ShantanuT01/DACTYL-Pretraining huggingface dataset:
Galaxies grow their supermassive black holes in concert with their stars, although the relationship between these major galactic components is poorly understood. Observations of the cosmic growth of stars and black holes in galaxies suffer from disjoint samples and the strong effects of dust attenuation. The thermal infrared holds incredible potential for simultaneously measuring both the star formation and black hole accretion rates in large samples of galaxies covering a wide range of physical conditions. Spitzer demonstrated this potential at low redshift, and by observing some of the most luminous galaxies at z~2. JWST will apply these methods to normal galaxies at these epochs, but will not be able to generate large spectroscopic samples or access the thermal infrared at high-redshift. An order of magnitude gap in our wavelength coverage will persist between JWST and ALMA. A large, cold infrared telescope can fill this gap to determine when (in cosmic time), and where (within the cosmic web), stars and black holes co-evolve, by measuring these processes simultaneously in statistically complete and unbiased samples of galaxies to z>8. A next-generation radio interferometer will have the resolution and sensitivity to measure star-formation and nuclear accretion in even the dustiest galaxies. Together, the thermal infrared and radio can uniquely determine how stars and supermassive blackholes co-evolve in galaxies over cosmic time.
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
We study the renormalization group (RG) equations of a pair of spin-boson systems coupled in the z-direction with each other. Each spin is coupled to a different bath of harmonic oscillators. We introduce a systematic adiabatic RG, which generalizes the first-order adiabatic renormalization previously used for the single spin-boson model, and we obtain the flow equations for the tunneling constant, the dissipation strength and the inter-spin coupling up to third order in the tunneling. If one of the two spins is treated as a constant magnetization the other spin is described by a biased spin-boson Hamiltonian. In this case the RG equations we find coincide with the ones obtained via a mapping to a long-range Ising chain. If the whole Ohmic two-spin system is considered the Kosterlitz-Thouless phase transition is replaced by a second-order phase transition. In the case of a sub-Ohmic bath our approach predicts that the two-spin system is always localized.
Current neutrino data are consistent with the so-called tribimaximal mixing scenario, which predicts \sin^2 \theta_{12}=1/3, zero U_{e3} and maximal \theta_{23}. This implies a special form of the neutrino mass matrix. Introducing small breaking terms in this mass matrix generates deviations from the tribimaximal scheme and leads to testable correlations between the parameters. They depend on where the perturbation is located in the mass matrix. A special case of such perturbations are radiative corrections. Alternative deviations from tribimaximal mixing may stem from contributions of the charged lepton sector. If there is quark-lepton-unification and it is the CKM matrix which corrects the tribimaximal mixing scheme, then almost maximal CP violation and sizable deviation from zero U_{e3} are implied.
Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.
We study the space of non-simple polarised abelian surfaces. Specifically, we describe for which pairs $(m,n)$ the locus of polarised abelian surfaces of type $(1,d)$ that contain two complementary elliptic curve of exponents $m,n$, denoted $\mathcal{E}_d(m,n)$ is non-empty. We show that if $d$ is square-free, the locus $\mathcal{E}_d(m,n)$ is an irreducible surface (if non-empty). We also show that the loci $\mathcal{E}_d(d,d)$ can have many components if $d$ is an odd square. As an application, we show that for a genus $3$ curve with a completely decomposable Jacobian (i.e. isogenous to a product of 3 elliptic curves) the degrees of complementary coverings $f_i:C\rightarrow E_i,\ i=1,2,3$ satisfy $lcm(deg(f_1),deg(f_2))=lcm(deg(f_1),deg(f_3))=lcm(deg(f_2),deg(f_3))$.
Let $K$ be a set of positive integers and let $G$ be an additive group. A $(G, K, 1)$ difference packing is a set of subsets of $G$ with sizes from $K$ whose list of differences covers every element of $G$ at most once. It is balanced if the number of blocks of size $k\in K$ does not depend on $k$. In this paper, we determine a balanced $(Z_{4u}\times Z_{8v},{4,5},1)$ difference packing of the largest possible size whenever $uv$ is odd. The corresponding optimal balanced $(4u, 8v,\{4,5\},1)$ optical orthogonal signature pattern codes are also obtained.
ZnO nanoparticles (NP) of size less than around 20 nm inside a chamber exhibits complete reduction in their visible photoluminescence (PL) intensity when partial pressure of oxygen in the surrounding gaseous environment is decreased by evacuation. However the visible PL from ZnO nanoparticles are insensitive to the gases like N2, He and Ar. The rate of change of PL intensity with pressure (or the sensitivity) is inversely proportional to the ambient air pressure. Sensitivity increases when surface to volume ratio increases for lower particle size. The charged oxygen vacancies are attributed as the responsible candidates for surface related visible PL from ZnO NP.
We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with probability $(1-r)$, it undergoes symmetric random walk, i.e., it hops to one of its neighboring sites, with equal probability $(1-r)/2$. For $r=0$, it reduces to a standard random walk whose typical distance grows as $\sqrt{n}$ for large $n$. In presence of a nonzero resetting rate $0<r\le 1$, we find that both the average maximum and the average position grow ballistically for large $n$, with a common speed $v(r)$. Moreover, the fluctuations around their respective averages grow diffusively, again with the same diffusion coefficient $D(r)$. We compute $v(r)$ and $D(r)$ explicitly. We also show that the probability distribution of the difference between the maximum and the location of the walker, becomes stationary as $n\to \infty$. However, the approach to this stationary distribution is accompanied by a dynamical phase transition, characterized by a weakly singular large deviation function. We also show that $r=0$ is a special `critical' point, for which the growth laws are different from the $r\to 0$ case and we calculate the exact crossover functions that interpolate between the critical $(r=0)$ and the off-critical $(r\to 0)$ behavior for finite but large $n$.
We present a study of the Faraday rotation of extragalactic sources lying behind the Large Magellanic Cloud. These data represent the most detailed study yet of magnetic field structures in any external galaxy, and are a demonstration of how magnetic fields in galaxies will best be studied with future instruments.
In this article, we are concerned with the following eigenvalue problem of a linear second order elliptic operator:   \begin{equation}   \nonumber   -D\Delta \phi -2\alpha\nabla m(x)\cdot \nabla\phi+V(x)\phi=\lambda\phi\ \ \hbox{ in }\Omega, \end{equation} complemented by a general boundary condition including Dirichlet boundary condition and Robin boundary condition:   $$   \frac{\partial\phi}{\partial n}+\beta(x)\phi=0 \ \ \hbox{ on }\partial\Omega,   $$ where $\beta\in C(\partial\Omega)$ allows to be positive, sign-changing or negative, and $n(x)$ is the unit exterior normal to $\partial\Omega$ at $x$. The domain $\Omega\subset\mathbb{R}^N$ is bounded and smooth, the constants $D>0$ and $\alpha>0$ are, respectively, the diffusive and advection coefficients, and $m\in C^2(\bar\Omega),\,V\in C(\bar\Omega)$ are given functions.   We aim to investigate the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as the diffusive coefficient $D\to0$ or $D\to\infty$. Our results, together with those of \cite{CL2,DF,Fr} where the Nuemann boundary case (i.e., $\beta=0$ on $\partial\Omega$) and Dirichlet boundary case were studied, reveal the important effect of advection and boundary conditions on the asymptotic behavior of the principal eigenvalue. We also apply our results to a reaction-diffusion-advection equation which is used to describe the evolution of a single species living in a heterogeneous stream environment and show some interesting behaviors of the species persistence and extinction caused by the buffer zone and small/large diffusion rate.
Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling schemes. We develop a stability analysis by functional inequalities for a nonlinear flow of probability measures describing the limit behavior of the algorithms as the number of particles tends to infinity. Stability results are derived both under global and local assumptions on the generator of the underlying Metropolis dynamics. This allows us to prove that the combined methods sometimes have good asymptotic stability properties in multimodal setups where traditional MCMC methods mix extremely slowly. For example, this holds for the mean field Ising model at all temperatures.
We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system (DTLS) with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group (RG) methods and accurate numerical renormalization group (NRG) we show that contrary to other dissipative models there is quantum frustration of decoherence and quasi-scaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility that can be measured in nuclear magnetic resonance (NMR) experiments. Our results may also have relevance to quantum computation.
In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose's work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space-time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the PDE literature. As a compromise, one might say that in "generic" or "physically reasonable" space-times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an appendix by Erik Curiel reviews the early history of the definition of a black hole.
The thermal desorption of ammonia (NH$_3$) from single crystal forsterite (010) has been investigated using temperature-programmed desorption. The effect of defects on the desorption process has been probed by the use of a rough cut forsterite surface prepared from the cleaved forsterite sample. Several approaches have been used to extract the desorption energy and pre-exponential factor describing the desorption kinetics. In the sub-monolayer coverage regime, the NH$_3$ desorption shows a broad distribution of desorption energies, indicating the presence of different adsorption sites, which results in an apparent coverage-dependent desorption energy. This distribution is sensitive to the surface roughness with the cut forsterite surface displaying a significantly broader distribution of desorption energies compared to the cleaved forsterite surface. The cut forsterite surface exhibits sites with desorption energies up to 62.5 kJ mol$^{-1} $ in comparison to a desorption energy of up to 58.0 kJ mol$^{-1} $ for the cleaved surface. Multilayer desorption is independent of the nature of the forsterite surface used, with a desorption energy of ($25.8\pm0.9$) kJ mol$^{-1} $. On astrophysically relevant heating time-scales, the presence of a coverage dependent desorption energy distribution results in a lengthening of the NH$_3$ desorption time-scale by $5.9\times 10^4$ yr compared to that expected for a single desorption energy. In addition, the presence of a larger number of high-energy adsorption sites on the rougher cut forsterite surface leads to a further lengthening of ca. 7000 yr.
In this paper, we show that, on average, the derivatives of $L$-functions of cuspidal Hilbert modular forms with sufficiently large weight $k$ do not vanish on the line segments $\Im(s)=t_{0}$, $\Re(s)\in(\frac{k-1}{2},\frac{k}{2}-\epsilon)\cup(\frac{k}{2}+\epsilon,\frac{k+1}{2})$. This is analogous to the case of classical modular forms.
Accurate cosmological parameter estimates using polarization data of the cosmic microwave background (CMB) put stringent requirements on map calibration, as highlighted in the recent results from the Planck satellite. In this paper, we point out that a model-dependent determination of polarization calibration can be achieved by the joint fit of the TE and EE CMB power spectra. This provides a valuable cross-check to band-averaged polarization efficiency measurements determined using other approaches. We demonstrate that, in $\Lambda$CDM, the combination of the TE and EE constrain polarization calibration with sub-percent uncertainty with Planck data and 2% uncertainty with SPTpol data. We arrive at similar conclusions when extending $\Lambda$CDM to include the amplitude of lensing $A_{\rm L}$, the number of relativistic species $N_{\rm eff}$, or the sum of the neutrino masses $\sum m_{\nu}$. The uncertainties on cosmological parameters are minimally impacted when marginalizing over polarization calibration, except, as can be expected, for the uncertainty on the amplitude of the primordial scalar power spectrum $\ln(10^{10} A_{\rm s})$, which increases by $20-50$%. However, this information can be fully recovered by adding TT data. For current and future ground-based experiments, SPT-3G and CMB-S4, we forecast the cosmological parameter uncertainties to be minimally degraded when marginalizing over polarization calibration parameters. In addition, CMB-S4 could constrain its polarization calibration at the level of $\sim$0.2% by combining TE and EE, and reach $\sim$0.06% by also including TT. We therefore conclude that relying on calibrating against Planck polarization maps, whose statistical uncertainty is limited to $\sim$0.5%, would be insufficient for upcoming experiments.
Adversarial adaptation models have demonstrated significant progress towards transferring knowledge from a labeled source dataset to an unlabeled target dataset. Partial domain adaptation (PDA) investigates the scenarios in which the source domain is large and diverse, and the target label space is a subset of the source label space. The main purpose of PDA is to identify the shared classes between the domains and promote learning transferable knowledge from these classes. In this paper, we propose a multi-class adversarial architecture for PDA. The proposed approach jointly aligns the marginal and class-conditional distributions in the shared label space by minimaxing a novel multi-class adversarial loss function. Furthermore, we incorporate effective regularization terms to encourage selecting the most relevant subset of source domain classes. In the absence of target labels, the proposed approach is able to effectively learn domain-invariant feature representations, which in turn can enhance the classification performance in the target domain. Comprehensive experiments on three benchmark datasets Office-31, Office-Home, and Caltech-Office corroborate the effectiveness of the proposed approach in addressing different partial transfer learning tasks.
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and same is true for the drift. However, the specific application of urn models with random replacement matrices motivates us to consider stochastic approximation in a setup where both the step sizes and the drift are random, but the sequence is uniformly bounded. The problem becomes interesting when the negligibility conditions on the errors hold only in probability. We first prove a result on stochastic approximation in this setup, which is new in the literature. Then, as an application, we study urn models with random replacement matrices.   In the urn model, the replacement matrices need neither be independent, nor identically distributed. We assume that the replacement matrices are only independent of the color drawn in the same round conditioned on the entire past. We relax the usual second moment assumption on the replacement matrices in the literature and require only first moment to be finite. We require the conditional expectation of the replacement matrix given the past to be close to an irreducible matrix, in an appropriate sense. We do not require any of the matrices to be balanced or nonrandom. We prove convergence of the proportion vector, the composition vector and the count vector in $L^1$, and hence in probability. It is to be noted that the related differential equation is of Lotka-Volterra type and can be analyzed directly.
We present multifrequency radio observations of two well known episodic FR\,II radio galaxies (J0116$-$4722 and J1158+2621) and a detailed investigation of the life-cycle of episodic radio galaxies from their spectral and radiative properties. Combining our previous work with the present results, we either constrain or place very good limits on the active and quiescent phases of a small sample of episodic FR\,II radio galaxies. The duration of the quiescent phase can be as small as the hotspot fading time of the previous episode, and as high as a few tens of Myr; however, for none of the sources in our sample is it close to the duration of the active phase of the previous episode. We also find that for many episodic radio galaxies, the nucleus is variable at radio wavelengths. For our small sample of 7 episodic radio galaxies, we find 4 to have strongly variable cores, a much larger proportion than is generally found in samples of normal FR\,II radio galaxies. Studies with larger samples will be required to establish a statistical association between core variability and episodic radio activity.
In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher regularity properties are investigated. As an illustration, an asymptotic expansion of the invariant probability measure for an autoregressive model with i.i.d. noises (with a non-standard probability density function) is obtained.
This paper focuses on weak solvability concepts for rate-independent systems in a metric setting. Visco-Energetic solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a `viscous' correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter $\mu$. The resulting solution notion is characterized by a stability condition and an energy balance analogous to those for Energetic solutions, but, in addition, it provides a fine description of the system behavior at jumps as Balanced Viscosity solutions do. Visco-Energetic evolution can be thus thought as `in-between' Energetic and Balanced Viscosity evolution. Here we aim to formalize this intermediate character of Visco-Energetic solutions by studying their singular limits as $\mu\downarrow 0$ and $\mu\uparrow \infty$. We shall prove convergence to Energetic solutions in the former case, and to Balanced Viscosity solutions in the latter situation.
We discuss the synchrotron emission of fast cooling electrons in shocks. The fast cooling electrons behind the shocks can generate a position-dependent inhomogeneous electron distribution if they do not have enough time to mix homogeneously. This would lead to a very different synchrotron spectrum in low-frequency bands to that in the homogeneous case due to the synchrotron absorption. In this paper, we calculate the synchrotron spectrum in the inhomogeneous case in a gamma-ray burst (GRB). Both the forward shock and the reverse shock are considered. We find for the reverse shock dominated case, we would expect a "reverse shock bump" in the low-frequency spectrum. The spectral bump is due to the combination synchrotron absorption in both the forward and reverse shock regions. In the forward shock spectrum in the low frequencies has two unconventional segments with spectral slopes of $\lesssim1$ and $11/8$. The slope of $11/8$ has been found by some authors, while the slope of $\lesssim1$ is new, which is due to the approximately constant electron temperature in the optically thick region. In the future, simultaneous observations in multiple bands (especially in the low frequency bands) in the GRB early afterglow or prompt emission phases will possibly reveal these spectral characteristics and enable us to identify the reverse shock component and distinguish between the forward and reverse shock emissions. This also may be a method with which to diagnose the electron distribution status (homogeneous or inhomogeneous) after fast cooling in the relativistic shock region.
We construct minor-closed addable families of graphs that are subcritical and contain all planar graphs. This contradicts (one direction of) a well-known conjecture of Noy.