ShantanuT01/DACTYL-Pretraining huggingface dataset:
By assuming a phenomenological form for the ratio of the DE and DM densities $\rho_X\propto \rho_{m} a^{\xi}$ (Dalal et al.2001), we discuss the cosmic coincidence problem in light of current observational data. $\xi$ is a key parameter to denote the severity of the coincidence problem. In this scenario, $\xi=3$ and $\xi=0$ correspond to $\Lambda$CDM and the self-similar solution without coincidence problem, respectively. Hence, any solution with a scaling parameter $0<\xi<3$ makes the coincidence problem less severe. In addition, the standard cosmology without interaction between DE and DM is characterized by $\xi+3\omega_X=0$, whereas the inequality $\xi+3\omega_X\neq 0$ represents non-standard cosmology. We place observational constraints on the parameters $(\Omega_{X,0},\omega_{X},\xi)$ of this model, by using the Constitution Set, the CMB shift parameter from the 5-year WMAP and the SDSS baryon acoustic peak. Combining the three samples, we get $\Omega_{X,0}=0.72\pm0.02$, $\omega_{X}=-0.98\pm0.07$ and $\xi=3.06\pm0.35$ at 68.3% confidence level. The result shows that the $\Lambda$CDM model still remains a good fit to the recent observational data, as well as, the coincidence problem indeed exists and is quite severe, in the framework of this simple phenomenological model. We further constrain the model with the transition redshift (deceleration / acceleration). It shows that if the transition from deceleration to acceleration happens at the redshit $z > 0.73$, within the framework of this model, we can conclude that the interaction between DE and DM is necessary.
The static electromagnetic properties of the $W$ boson, $\Delta \kappa$ and $\Delta Q$, are calculated in the $SU_L(3)} \times U_X(1)$ model with right-handed neutrinos. The new contributions from this model arise from the gauge and scalar sectors. In the gauge sector there is a new contribution from a complex neutral gauge boson $Y^0$ and a singly-charged gauge boson $Y^\pm$. The mass of these gauge bosons, called bileptons, is expected to be in the range of a few hundreds of GeV according to the current bounds from experimental data. If the bilepton masses are of the order of 200 GeV, the size of their contribution is similar to that obtained in other weakly coupled theories. However the contributions to both $\Delta Q$ and $\Delta \kappa$ are negligible for very heavy or degenerate bileptons. As for the scalar sector, an scenario is examined in which the contribution to the $W$ form factors is identical to that of a two-Higgs-doublet model. It is found that this sector would not give large corrections to $\Delta \kappa$ and $\Delta Q$.
While present standard model of cosmology yields no clear prediction for the initial magnetic field strength, efficient dynamo action may compensate for initially weak seed fields via rapid amplification. In particular, the small-scale dynamo is expected to exponentially amplify any weak magnetic field in the presence of turbulence. We explore whether this scenario is viable using cosmological magneto-hydrodynamics simulations modeling the formation of the first galaxies, which are expected to form in so-called atomic cooling halos with virial temperatures $\rm T_{vir} \geq 10^{4}$ K. As previous calculations have shown that a high Jeans resolution is needed to resolve turbulent structures and dynamo effects, our calculations employ resolutions of up to 128 cells per Jeans length. The presence of the dynamo can be clearly confirmed for resolutions of at least 64 cells per Jeans length, while saturation occurs at approximate equipartition with turbulent energy. As a result of the large Reynolds numbers in primordial galaxies, we expect saturation to occur at early stages, implying magnetic field strengths of \sim0.1 $\mu$G at densities of 10^4 cm^{-3}.
A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the Random Field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional (3D) microstructure formation and on avalanche statistics.
Specific heat of polycrystalline BaTiO3 thin films on the fused quartz substrate was measured by ac-hot probe method. Phase transition temperature, excess entropy and spontaneous polarization were determined as a function of film thickness and grain size. The variation of the latter was obtained in the limits 30 - 150 nm by changing of the temperature of the substrate during sputtering while thickness of films 20 - 1100 nm was controlled by the conditions of sputtering. It was found that the relation between the thickness and grain size is important for the size effects in polycrystalline films.
Numerous studies have demonstrated the ability of Convolutional Neural Networks (CNNs) to classify large numbers of galaxies in a manner which mimics the expertise of astronomers. Such classifications are not always physically motivated, however, such as categorising galaxies by their morphological types. In this work, we consider the use of CNNs to classify simulated S0 galaxies based on fundamental physical properties. In particular, we undertake two investigations: (1) the classification of simulated S0 galaxies into three distinct evolutionary paths (isolated, tidal interaction in a group halo, and Spiral-Spiral merger), and (2) the prediction of the mass ratio for the S0s formed via mergers. To train the CNNs, we first run several hundred N-body simulations to model the formation of S0s under idealised conditions; and then we build our training datasets by creating images of stellar density and two dimensional kinematic maps for each simulated S0. Our trained networks have remarkable accuracies exceeding 99% when classifying the S0 formation pathway. For the case of predicting merger mass ratios, the mean predictions are consistent with the true values to within roughly one standard deviation across the full range of our data. Our work demonstrates the potential of CNNs to classify galaxies by the fundamental physical properties which drive their evolution.
The chromosphere is a highly complex and dynamic layer of the Sun, that serves as a conduit for mass and energy supply between two, very distinct regions of the solar atmosphere, namely, the photosphere and corona. Inferring magnetic fields in the chromosphere, has thus become an important topic, that can be addressed with large-aperture solar telescopes to carry out highly sensitive polarimetric measurements. In this article, we present a design of a polarimeter for investigating the chromospheric magnetic field. The instrument consists of a number of lenses, two ferro-electric liquid crystals, a Wollaston prism, and a CCD camera. The optical design is similar to that of a commercial zoom lens which allows a variable f-number while maintaining focus and aberrations well within the Airy disc. The optical design of the Adaptable ChRomOspheric POLarimeter (ACROPOL) makes use of off-the-shelf components and is described for the 70 cm Vacuum Tower Telescope and the 1.5 m GREGOR telescope at Observatorio del Teide, Tenerife, Spain. Our design shows that the optical train can be separated into two units where the first unit, consisting of a single lens, has to be changed while going from the VTT to the GREGOR configuration. We also discuss the tolerances within which, diffraction limited performance can be achieved with our design.
In the present paper we consider biologically motivated reduction operations on double occurrence words. Then we define the nesting index of a double occurrence word to be the least number of reduction operations it takes for a word to be reduced to the empty word. We use chord diagrams and circle graphs as tools to study the nesting index of double occurrence words.
Mass loss rates for the tenuous, hot winds of cool stars are extremely difficult to measure, yet they are a crucial ingredient in the stars' rotational evolution. We present a new method for measuring these mass loss rates in young, rapidly-rotating stars. These stars are known to support systems of "slingshot prominences" fed by hot wind material flowing up from the stellar surface into the summits of closed magnetic loop structures. The material gathers and cools near the co-rotation radius until its density becomes large enough that it is visible as a transient absorption feature in the hydrogen Balmer lines and strong resonance lines such as Ca II H \&\ K. Here we present the key insight that the sonic point usually lies well below the condensation region. The flow at the wind base is therefore unaffected by the presence of an overlying prominence, so we can use the observed masses and recurrence times of the condensations to estimate the mass flux in the wind. These measurements extend the relationship between mass loss rate per unit surface area and X-ray flux to span 5 orders of magnitude. They demonstrate no evidence of the suspected weakening of stellar mass loss rates at high X-ray flux levels.
The Catalan numbers $C_k$ were first studied by Euler, in the context of enumerating triangulations of polygons $P_{k+2}$. Among the many generalizations of this sequence, the Fuss-Catalan numbers $C^{(d)}_k$ count enumerations of dissections of polygons $P_{k(d-1)+2}$ into $(d+1)$-gons. In this paper, we provide a formula enumerating polygonal dissections of $(n+2)$-gons, classified by partitions $\lambda$ of $[n]$. We connect these counts $a_{\lambda}$ to reverse series arising from iterated polynomials. Generalizing this further, we show that the coefficients of the reverse series of polynomials $x=z-\sum_{j=0}^{\infty} b_j z^{j+1}$ enumerate colored polygonal dissections.
It has been widely recognized that the success of deep learning in image segmentation relies overwhelmingly on a myriad amount of densely annotated training data, which, however, are difficult to obtain due to the tremendous labor and expertise required, particularly for annotating 3D medical images. Although self-supervised learning (SSL) has shown great potential to address this issue, most SSL approaches focus only on image-level global consistency, but ignore the local consistency which plays a pivotal role in capturing structural information for dense prediction tasks such as segmentation. In this paper, we propose a PriorGuided Local (PGL) self-supervised model that learns the region-wise local consistency in the latent feature space. Specifically, we use the spatial transformations, which produce different augmented views of the same image, as a prior to deduce the location relation between two views, which is then used to align the feature maps of the same local region but being extracted on two views. Next, we construct a local consistency loss to minimize the voxel-wise discrepancy between the aligned feature maps. Thus, our PGL model learns the distinctive representations of local regions, and hence is able to retain structural information. This ability is conducive to downstream segmentation tasks. We conducted an extensive evaluation on four public computerized tomography (CT) datasets that cover 11 kinds of major human organs and two tumors. The results indicate that using pre-trained PGL model to initialize a downstream network leads to a substantial performance improvement over both random initialization and the initialization with global consistency-based models. Code and pre-trained weights will be made available at: https://git.io/PGL.
Using the basic ingredient of supersymmetry, a general procedure for the treatment of quantum states having nonzero angular momenta is presented.
We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution PDEs with constant coefficients in one space variable. The prototypical such PDE is the heat equation, for which problems of this form model physical phenomena in chemistry and for which we formulate and prove a full result. We also consider the third order case, which is much less studied and has been shown by the authors to have very different structural properties in general.   The nonlocal conditions we consider can be reformulated as \emph{multipoint conditions}, and then an explicit representation for the solution of the problem is obtained by an application of the Fokas transform method. The analysis is carried out under the assumption that the problem being solved is well posed, i.e.\ that it admits a unique solution. For the second order case, we also give criteria that guarantee well-posedness.
In the framework of the light-front quantum theory developed by Karmanov et al. an analysis of the experimental data on the tensor analyzing power of the nuclear fragmentation of relativistic deuterons with the large transversal momentum proton emission has been made. With the Karmanov's wave function taken in system in which z-axis directed along the deuteron beam we have managed to explain the existing data without invoking additional to nucleons degrees of freedom.
We provide a new convergence proof of the celebrated Merriman-Bence-Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface tensions and mobilities, including typical choices for modeling grain growth. The basis of the proof are the minimizing movements interpretation of Esedo\u{g}lu and Otto and De Giorgi's general theory of gradient flows. Under a typical energy convergence assumption we show that the limit satisfies a sharp energy-dissipation relation.
Using collective atom phase control a population inversion-free photon echo scheme has been studied for quantum memory applications. For the inversion-free photon echoes a double rephasing method is combined with optical locking, where the optical locking coherently controls each atom phase excited by weak data pulses. As a result, intensity flattened, normally ordered, storage time-extended, and noise-free photon echoes are obtained.
We introduce a class of rotationally invariant manifolds, which we call \emph{admissible}, on which the wave flow satisfies smoothing and Strichartz estimates. We deduce the global existence of equivariant wave maps from admissible manifolds to general targets, for small initial data of critical regularity $H^{\frac n2}$. The class of admissible manifolds includes in particular asymptotically flat manifolds and perturbations of real hyperbolic spaces $\mathbb{H}^{n}$ for $n\ge3$.
In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 (Mrk 421) at X-ray and TeV Gamma-ray energies with the Rossi X-Ray Timing Explorer (RXTE) and the stereoscopic Cherenkov Telescope system of the HEGRA (High Energy Gamma Ray Astronomy) experiment, respectively. The source was monitored from February 2nd to February 16th and from May 3rd to May 8th, 2000. We discuss in detail the temporal and spectral properties of the source. Remarkably, the TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale. We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton (SSC) model. The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher. The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones.
Let $S$ be a $p$-subgroup of the $\mathbb K$-automorphism group $Aut(\mathcal X)$ of an algebraic curve $\mathcal X$ of genus $g\ge 2$ and $p$-rank $\gamma$ defined over an algebraically closed field $\mathbb{K}$ of characteristic $p\geq 3$. Nakajima proved that if $\gamma \ge 2$ then $|S|\leq \textstyle\frac{p}{p-2}(g-1)$. If equality holds, $\mathcal X$ is a Nakajima extremal curve. We prove that if $$|S|>\textstyle\frac{p^2}{p^2-p-1}(g-1)$$ then one of the following cases occurs:   (i) $\gamma=0$ and the extension $\mathbb K(\mathcal X)|\mathbb K(\mathcal X)^S$ completely ramifies at a unique place, and does not ramify elsewhere.   (ii) $|S|=p$, and $\mathcal X$ is an ordinary curve of genus $g=p-1$.   (iii) $\mathcal X$ is an ordinary, Nakajima extremal curve, and $\mathbb K(\mathcal X)$ is an unramified Galois extension of a function field of a curve given in (ii). There are exactly $p-1$ such Galois extensions. Moreover, if some of them is an abelian extension then $S$ has maximal nilpotency class.   The full $\mathbb{K}$-automorphism group of any Nakajima extremal curve is determined, and several infinite families of Nakajima extremal curves are constructed by using their pro-$p$ fundamental groups.
We investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of a radiating Schwarzschild black hole. We show that evaporation process is in such a way that black hole reaches to a maximum temperature before its final stage of evolution and then cools down to a nonsingular remnant with zero temperature and entropy. We compare our results with more reliable results of string theory. This comparison Shows that GUP and space noncommutativity are similar concepts at least from view point of black hole thermodynamics.
We have formed ``composite spectra'' by combining the integrated-light spectra of individual galaxies in 8 intermediate-redshift and 12 low-redshift clusters of galaxies. Because these composite spectra have much higher signal-to-noise ratios than individual galaxy spectra, they are particularly useful in quantifying general trends in star formation for galaxy populations in distant clusters, z > 0.3. By measuring diagnostic features that represent stellar populations of very different ages, a grand-composite spectrum can reflect the fractions of those populations as accurately as if excellent spectral measurements were available for each galaxy.   Measuring the equivalent widths of spectral features in composite spectra is especially well-suited for comparing cosmic variance of star formation in clusters at a given redshift, or comparing clusters over a range of redshifts. When we do this we find that [O II] emission and especially Balmer absorption is strong in each of our intermediate-redshift clusters, and completely separable from a sample of 12 present-epoch clusters, where these features are weak. Specifically, we show by comparing to the H-delta strengths of present-epoch populations of continuously star-forming galaxies that the higher-redshift samples must contain a much higher fraction of starburst galaxies than are found today in any environment.
We analyse a non-equilibrium exclusion process in which particles are created and annihilated in pairs and hop to the the right or to the left with different transition rates, $p$ and $q$, respectively. We have studied the dynamics of a single particle, and exactly determined the entropy, entropy production rate and entropy flux as functions of time. In the system of many particles, we have characterised the system by its probability distribution, as well as the entropy production rate in close forms, provided that $p+q$ equals the sum of dimers creation and annihilation rates. The general case, where this constraint is absent, was considered at pair approximation level; the time-dependent behaviour of the system was analysed, and the stationary entropy production was determined. In all cases, in the stationary regime, we showed that the entropy production rate is a bilinear form in the current of particles and the force $\ln(p/q)$.
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the same label can appear in distinct branches of the tree. In the course of the analysis we develop a method to extract asymptotic information on the coefficients of purely formal power series. The method is based on an approximate Borel transform (or, more generally, Mittag-Leffler transform) which enables us to quickly guess the exponential growth rate. With this guess the sequence is then rescaled and a singularity analysis of the generating function of the scaled counting sequence yields accurate asymptotics. The actual analysis is based on differential equations and a Tauberian argument. The counting problem for trees of size n exhibits interesting asymptotics involving powers of n with irrational exponents.
In this paper, we study families of immersed curves $\gamma:(-1,1)\times[0,T)\rightarrow\mathbb{R}^2$ with free boundary supported on parallel lines $\{\eta_1, \eta_2\}:\mathbb{R}\rightarrow\mathbb{R}^2$ evolving by the curve diffusion flow and the curve straightening flow. The evolving curves are orthogonal to the boundary and satisfy a no-flux condition. We give estimates and monotonicity on the normalised oscillation of curvature, yielding global results for the flows.
We prove a nonequilibirum central limit theorem for the position of a tagged particle in the one-dimensional nearest-neighbor symmetric simple exclusion process under diffusive scaling starting from a Bernoulli product measure associated to a smooth profile $\rho_0:\bb R\to [0,1]$.
Let f be a map-germ of corank 1 from complex n-space to complex (n+1)-space, and, for k less than or equal to the multiplicity of f, let $D^k(f)$ be its k'th multiple-point scheme -- the closure of the set of ordered k-tuples of pairwise distinct points sharing the same image. There are natural projections from $D^{k+1}(f)$ to $D^k(f)$, determined by forgetting one member of the (k+1)-tuple. We prove that the matrix of a presentation of $\OO_{D^{k+1}(f)}$ over $\OO_{D^k(f)}$ appears as a certain submatrix of the matrix of a suitable presentation of $\OO_{\CC^n}$ over $\OO_{\CC^{n+1}}$. This does not happen for germs of corank greater than 1.
By using the coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if a<1/2, while for a>1/2, there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter a exceeds a critical point ac1. The precise critical point ac1 can be determined by using the coupled cluster method and the numerical exact diagonalization method separately. The results of the coupled cluster method and the exact diagonalization method both disclose that the type of phase transition occurring at ac1 changes from a classical second-order transition to a quantum first-order transition due to quantum fluctuation. Although there is another critical point ac2 in a finite system at which the ground state evolves from the canted state to the collinear Neel plus ferromagnetic state, that state is absent because ac2 tends to infinity in the thermodynamic limit.
We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growth, division and up-take). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulations.