjunction probability defined as $\PP \left( \exists t\in S: \, X_i(t) \geq u, \, \forall i=1,2,\ldots,n \right)$ for a given threshold level $u$. As $u\rightarrow \infty$, we will provide an asymptotic formula for the conjunction probability. This asymptotic formula is derived from the behaviour of the volume of the set of local maximum points. The proof relies on a result of Aza\"\i s and Wschebor describing the shape of the excursion set of a stationary centered Gaussian field. Our result confirms partially the validity of Euler characteristic method.
Since the discovery of the spectral peculiarities of their prototype alpha2 Canum Venaticorum in 1897, the so-called ACV variables, which are comprised of several groups of chemically peculiar stars of the upper main sequence, have been the target of numerous photometric and spectroscopic studies. Especially for the brighter ACV variables, continuous observations over about a century are available, which are important to study long-term effects such as period changes or magnetic cycles in these objects. The present work presents an analysis of 165 Ap/CP2 and He-weak/CP4 stars using light curves obtained by the Solar Mass Ejection Imager (SMEI) between the years 2003 and 2011. These data fill an important gap in observations for bright ACV variables between the Hipparcos and TESS satellite missions. Using specifically tailored data treatment and period search approaches, we find variability in the accuracy limit of the employed data in 84 objects. The derived periods are in excellent agreement with the literature; for one star, the here presented solution represents the first published period. We discuss the apparently constant stars and the corresponding level of non-variability. From an investigation of our target star sample in the Hertzsprung-Russell diagram, we deduce ages between 100 Myr and 1 Gyr for the majority of our sample stars. Our results support that the variable CP2/4 stars are in a more advanced evolutionary state and that He and Si peculiarities, preferentially found in the hotter, and thus more massive, CP stars, produce larger spots or spots of higher contrast.
We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients modulo actions of certain algebraic groups. In most cases we give concrete geometric descriptions of the strata.
We describe the computation of a catalogue containing all matroids with up to nine elements, and present some fundamental data arising from this cataogue. Our computation confirms and extends the results obtained in the 1960s by Blackburn, Crapo and Higgs. The matroids and associated data are stored in an online database, and we give three short examples of the use of this database.
Context. Classical novae are explosive phenomena that take place in stellar binary systems. They are powered by mass transfer from a low-mass main sequence star onto a white dwarf (either CO or ONe). The material accumulates for 10+4 - 10+5 yr until ignition under degenerate conditions, resulting in a thermonuclear runaway. The nuclear energy released produces peak temperatures of about 0.1 - 0.4 GK. During these events, 10-7 - 10-3 Msun enriched in intermediate-mass elements (with respect to solar abundances) are ejected into the interstellar medium. However, the origin of the large metallicity enhancements and the inhomogeneous distribution of chemical species observed in high-resolution spectra of ejected nova shells is not fully understood. Aims. Recent multidimensional simulations have demonstrated that Kelvin-Helmholtz instabilities that operate at the core-envelope interface can naturally produce self-enrichment of the accreted envelope with material from the underlying white dwarf at levels that agree with observations. However, such multidimensional simulations have been performed for a small number of cases, and much of the parameter space remains unexplored. Methods. Here we investigate the dredge-up, driven by Kelvin-Helmholtz instabilities, for white dwarf masses in the range 0.8-1.25 Msun and different core compositions (CO-rich and ONe-rich substrates). We present a set of five numerical simulations performed in two dimensions aimed at analyzing the possible impact of the white dwarf mass (and composition) on the metallicity enhancement and on the explosion characteristics. Results. We observe greater mixing (about 30 per cent higher when measured in the same conditions), at the time we stop the simulations, and more energetic outbursts for ONe-rich substrates than for CO-rich substrates and for more massive white dwarfs.
We report on magneto-transport properties of the Kondo semiconducting compound CeRu$_2$Al$_{10}$, focusing on its exotic phase below $T_0$ = 27 K. In this phase, an excess thermal conductivity $\kappa$ emerges and is gradually suppressed by magnetic field, strikingly resembling those observed in the hidden-order phase of URu$_2$Si$_2$. Our analysis indicates that low-energy magnetic excitation is the most likely origin, as was also proposed for URu$_2$Si$_2$ recently, despite the largely reduced magnetic moments. Likewise, other transport properties such as resistivity, thermopower and Nernst effect exhibit distinct features characterizing the very different charge dynamics above and below $T_0$, sharing similarities to URu$_2$Si$_2$, too. Given the exotic nature of the ordered phases in both compounds, whether a unified interpretation to all these observations exists appears to be extremely interesting.
We locate almost all the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.
Steganography is the science of hiding a secret message within an ordinary public message. Over the years, steganography has been used to encode a lower resolution image into a higher resolution image by simple methods like LSB manipulation. We aim to utilize deep neural networks for the encoding and decoding of multiple secret images inside a single cover image of the same resolution.
The $SL(3)$ Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on $SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with complicated oscillating factors; this is the primary obstruction to its use. By describing them as solutions to systems of differential equations, we give power series and Mellin-Barnes integral representations of minimal dimension for these weight functions. This completes the role of harmonic analysis on symmetric spaces on the geometric side of the Kuznetsov formula, so that further study may be done through classical analytic techniques.
Let $Y$ be the zero loci of a regular section of a convex vector bundle $E$ over $X$. We provide a new proof of a conjecture of Cox, Katz and Lee for the virtual class of the genus zero moduli of stable maps to $Y$. This in turn yields the expected relationship between Gromov-Witten theories of $Y$ and $X$ which together with Mirror Theorems allows for the calculation of enumerative invariants of $Y$ inside of $X$.
This paper deduces exponential matrix concentration from a Poincar\'e inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof relies on the subadditivity of Poincar\'e inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. It also uses a symmetrization technique to avoid difficulties associated with a direct extension of the classic scalar argument.
A detailed investigation of the charge-ordered charge-transfer salt \delta-(EDT-TTF-CONMe$_{2}$)$_{2}$Br by thermal-expansion measurements and dielectric spectroscopy reveals three dynamic processes of relaxational character. The slowest one exhibits the characteristics of glassy freezing and is ascribed to the conformational dynamics of terminal ethylene groups of the organic molecules. Such a process was previously found for related charge-transfer salts where, however, the anions form polymerlike chains, in contrast to the spherical anions of the present material. Dielectric spectroscopy reveals two additional relaxational processes. The characteristics of the faster one are consistent with excitations of a one-dimensional Wigner lattice as recently observed in this material by infrared spectroscopy, which are also accompanied by conformational changes of the molecules. However, at low temperature the ethylene-group relaxation exhibits the cooperativity-induced dramatic slowing down that is typical for glassy freezing, while the defect-related Wigner-lattice excitation follows thermally activated behavior as expected for single-dipole relaxations.
(abridged) Although discovered 40 years ago, the emission mechanism responsible for the observed pulsar radiation remains unclear. However, the high-energy pulsed emission is usually explained in the framework of either the polar cap or the outer gap model. The purpose of this work is to study the pulsed component, that is the light-curves as well as the spectra of the high-energy emission, above 10 MeV, emanating from the striped wind model. Gamma rays are produced by scattering off the soft cosmic microwave background photons on the ultrarelativistic leptons flowing in the current sheets. We compute the time-dependent inverse Compton emissivity of the wind, in the Thomson regime, by performing three-dimensional numerical integration in space over the whole striped wind. The phase-dependent spectral variability is then calculated as well as the change in pulse shape when going from the lowest to the highest energies. Several light curves and spectra of inverse Compton radiation with phase resolved dependence are presented. We apply our model to the well-known gamma-ray pulsar Geminga. We are able to fit the EGRET spectra between 10 MeV and 10 GeV as well as the light curve above 100 MeV with good accuracy.
A flare of maser radio emission in the OH-line 1665 MHz has been discovered in the star forming region W75 N in 2003, with the flux density of about 1000 Jy. At the time it was the strongest OH maser detected during the whole history of observations since the discovery of cosmic masers in 1965. The flare emission is linearly polarized with a degree of polarization near 100%. A weaker flare with a flux of 145 Jy was observed in this source in 2000 - 2001, which was probably a precursor of the powerful flare. Intensity of two other spectral features has decreased after beginning of the flare. Such variation of the intensity of maser condensation emission (increasing of one and decreasing of the other) can be explained by passing of the magneto hydrodynamic shock across regions of enhanced gas concentration.
We present a theoretical study of a spin field-effect transistor realized in a quantum well formed in a p--doped ferromagnetic-semiconductor- nonmagnetic-semiconductor-ferromagnetic-semiconductor hybrid structure. Based on an envelope-function approach for the hole bands in the various regions of the transistor, we derive the complete theory of coherent transport through the device, which includes both heavy- and light-hole subbands, proper modeling of the mode matching at interfaces, integration over injection angles, Rashba spin precession, interference effects due to multiple reflections, and gate-voltage dependences. Numerical results for the device current as a function of externally tunable parameters are in excellent agreement with approximate analytical formulae.
A uniform hypergraph $H$ is called $k$-Ramsey for a hypergraph $F$, if no matter how one colors the edges of $H$ with $k$ colors, there is always a monochromatic copy of $F$. We say that $H$ is minimal $k$-Ramsey for $F$, if $H$ is $k$-Ramsey for $F$ but every proper subhypergraph of $H$ is not. Burr, Erd\H{o}s and Lovasz studied various parameters of minimal Ramsey graphs. In this paper we initiate the study of minimum degrees and codegrees of minimal Ramsey $3$-uniform hypergraphs. We show that the smallest minimum vertex degree over all minimal $k$-Ramsey $3$-uniform hypergraphs for $K_t^{(3)}$ is exponential in some polynomial in $k$ and $t$. We also study the smallest possible minimum codegrees over minimal $2$-Ramsey $3$-uniform hypergraphs.
We present the analysis of SN 2020wnt, an unusual hydrogen-poor super-luminous supernova (SLSN-I), at a redshift of 0.032. The light curves of SN 2020wnt are characterised by an early bump lasting $\sim5$ days, followed by a bright main peak. The SN reaches a peak absolute magnitude of M$_{r}^{max}=-20.52\pm0.03$ mag at $\sim77.5$ days from explosion. This magnitude is at the lower end of the luminosity distribution of SLSNe-I, but the rise-time is one of the longest reported to date. Unlike other SLSNe-I, the spectra of SN 2020wnt do not show O II, but strong lines of C II and Si II are detected. Spectroscopically, SN 2020wnt resembles the Type Ic SN 2007gr, but its evolution is significantly slower. Comparing the bolometric light curve to hydrodynamical models, we find that SN 2020wnt luminosity can be explained by radioactive powering. The progenitor of SN 2020wnt is likely a massive and extended star with a pre-SN mass of 80 M$_\odot$ and a pre-SN radius of 15 R$_\odot$ that experiences a very energetic explosion of $45\times10^{51}$ erg, producing 4 M$_\odot$ of $^{56}$Ni. In this framework, the first peak results from a post-shock cooling phase for an extended progenitor, and the luminous main peak is due to a large nickel production. These characteristics are compatible with the pair-instability SN scenario. We note, however, that a significant contribution of interaction with circumstellar material cannot be ruled out.
Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [M. Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.
We investigate the vortex patterns appearing in a two-dimensional annular Bose-Einstein condensate rotating in a quadratic plus quartic confining potential. We show that in the limit of small anharmonicity the Gross-Pitaevskii energy can be minimized amongst the Lowest Landau Level wave functions and use this particular form to get theoretical results in the spirit of [A. Aftalion X. Blanc F. Nier, Phys. Rev. A 73, 011601(R) (2006)]. In particular, we show that the vortex pattern is infinite but not uniform. We also compute numerically the complete vortex structure: it is an Abrikosov lattice strongly distorted near the edges of the condensate with multiply quantized vortices appearing at the center of the trap.
In a Kaluza-Klein background $V^4\otimes S^3$, we provide a way to reproduce, by the dimensional reduction, a 4-spinor with a SU(2) gauge coupling. Since additional gauge violating terms cannot be avoided, we compute their order of magnitude by virtue of the application to the Electro-Weak model.
We study the quantum theory of the mass-less vector fields on the Rindler space. We evaluate the Bogoliubov coefficients by means of a new technique based upon the use of light-front coordinates and Mellin transform. We briefly comment about the ensuing Unruh effect and its consequences.
We present an extension of the spectral deconvolution method (Sparks & Ford 2002) to achieve very high contrast at small inner working radii. We apply the method to the specific case of ground based adaptive optics fed integral field spectroscopy (without a coronagraph). Utilising the wavelength dependence of the Airy and speckle patterns, we make an accurate estimate of the PSF that can be scaled and subtracted from the data cube. The residual noise in the resulting spectra is very close to the photon noise from the starlight halo. We utilise the technique to extract a very high SNR H & K band spectrum of AB Dor C, the low mass companion to AB Dor A. By effectively eliminating all contamination from AB Dor A, the extracted spectrum retains both continuum and spectral features. The achieved 1 sigma contrast is 9 mag at 0.2", 11 mag at 0.5", in 20 mins exposure time, at an effective spectral bandwidth of 5.5 nm, proving that the method is applicable even in low Strehl regimes.   The spectral deconvolution method clearly demonstrates the efficacy of image slicer based IFUs in achieving very high contrast imaging spectroscopy at small angular separations, validating their use as high contrast spectrographs/imagers for extreme adaptive optics systems.
Alhena A ($\gamma$ Gem A) is a bright Am star, with the strongest disc-integrated magnetic field strength reported so far for an Am star. Its spectrum exhibits standard circularly polarized Zeeman signatures, contrary to all previously studied Am stars that display abnormal signatures dominated by a single-signed lobe.   We present here the result of follow-up observations of Alhena, using very high signal-to-noise spectropolarimetric data obtained over 25 observing nights with NARVAL at T\'elescope Bernard Lyot, in the frame of the BRITE (BRIght Target Explorer) spectropolarimetric survey.   We confirm that Alhena A is magnetic and we determine its surface magnetic properties using different methods. Inclined dipole models are used to reproduce the longitudinal field measurements, as well as the Stokes V line profiles themselves. In both cases, the model is consistent with a polar field strength of $\sim$ 30 G. This is confirmed by a Zeeman-Doppler Imaging (ZDI) model, which also unveils smaller scale magnetic structures. A rotational period of 8.975 days was identified using intensity line profile variations. The ZDI inversion suggests that the surface magnetic field is sheared by differential rotation, with a difference in rotation rate between high and low latitudes at about 15\% of the solar value. This result challenges theories of the development of surface differential rotation in intermediate mass main sequence stars.