ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have observed a small sample of powerful double radio sources (radio galaxies and quasars) at frequencies around 90 GHz with the BIMA millimetre array, with the intention of constraining the resolved high-frequency spectra of radio galaxies. When combined with other sources we have previously observed and with data from the BIMA archive, these observations allow us for the first time to make general statements about the high-frequency behaviour of compact components of radio galaxies -- cores, jets and hotspots. We find that cores in our sample remain flat-spectrum up to 90 GHz; jets in some of our targets are detected at 90 GHz for the first time in our new observations; and hotspots are found to be almost universal, but show a wide range of spectral properties. Emission from the extended lobes of radio galaxies is detected in a few cases and shows rough consistency with the expectations from standard spectral ageing models, though our ability to probe this in detail is limited by the sensitivity of BIMA. We briefly discuss the prospects for radio-galaxy astrophysics with ALMA.
A map-guided superpixel segmentation method for hyperspectral imagery is developed and introduced. The proposed approach develops a hyperspectral-appropriate version of the SLIC superpixel segmentation algorithm, leverages map information to guide segmentation, and incorporates the semi-supervised Partial Membership Latent Dirichlet Allocation (sPM-LDA) to obtain a final superpixel segmentation. The proposed method is applied to two real hyperspectral data sets and quantitative cluster validity metrics indicate that the proposed approach outperforms existing hyperspectral superpixel segmentation methods.
Given a bounded finely open set $V$ and a function $f$ on the fine boundary of $V$, we introduce four types of upper Perron solutions to the nonlinear Dirichlet problem for $p$-energy minimizers, $1<p<\infty$, with $f$ as boundary data. These solutions are given as pointwise infima of suitable families of fine $p$-superminimizers in $V$. We show (under natural assumptions) that the four upper Perron solutions are equal quasieverywhere and that they are fine $p$-minimizers of the $p$-energy integral. We moreover show that the upper and lower Perron solutions coincide quasieverywhere for Sobolev and for uniformly continuous boundary data, i.e.\ that such boundary data are resolutive. For the uniformly continuous boundary data, the Perron solutions are also shown to be finely continuous and thus finely $p$-harmonic. We prove our results in a complete metric space $X$ equipped with a doubling measure supporting a $p$-Poincar\'e inequality, but they are new also in unweighted $\mathbf{R}^n$.
Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula. Minimal solutions are determined for the integrable boundary perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon models and the two point functions calculated from them are checked against the exact solutions in the free cases and against the conformal data in the ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion the dimension of the solution space of the boundary form factor equation is shown to match the number of independent local operators. We obtain excellent agreement which proves not only the correctness of the solutions but also confirms the form factor axioms.
We report results of micro-Raman spectroscopy investigation of the "graphene-like" mechanically exfoliated single-crystal bismuth telluride films with the thickness ranging from a few-nm-range to bulk limit. It is found that the optical phonon mode A1u, which is not-Raman active in bulk bismuth telluride crystals, appears in the atomically-thin films due to crystal-symmetry breaking. The intensity ratios of the out-of-plane A1u and A1g modes to the in-plane Eg mode grow with decreasing film thickness. The evolution of Raman signatures with the film thickness can be used for identification of bismuth telluride crystals with the thickness of few-quintuple layers, which are important for topological insulator and thermoelectric applications.
The persistent spin current in anisotropic spin ring penetrated by a SU(2) flux is studied by the Schwinger-boson mean field approach. The anisotropy in spin coupling can facilitate the persistent spin current. Ground-state energy and excitation energy gap are also studied. The peak of spin current occurs at the maximum value of the ground-state energy.
We develop the mathematics of a filtration shrinkage model that has recently been considered in the credit risk modeling literature. Given a finite collection of points $x_1<...<x_N$ in $\mathbb{R}$, the region indicator function $R(x)$ assumes the value $i$ if $x\in(x_{i-1},x_i]$. We take $\mathbb{F}$ to be the filtration generated by $(R(X_t))_{t\geq0}$, where $X$ is a diffusion with infinitesimal generator $\mathcal{A}$. We prove a martingale representation theorem for $\mathbb{F}$ in terms of stochastic integrals with respect to $N$ random measures whose compensators have a simple form given in terms of certain L\'{e}vy measures $F^{j\pm}_i$, which are related to the differential equation $\mathcal{A}u=\lambda u$.
We present numerical evidence for the presence of a finite-temperature ($T$) phase transition separating paramagnet and quantum spin liquid in a three-dimensional variant of the Kitaev model defined on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from quantum spin liquid to paramagnet at a finite critical temperature $T_c$. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above $T_c$, while it obeys the Curie law at high $T$ and approaches a nonzero Van Vleck-type constant at low $T$. Although the susceptibility changes continuously at $T_c$, its $T$ derivative shows critical divergence at $T_c$. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to the discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables as well as the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition is interpreted as the one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. A correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently-discovered hyperhoneycomb compound, $\beta$-Li$_2$IrO$_3$, is mentioned.
The importance of imposing physical boundary conditions on the $T$-matrix to remove the nonperturbative renormalization prescription dependence is stressed and demonstrated in two diagonal channels, $^1P_1$ and $^1D_2$, with the help of Pad\'e expansion.
22 GHz water and 6.7 GHz methanol masers are usually thought as signposts of early stages of high-mass star formation but little is known about their associations and the physical environments they occur in.   The aim was to obtain accurate positions and morphologies of the water maser emission and relate them to the methanol maser emission recently mapped with Very Long Baseline Interferometry. A sample of 31 methanol maser sources was searched for 22 GHz water masers using the VLA and observed in the 6.7 GHz methanol maser line with the 32 m Torun dish simultaneously. Water maser clusters were detected towards 27 sites finding 15 new sources. The detection rate of water maser emission associated with methanol sources was as high as 71%. In a large number of objects (18/21) the structure of water maser is well aligned with that of the extended emission at 4.5 $\mu$m confirming the origin of water emission from outflows. The sources with methanol emission with ring-like morphologies, which likely trace a circumstellar disk/torus, either do not show associated water masers or the distribution of water maser spots is orthogonal to the major axis of the ring. The two maser species are generally powered by the same high-mass young stellar object but probe different parts of its environment. The morphology of water and methanol maser emission in a minority of sources is consistent with a scenario that 6.7 GHz methanol masers trace a disc/torus around a protostar while the associated 22 GHz water masers arise in outflows. The majority of sources in which methanol maser emission is associated with the water maser appears to trace outflows. The two types of associations might be related to different evolutionary phases.
Employing the non-linear $\sigma$-model we analyze current fluctuations in coherent composite conductors which contain a diffusive element in-between two tunnel barriers. For such systems we explicitly evaluate the frequency-dependent third current cumulant which also determines the leading Coulomb interaction correction to shot noise. Our predictions can be directly tested in future experiments.
We investigate efficient algorithmic realisations for robust deconvolution of grey-value images with known space-invariant point-spread function, with emphasis on 1D motion blur scenarios. The goal is to make deconvolution suitable as preprocessing step in automated image processing environments with tight time constraints. Candidate deconvolution methods are selected for their restoration quality, robustness and efficiency. Evaluation of restoration quality and robustness on synthetic and real-world test images leads us to focus on a combination of Wiener filtering with few iterations of robust and regularised Richardson-Lucy deconvolution. We discuss algorithmic optimisations for specific scenarios. In the case of uniform linear motion blur in coordinate direction, it is possible to achieve real-time performance (less than 50 ms) in single-threaded CPU computation on images of $256\times256$ pixels. For more general space-invariant blur settings, still favourable computation times are obtained. Exemplary parallel implementations demonstrate that the proposed method also achieves real-time performance for general 1D motion blurs in a multi-threaded CPU setting, and for general 2D blurs on a GPU.
We give upper bounds for the dimension of the set of hypersurfaces of $\mathbb{P}^N$ whose intersection with a fixed integral projective variety is not integral. Our upper bounds are optimal. As an application, we construct, when possible, hypersurfaces whose intersections with all the varieties of a family of integral projective varieties are integral. The degree of the hypersurfaces we construct is explicit.   -----   On majore la dimension de l'ensemble des hypersurfaces de $\mathbb{P}^N$ dont l'intersection avec une vari\'et\'e projective int\`egre fix\'ee n'est pas int\`egre. Les majorations obtenues sont optimales. Comme application, on construit, quand c'est possible, des hypersurfaces dont les intersections avec toutes les vari\'et\'es d'une famille de vari\'et\'es projectives int\`egres sont int\`egres. Le degr\'e des hypersurfaces construites est explicite.
We discuss the results of numerical simulations of colliding wavepackets in $SU(2)$ Yang--Mills theory. We investigate their behavior as a function of amplitude and momentum distribution. We find regions in our parameter space in which initial wave packets scatter into final configurations with dramatically different momentum distributions. These results constitute new classical trajectories with multiparticle boundary conditions. We explain their relevance for the calculation of scattering amplitudes in the semiclassical approximation. Finally, we give directions for future work.
We present a novel method for generation of sets of the Cosmic Microwave Background (CMB) anisotropy maps, which reproduces the $\Delta \l=2$ correlations associated with Alfv\'en turbulence. The method is based on the non-linear transformation of the CMB maps, which is obtained from the Monte Carlo simulation of the statistically isotropic Gaussian signal. Our method is computationally fast and efficient.   We have applied two estimators (the cross-correlation estimator in multipole domain for $\l+1,m$ and $\l-1,m$ modes and circular phase moments) to test the statistical properties of derived maps. Both of these statistics confirm the effectiveness of our generation method. We believe that our method can be useful for fast generation of the non-Gaussian maps in the presence of the primordial magnetic field, and be a valuable tool for the non-Gaussianity investigation of the CMB in the framework of the future PLANCK data analysis.
We present the analysis of FUSE observations of the metal-deficient dwarf galaxy IZw18. We measured column densities of HI, NI, OI, ArI, SiII, and FeII. The OI/HI ratio (log(OI/HI)=-4.7^{+0.8}_{-0.6}) is consistent with the O/H ratio observed in the HII regions (all uncertainties are 2-sigma). If the oxygen is depleted in the HI region compared to the HII regions, the depletion is at most 0.5dex. This is also consistent with the log(O/H) ratios ~-5 measured with FUSE in the HI regions of other blue compact dwarf galaxies. With log(NI/OI)=-2.4^{+0.6}_{-0.8}, the measured NI/OI ratio is lower than expected for primary nitrogen. The determination of the NII column density is needed to discriminate between a large ionization of NI or a possible nitrogen deficiency. The neutral argon is also apparently underabundant, indicating that ionization into ArII is likely important. The column densities of the other alpha-chain elements SiII and ArI favor the lower edge of the permitted range of OI column density, log(N(OI))~16.3.
We study the functional codes $C_2(X)$ defined on a projective variety $X$, in the case where $X \subset {\mathbb{P}}^3$ is a non-degenerate hermitian surface. We first give some bounds for $# X_{Z(\mathcal{Q})}(\mathbb{F}_{q})$, which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code $C_2(X)$.
Given a positive integer $n$ we let $A_k(n)$ be the number of positive integers $a$ such that $\frac{a}{n}=\frac{1}{m_1}+\frac{1}{m_2}+\cdots+\frac{1}{m_k}$ for some $m_1,m_2,\ldots,m_k\in {\mathbb N}$. We show that $x(\log x)^3\ll \sum_{p\le x} A_3(p)\ll x(\log x)^5$ as $x\rightarrow\infty$.
In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.
In this paper, we prove a threshold result for the Robin problem of semilinear parabolic equations
I discuss the elliptic flows of $\psi(2S)$ with different production mechanisms in $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb collisions. If the final $\psi(2S)$s are mainly from the recombination of uncorrelated charm and anticharm quarks at $T\approx T_c$, charm and anticharm quarks will carry large collective flows of the bulk medium, which will be inherited by the regenerated $\psi(2S)$s. This indicates a larger elliptic flow of $\psi(2S)$ than that of $J/\psi$ which can be regenerated at $T\ge T_c$, $v_2^{\psi(2S)}>v_2^{J/\psi}$. However, if the final $\psi(2S)$s are mainly from the transitions of $J/\psi\rightarrow \psi(2S)$ caused by the color screening of QGP, its elliptic flow should be close to the elliptic flow of $J/\psi$, $v_2^{\psi(2S)}\sim v_2^{J/\psi}$. Therefore, $\psi(2S)$ elliptic flow is a sensitive probe for its production mechanisms in relativistic heavy ion collisions.
We use the finite lattice method to calculate the radius of gyration, the first and second area-weighted moments of self-avoiding polygons on the square lattice. The series have been calculated for polygons up to perimeter 82. Analysis of the series yields high accuracy estimates confirming theoretical predictions for the value of the size exponent, $\nu=3/4$, and certain universal amplitude combinations. Furthermore, a detailed analysis of the asymptotic form of the series coefficients provide the firmest evidence to date for the existence of a correction-to-scaling exponent, $\Delta = 3/2$.
Buzzoni's (1989) grid of synthetic spectral energy distributions, representative of old stellar populations, was used to derive colours in different photometric systems, and to compare the theoretical predictions with the observational data referring to about $120$ globular clusters in the Galaxy and to $159$ objects of the globular cluster system of M31. Synthetic and observed indices display an overall agreement in the composite planes of two-colour diagrams, thus in agreement with the standard evolutionary scenario leading, for globular clusters, to old stellar populations consistent with an age of $15$ Gyr and a Salpeter initial mass function (IMF). The two main parameters modulating the cluster colour distributions are, as known, metallicity and horizontal branch morphology, while IMF slope and mass loss rate from stars in the red-giant branch and asymptotic-giant branch evolutionary stages produce only minor, although not negligible, effects on the integrated colours. The M31 and Galactic cluster populations are found to be substantially similar, at least as far as the spectral energy distribution characteristics in the $U \to V$ spectral range are concerned.
Perrin-Riou has formulated a form of the Iwasawa main conjecture, which relates Heegner points to the Selmer group of an elliptic curve as one goes up the anticyclotomic Z_p extension of a quadratic imaginary field K. Building on the earlier work of Bertolini on this conjecture, and making use of the recent work of Mazur and Rubin on Kolyvagin's theory of Euler systems, we prove one divisibility of Perrin-Riou's conjectured equality. As a consequence, one obtains an upper bound on the rank of the Mordell-Weil group E(K) in terms of Heegner points.
We consider stochastic differential equations of the form $dY_t=V(Y_t)\,dX_t+V_0(Y_t)\,dt$ driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields $V_0$ and $V=(V_1,\ldots,V_d)$ satisfy H\"{o}rmander's bracket condition, we demonstrate that $Y_t$ admits a smooth density for any $t\in(0,T]$, provided the driving noise satisfies certain nondegeneracy assumptions. Our analysis relies on relies on an interplay of rough path theory, Malliavin calculus and the theory of Gaussian processes. Our result applies to a broad range of examples including fractional Brownian motion with Hurst parameter $H>1/4$, the Ornstein-Uhlenbeck process and the Brownian bridge returning after time $T$.
The interstellar medium (ISM) is a key ingredient in galaxy formation and evolution as it provides the molecular gas reservoir which fuels star formation and supermassive black hole accretion. Yet the ISM is one of the least studied aspects of distant galaxies. Molecular and atomic transitions at (sub)millimetre wavelengths hold great promise in measuring macroscopic properties (e.g. masses, morphologies, star formation laws), as well as microscopic properties (e.g. gas densities, temperatures, cooling) of high-z galaxies. In this overview I summarize the growing number of high-z molecular line detections, highlighting some of the most intriguing results along the way. I end by discussing a few areas where future facilities (e.g. ALMA, EVLA, CCAT, LMT) will drastically improve on the current state of affairs.
In this paper we study the semiclassical limit for the singularly perturbed Choquard equation   $$   -\vr^2\Delta u +V(x)u =\vr^{\mu-3}\Big(\int_{\R^3} \frac{Q(y)G(u(y))}{|x-y|^\mu}dy\Big)Q(x)g(u) \quad \mbox{in $\R^3$},   $$ where $0<\mu<3$, $\vr$ is a positive parameter, $V,Q$ are two continuous real function on $\R^3$ and $G$ is the primitive of $g$ which is of critical growth due to the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on the nonlinearity $g$, we first establish the existence of ground states for the critical Choquard equation with constant coefficients in $\R^3$. Next we establish existence and multiplicity of semi-classical solutions and characterize the concentration behavior by variational methods.
We study a symmetric generalization $\mathfrak{p}^{(N)}_k(\eta, \alpha)$ of the binomial distribution recently introduced by Bergeron et al, where $\eta \in [0,1]$ denotes the win probability, and $\alpha$ is a positive parameter. This generalization is based on $q$-exponential generating functions ($e_{q^{gen}}^z \equiv [1+(1-q^{gen})z]^{1/(1-q^{gen})};\,e_{1}^z=e^z)$ where $q^{gen}=1+1/\alpha$. The numerical calculation of the probability distribution function of the number of wins $k$, related to the number of realizations $N$, strongly approaches a discrete $q^{disc}$-Gaussian distribution, for win-loss equiprobability (i.e., $\eta=1/2$) and all values of $\alpha$. Asymptotic $N\to \infty$ distribution is in fact a $q^{att}$-Gaussian $e_{q^{att}}^{-\beta z^2}$, where $q^{att}=1-2/(\alpha-2)$ and $\beta=(2\alpha-4)$. The behavior of the scaled quantity $k/N^\gamma$ is discussed as well. For $\gamma<1$, a large-deviation-like property showing a $q^{ldl}$-exponential decay is found, where $q^{ldl}=1+1/(\eta\alpha)$. For $\eta=1/2$, $q^{ldl}$ and $q^{att}$ are related through $1/(q^{ldl}-1)+1/(q^{att}-1)=1$, $\forall \alpha$. For $\gamma=1$, the law of large numbers is violated, and we consistently study the large-deviations with respect to the probability of the $N\to\infty$ limit distribution, yielding a power law, although not exactly a $q^{LD}$-exponential decay. All $q$-statistical parameters which emerge are univocally defined by $(\eta, \alpha)$. Finally we discuss the analytical connection with the P\'{o}lya urn problem.
We propose two 3-3-1 models (with either neutral fermions or right-handed neutrinos) based on S_3 flavor symmetry responsible for fermion masses and mixings. The models can be distinguished upon the new charge embedding (\mathcal{L}) relevant to lepton number. The neutrino small masses can be given via a cooperation of type I and type II seesaw mechanisms. The latest data on neutrino oscillation can be fitted provided that the flavor symmetry is broken via two different directions S_3 \rightarrow Z_2 and S_3 \rightarrow Z_3 (or equivalently in the sequel S_3 \rightarrow Z_2 \rightarrow Identity), in which the second direction is due to a scalar triplet and another antisextet as small perturbation. In addition, breaking of either lepton parity in the model with neutral fermions or lepton number in the model with right-handed neutrinos must be happened due to the \mathcal{L}-violating scalar potential. The TeV seesaw scale can be naturally recognized in the former model. The degenerate masses of fermion pairs (\mu, \tau), (c, t) and (s, b) are respectively separated due to the S_3 \rightarrow Z_3 breaking.
The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and Mo isotopes, including both even-even and odd-A nuclei, is studied within a self-consistent mean-field approximation based on the D1S Gogny interaction. Neutron separation energies and charge radii are calculated and compared with available data. A correlation between a shape transition and a discontinuity in those observables is found microscopically. While in Sr and Zr isotopes the steep behavior observed in the isotopic dependence of the charge radii is a consequence of a sharp prolate-oblate transition, the smooth behavior found in Mo isotopes has its origin in an emergent region of triaxiality.