ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $Y_{3,2}$ be the $3$-uniform hypergraph with two edges intersecting in two vertices. Our main result is that any $n$-vertex 3-uniform hypergraph with at least $\binom{n}{3} - \binom{n-m+1}{3} + o(n^3)$ edges contains a collection of $m$ vertex-disjoint copies of $Y_{3,2}$, for $m\le n/7$. The bound on the number of edges is asymptotically best possible. This problem generalizes the Matching Conjecture of Erd\H{o}s. We then use this result combined with the absorbing method to determine the asymptotically best possible minimum $(k-3)$-degree threshold for $\ell$-Hamiltonicity in $k$-graphs, where $k\ge 7$ is odd and $\ell=(k-1)/2$. Moreover, we give related results on $ Y_{k,b} $-tilings and Hamilton $ \ell $-cycles with $ d $-degree for some other values of $ k,\ell,d $.
We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-machines generate, and how these systems of functional equations can frequently be solved by either the kernel method or, much more easily, by guessing and checking. General results about the rationality, algebraicity, and the existence of Wilfian formulas for some classes generated by $\mathcal{C}$-machines are given. We also draw attention to some relatively small permutation classes which, although we can generate thousands of terms of their enumerations, seem to not have D-finite generating functions.
Epitaxial bilayered thin films consisting of La0.6Sr0.4MnO3 (LSMO) and 0.7 Pb(Mg1/3Nb2/3)O3 0.3 PbTiO3 (PMN-PT) layers of relatively different thicknesses were fabricated on LaNiO3 coated LaAlO3 (100) single crystal substrates by pulsed laser ablation technique. Ferroelectric and ferromagnetic characteristics of these heterostructures confirmed their biferroic nature. The magnetization and ferroelectric polarization of the bilayered heterostructures were enhanced with increasing PMN-PT layer thickness owing to the effect of lattice strain. Dielectric properties of these heterostructures studied over a wide range of temperature under different magnetic field strength suggested a possible role of elastic strain mediated magnetoelectric coupling behind the observed magneto-dielectric effect in addition to the influence of rearrangement of the interfacial charge carriers under an applied magnetic field.
The first-year WMAP data release showed that the reionization optical depth to CMB photons is greater than previously thought. This follows from unexpectedly high values of the C^TE_l spectrum, for l up to ~30, presumably allowing a measurement of the E-mode polarization spectrum C^E_l sooner than expected. This note aims to test the capability of large-angle polarization experiments to explore the history of the cosmological reionization, considering also the impact of cosmic variance. In particular, here we discuss how well the ionized fraction x_e and the reionization redshift z_r can be separately measured, at various levels of instrumental noise.
We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at least $s$. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants $0<A<B$ such that (under optimal play) Proposer wins with high probability if $s<A\sqrt{n}\log{n}$, while Decider wins with high probability if $s>B\sqrt{n}\log{n}$. This is a factor of $\Theta(\sqrt{\log{n}})$ larger than the lower bound coming from the off-diagonal Ramsey number $r(3,s)$.
In this work we introduce a new channel to indirect search for the light charged Higgs bosons, which are predicted in several extensions of the standard model (SM) such as the two-Higgs-doublet models (2HDMs). We calculate the ${\cal O}(\alpha_s)$ QCD radiative corrections to the energy distribution of bottom- and charmed-flavored hadrons ($B/D$) produced in the dominant decays of the polarized top quark in the 2HDM, i.e. $t(\uparrow)\longrightarrow b(\to B/D+\text{jet})+H^+(\to \tau^+\nu_\tau)$. %This analysis is studied in a specific helicity coordinate system where the polarization vector of the top quark is evaluated with respect to the momentum direction of the bottom quark. Generally, the energy distribution of hadrons is governed by the unpolarized rate and the polar and the azimuthal correlation functions which are related to the density matrix elements of the decay $t(\uparrow)\rightarrow bH^+$. In our proposed channel, any deviation of the $B/D$-meson energy spectrum from its corresponding SM predictions can be considered as a signal for the existence of charged Higgs at the LHC. We also calculate, for the first time, the azimuthal correlation rate $\Gamma_\phi$ at next-to-leading order which vanishes at the Born level.
We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and how can oscillations be used to diagnose the plasma parameters and the magnetic field. In particular, we aim to analyse how the temporal dependence of the loop length (here modelling the expansion) will affect the P1 /P2 period ratio of transverse loop oscillations.   Due to the uncertainty of the loop's shape through its expansion, we discuss separately the case of the loop that maintains its initial semi-circular shape and the case of the loop that from a semi-circular shape evolve into an elliptical shape loop. The equations that describe the oscillations in expanding flux tube are complicated due to the spatial and temporal dependence of coefficients. Using the WKB approximation we find approximative values for periods and their evolution, as well as the period ratio. For small values of time (near the start of the expansion) we can employ a regular perturbation method to find approximative relations for eigenfunctions and eigenfrequencies.   Using simple analytical and numerical methods we show that the period of oscillations are affected by the rising of the coronal loop. The change in the period due to the increase in the loop's length is more pronounced for those loops that expand into a more structured (or cooler corona). The deviation of periods will have significant implications in determining the degree of stratification in the solar corona. The effect of expansion on the periods of oscillations is considerable only in the process of expansion of the loop but not when it reached its final stage.
Subordinating a multivariate L\'evy process, the subordinate, with a univariate subordinator gives rise to a pathwise construction of a new L\'evy process, provided the subordinator and the subordinate are independent processes. The variance-gamma model in finance was generated accordingly from a Brownian motion and a gamma process. Alternatively, multivariate subordination can be used to create L\'evy processes, but this requires the subordinate to have independent components. In this paper, we show that there exists another operation acting on pairs $(T,X)$ of L\'evy processes which creates a L\'evy process $X\odot T$. Here, $T$ is a subordinator, but $X$ is an arbitrary L\'evy process with possibly dependent components. We show that this method is an extension of both univariate and multivariate subordination and provide two applications. We illustrate our methods giving a weak formulation of the variance-$\alpha$-gamma process that exhibits a wider range of dependence than using traditional subordination. Also, the variance generalised gamma convolution class of L\'evy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination.
Superradiance typically requires preparation of atoms in highly entangled multi-particle states, the so-called Dicke states. In this paper we discuss an alternative route where we prepare such states from initially uncorrelated atoms by a measurement process. By measuring higher order intensity intensity correlations we demonstrate that we can simulate the emission characteristics of Dicke superradiance by starting with atoms in the fully excited state. We describe the essence of the scheme by first investigating two excited atoms. Here we demonstrate how via Hanbury Brown and Twiss type of measurements we can produce Dicke superradiance and subradiance displayed commonly with two atoms in the single excited symmetric and antisymmetric Dicke states, respectively. We thereafter generalize the scheme to arbitrary numbers of atoms and detectors, and explain in detail the mechanism which leads to this result. The approach shows that Hanbury Brown and Twiss type intensity interference and the phenomenon of Dicke superradiance can be regarded as two sides of the same coin. We also present a compact result for the characteristic functional which generates all order intensity intensity correlations.
Surface photometry is a necessary tool to establish the dynamical state of stars clusters. We produce realistic HST-like images from N-body models of star clusters with and without central intermediate-mass black holes (IMBHs) in order to measure their surface brightness profiles. The models contain ~600,000 individual stars, black holes of various masses between 0% to 2% of the total mass, and are evolved for a Hubble time. We measure surface brightness and star count profiles for every constructed image in order to test the effect of intermediate mass black holes on the central logarithmic slope, the core radius, and the half-light radius. We use these quantities to test diagnostic tools for the presence of central black holes using photometry. We find that the the only models that show central shallow cusps with logarithmic slopes between -0.1 and -0.4 are those containing central black holes. Thus, the central logarithmic slope seems to be a good way to choose clusters suspect of containing intermediate-mass black holes. Clusters with steep central cusps can definitely be ruled out to host an IMBH. The measured r_c/r_h ratio has similar values for clusters that have not undergone core-collapse, and those containing a central black hole. We notice that observed Galactic globular clusters have a larger span of values for central slope and r_c/r_h than our modeled clusters, and suggest possible reasons that could account for this and contribute to improve future models.
The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles and two identical spin-1/2 fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to arbitrary potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where for example large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving is substantial.
This editorial presents the quantum field theoretic ambiance in which Elko and mass dimension one fermions come to exist. This may serve not only to introduce Elko, and the associated quantum field, but it may also open a door to a new class of spin one half fermions and bosons. These new particles, as it will be argued in this volume, are first-principle candidates for dark matter.
For one-dimensional vibrating cavity systems appearing in the standard illustration of the dynamical Casimir effect, we propose an approach to the construction of exact closed-form solutions. As new results, we obtain solutions that are given for arbitrary frequencies, amplitudes and time regions. In a broad range of parameters, a vibrating cavity model exhibits the general property of exponential instability. Marginal behavior of the system manifests in a power-like growth of radiated energy.
Large classes of AdS$_p$ supergravity backgrounds describing the IR dynamics of $p$-branes wrapped on a Riemann surface are determined by a solution to the Liouville equation. The regular solutions of this equation lead to the well-known wrapped brane supergravity solutions associated with the constant curvature metric on a compact Riemann surface. We show that some singular solutions of the Liouville equation have a physical interpretation as explicit point-like brane sources on the Riemann surface. We uncover the details of this picture by focusing on $\mathcal{N}=1$ theories of class $\mathcal{S}$ arising from M5-branes on a punctured Riemann surface. We present explicit AdS$_5$ solutions dual to these SCFTs and check the holographic duality by showing the non-trivial agreement of 't Hooft anomalies.
A consistent description of low-energy charge and spin responses of the insulating Sr_2CuO_2Cl_2 lamellar system is found in the framework of a one-band Hubbard model which besides $U$ includes hoppings up to 3^{rd} nearest-neighbors. By combining mean-field calculations, exact diagonalization (ED) results, and Quantum Monte Carlo simulations (QMC), we analyze both charge and spin degrees of freedom responses as observed by optical conductivity, ARPES, Raman and inelastic neutron scattering experiments. Within this effective model, long-range hopping processes flatten the quasiparticle band around $(0,\pi)$. We calculate also the non-resonant A_{1g} and B_{1g} Raman profiles and show that the latter is composed by two main features, which are attributed to 2- and 4-magnon scattering.
We present the bounds in terms of other important graph parameters for general Sombor index which generalises both the forgotten index and the Sombor index. We also explore the Nordhaus-Gaddum-type result for the general Sombor index. We present further the relations between general Sombor index and other generalised indices: general Randi\'c index and general sum-connectivity index.
We present the optimal reconstruction of the thermal Sunyaev-Zel'dovich (tSZ) effect signal based on the combination of a heterogeneous dataset consisting of ACT and Planck data, with different numbers of channels, angular resolutions and noise levels. We combine both datasets using two different approaches, a Matched Multi-Filter (MMF) technique and an optimised Internal Linear Combination (ILC). We show that when applying the MMF to the combination of ACT and Planck data, the size-flux degeneracy is reduced and the signal-to-noise of clusters detected with their SZ signal improves by up to a factor of three. In the case of the optimised ILC method, we show that the tSZ map is reconstructed with a resolution of $\sim 1.5$ arcmin. This is more than a factor two improvement compared with the Planck resolution, and with a very good control of noise, i.e. limited only by the intrinsic noise of the individual experiments. The combination of ACT and Planck data offers a unique opportunity to improve on the study of the pressure profiles and to study substructure in clusters through their tSZ.
Planar flames are intrinsically unstable in open domains due to the thermal expansion across the burning front--the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface, and corresponding acceleration of the flame, until it is stabilized by cusp formation. We look at the Landau-Darrieus instability for C/O thermonuclear flames at conditions relevant to the late stages of a Type Ia supernova explosion. Two-dimensional direct numerical simulations of both single-mode and multi-mode perturbations using a low Mach number hydrodynamics code are presented. We show the effect of the instability on the flame speed as a function of both the density and domain size, demonstrate the existence of the small scale cutoff to the growth of the instability, and look for the proposed breakdown of the non-linear stabilization at low densities. The effects of curvature on the flame as quantified through measurements of the growth rate and computation of the corresponding Markstein number. While accelerations of a few percent are observed, they are too small to have any direct outcome on the supernova explosion.
We assess the relationships between the surface densities of the gas and star formation rate (SFR) within spiral arms of the nearby late-type spiral galaxies M81 and M101. By analyzing these relationships locally, we derive empirically a kiloparsec scale Kennicutt-Schmidt Law. Both M81 and M101 were observed with the Far-Infrared Surveyor (FIS) aboard AKARI in four far-infrared bands at 65, 90, 140, and 160 um. The spectral energy distributions of the whole galaxies show the presence of the cold dust component (Tc~20 K) in addition to the warm dust component (Tw~60 K). We deconvolved the cold and warm dust emission components spatially by making the best use of the multi-band photometric capability of the FIS. The cold and warm dust components show power-law correlations in various regions, which can be converted into the gas mass and the SFR, respectively. We find a power-law correlation between the gas and SFR surface densities with significant differences in the power law index N between giant HII regions (N=1.0) and spiral arms (N=2.2) in M101. The power-law index for spiral arms in M81 is similar (N=1.9) to that of spiral arms in M101. Conclusions: The power-law index is not always constant within a galaxy. The difference in the power-law index can be attributed to the difference in the star formation processes on a kiloparsec scale. N~2 seen in the spiral arms in M81 and M101 supports the scenario of star formation triggered by cloud-cloud collisions enhanced by spiral density wave, while N~1 derived in giant HII regions in M101 suggests the star formation induced by the Parker instability triggered by high velocity HI gas infall. The present method can be applied to a large galaxy sample for which the AKARI All Sky Survey provides the same 4 far-infrared band data.
We present a new method for sampling the Levy area for a two-dimensional Wiener process conditioned on its endpoints. An efficient sampler for the Levy area is required to implement a strong Milstein numerical scheme to approximate the solution of a stochastic differential equation driven by a two-dimensional Wiener process whose diffusion vector fields do not commute. Our method is simple and complementary to those of Gaines-Lyons and Wiktorsson, and amenable to quasi-Monte--Carlo implementation. It is based on representing the Levy area by an infinite weighted sum of independent Logistic random variables. We use Chebychev polynomials to approximate the inverse distribution function of sums of independent Logistic random variables in three characteristic regimes. The error is controlled by the degree of the polynomials, we set the error to be uniformly 10^(-12). We thus establish a strong almost-exact Levy area sampling method. The complexity of our method is square logarithmic. We indicate how our method can contribute to efficient sampling in higher dimensions.
Recent work on exact renormalization group flow equations has pointed out the possibility to study critical phenomena in continuous dimension D of space. In an investigation of the O(N) model the dimension N of the fields may be seen as a continuous parameter as well. One may conjecture that a variation of D or N in the vicinity of a second order phase transition yields the same critical exponents as a variation of the temperature. A numerical computation confirms this.
In this article we compute the mass associated to any unimodular lattice in a Hermitian space over an arbitrary CM field under a condition at 2. We study the geometry and arithmetic of the basic locus of the GU(r,s)-Shimura variety associated to an imaginary quadratic field modulo a good prime p>2. We give explicit formulas for the numbers of irreducible and connected components of the basic locus, and of points of the zero-dimensional Ekedahl-Oort (EO) stratum, as well as of the irreducible components of basic EO strata when the signature is either (1, n-1) or (2,2).
Magnetic fields on the surface of the Sun and stars in general imprint or modify the polarization state of the electromagnetic radiation that is leaving from the star. The inference of solar/stellar magnetic fields is performed by detecting, studying and modeling polarized light from the target star. In this review we present an overview of techniques that are used to study the atmosphere of the Sun, and particularly those that allow to infer magnetic fields. We have combined a small selection of theory on polarized radiative transfer, inversion techniques and we discuss a number of results from chromospheric inversions.
This paper addresses some fundamental issues in nonconvex analysis. By using pure complementary energy principle proposed by the author, a class of fully nonlinear partial diforerential equations in nonlinear elasticity is able to converted a unified algebraic equation, a complete set of analytical solutions are obtained for 3-D finite deformation problems governed by generalized neo-Hookean model. Both global and local extremal solutions to the nonconvex variational problem are identifored by a triality theory. Connection between challenges in nonlinear analysis and NP-hard problems in computational science is revealed. Results show that Legendre-Hadamard condition can only guarantee ellipticity for convex problems. For nonconvex systems, the ellipticity depends not only on the stored energy, but also on the external force field. Uniqueness is proved based on a quasiconvexity and a generalized ellipticity condition. Application is illustrated for logarithm stored energy.
Autonomous driving is a challenging problem where there is currently an intense focus on research and development. Human drivers are forced to make thousands of complex decisions in a short amount of time,quickly processing their surroundings and moving factors. One of these aspects, recognizing regions on the road that are driveable is vital to the success of any autonomous system. This problem can be addressed with deep learning framed as a region proposal problem. Utilizing a Mask R-CNN trained on the Berkeley Deep Drive (BDD100k) dataset, we aim to see if recognizing driveable areas, while also differentiating between the car's direct (current) lane and alternative lanes is feasible.
We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes function and, as a consequence, the paradiagonal Pade approximants converge to the coupling in the entire $Q^2$-plane except on the time-like semiaxis below the cut. The equivalence between the narrow width approximation of the discontinuity function of the coupling, on the one hand, and this Pade (rational) approximation of the coupling, on the other hand, is shown. We approximate the analytic analogs of the higher powers of mMA coupling by rational functions in such a way that the singularity region is respected by the approximants.Several comparisons, for real and complex arguments $Q^2$, between the exact and approximate expressions are made and the speed of convergence is discussed. Motivated by the success of these approximants, an improvement of the mMA coupling is suggested, and possible uses in the reproduction of experimental data are discussed.
We provide a novel search technique, which uses a hierarchical model and a mutual information gain heuristic to efficiently prune the search space when localizing faces in images. We show exponential gains in computation over traditional sliding window approaches, while keeping similar performance levels.