ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose a quantitative test for the validity of the semi-classical approximation in gravity, namely that the solutions to the semi-classical equations should be stable to linearized perturbations, in the sense that no gauge invariant perturbation should become unbounded in time. We show that a self-consistent linear response analysis of these perturbations based upon an invariant effective action principle involves metric fluctuations about the mean semi-classical geometry and brings in the two-point correlation function of the quantum energy-momentum tensor in a natural way. The properties of this correlation function are discussed and it is shown on general grounds that it contains no state-dependent divergences and requires no new renormalization counterterms beyond those required in the leading order semi-classical approximation.
The PAMELA collaboration recently released the $e^+$ absolute spectrum between 1 and 300 GeV in addition to the positron fraction and the $e^-$ spectrum previously measured in the same period. We use the newly developed three-dimensional upgrade of the DRAGON package to model those data. This code allows us to consider a realistic spiral arm source distribution in the Galaxy, which impacts the high-energy shape of the propagated spectra. At low energy we treat solar modulation with the HelioProp code and compare its results with those obtained using the usual force-field approximation. We show that all PAMELA data sets can be consistently, and accurately, described in terms of a standard background on top of which a charge symmetric $e^+$ + $e^-$ extra component with harder injection spectrum is added; this extra contribution is peaked at about 1 - 10 TeV and may originate from a diffuse population of sources located in the Galactic arms. For the first time, we compute the energy required to sustain such a relevant positron flux in the Galaxy, finding that it is naturally compatible with an astrophysical origin. We considered several reference propagation setups; we find that models with a low (or null) reacceleration - tuned against light nuclei data - nicely describe both PAMELA leptonic and hadronic data with no need to introduce a low-energy break in the proton and helium spectra, as it would be required for high reacceleration models. We also compare our models with the preliminary $e^-$ and $e^+$ absolute spectra recently measured by AMS-02. We find that those data, differently from what is inferred from the positron fraction alone, favor a high energy cutoff (about 10 TeV) of the extra component if this is uniquely generated in the Galactic arms. A lower cutoff may be allowed if a relevant contribution from powerful $e^-$ + $e^+$ nearby accelerators is invoked.
Planck data towards the active galaxy Centaurus A are analyzed in the 70, 100 and 143 GHz bands. We find a temperature asymmetry of the northern radio lobe with respect to the southern one that clearly extends at least up to 5 degrees from the Cen A center and diminishes towards the outer regions of the lobes. That transparent parameter - the temperature asymmetry - thus has to carry a principal information, i.e. indication on the line-of-sight bulk motion of the lobes, while the increase of that asymmetry at smaller radii reveals the differential dynamics of the lobes as expected at ejections from the center.
Tens of early type galaxies have been recently reported to possess prolate rotation, i.e. significant amount of rotation around the major axis, including two cases in the Local Group. Although expected theoretically, this phenomenon is rarely observed and remains elusive. In order to explore its origin we study the population of well-resolved galaxies in the Illustris cosmological simulation. We identify 59 convincing examples of prolate rotators at the present time, more frequently among more massive galaxies, with the number varying very little with redshift. We follow their evolution back in time using the main progenitor branch galaxies of the Illustris merger trees. We find that the emergence of prolate rotation is strongly correlated with the time of the last significant merger the galaxy experienced, although other evolutionary paths leading to prolate rotation are also possible. The transition to prolate rotation most often happens around the same time as the transition to prolate shape of the stellar component. The mergers leading to prolate rotation have slightly more radial orbits, higher mass ratios, and occur at more recent times than mergers in the reference sample of twin galaxies we construct for comparison. However, they cover a wide range of initial conditions in terms of the mass ratio, merger time, radiality of the progenitor orbits, and the relative orientations of spins of the progenitors with respect to the orbital angular momenta. About half of our sample of prolate rotators were created during gas-rich mergers and the newly formed stars usually support prolate rotation.
The Void Galaxy Survey (VGS) is a multi-wavelength program to study $\sim$60 void galaxies. Each has been selected from the deepest interior regions of identified voids in the SDSS redshift survey on the basis of a unique geometric technique, with no a prior selection of intrinsic properties of the void galaxies. The project intends to study in detail the gas content, star formation history and stellar content, as well as kinematics and dynamics of void galaxies and their companions in a broad sample of void environments. It involves the HI imaging of the gas distribution in each of the VGS galaxies. Amongst its most tantalizing findings is the possible evidence for cold gas accretion in some of the most interesting objects, amongst which are a polar ring galaxy and a filamentary configuration of void galaxies. Here we shortly describe the scope of the VGS and the results of the full analysis of the pilot sample of 15 void galaxies.
We extend the theory of neural fields which has been developed in a deterministic framework by considering the influence spatio-temporal noise. The outstanding problem that we here address is the development of a theory that gives rigorous meaning to stochastic neural field equations, and conditions ensuring that they are well-posed. Previous investigations in the field of computational and mathematical neuroscience have been numerical for the most part. Such questions have been considered for a long time in the theory of stochastic partial differential equations, where at least two different approaches have been developed, each having its advantages and disadvantages. It turns out that both approaches have also been used in computational and mathematical neuroscience, but with much less emphasis on the underlying theory. We present a review of two existing theories and show how they can be used to put the theory of stochastic neural fields on a rigorous footing. We also provide general conditions on the parameters of the stochastic neural field equations under which we guarantee that these equations are well-posed. In so doing we relate each approach to previous work in computational and mathematical neuroscience. We hope this will provide a reference that will pave the way for future studies (both theoretical and applied) of these equations, where basic questions of existence and uniqueness will no longer be a cause for concern.
This paper considers various fermion pairings of interest for the QCD phases. The effects of an external magnetic field on the pairing mechanisms, on the realization of new condensates, and on the properties of the magnetized phases are all explored and discussed.
For any admissible subcategory of the bounded derived category of coherent sheaves on a smooth proper variety, we prove that sections of the canonical bundle impose a strong constraint on the supports of the objects of the subcategory or its semiorthogonal complement. We also show that admissible subcategories are rigid under the actions of topologically trivial autoequivalences. As applications of these results, we prove that the derived category of various minimal varieties in the sense of the minimal model program admit no non-trivial semiorthogonal decompositions, generalizing the result for curves due to the second author to higher dimensions. The case of minimal surfaces is further investigated in detail.
We review four mechanisms for forming brown dwarfs: (i) turbulent fragmentation (producing very low-mass prestellar cores); (ii) gravitational instabilities in discs; (iii) dynamical ejection of stellar embryos from their placental cores; and (iv) photo-erosion of pre-existing cores in HII regions. We argue (a) that these are simply the mechanisms of low-mass star formation, and (b) that they are not mutually exclusive. If, as seems possible, all four mechanisms operate in nature, their relative importance may eventually be constrained by their ability to reproduce the binary statistics of brown dwarfs, but this will require fully 3-D radiative magneto-hydrodynamic simulations.
We present Spitzer MIPS 24-micron observations of 16 0.4<z<0.8 galaxy clusters drawn from the ESO Distant Cluster Survey (EDisCS). This is the first large 24-micron survey of clusters at intermediate redshift. The depth of our imaging corresponds to a total IR luminosity of 8x10^10 Lsun, just below the luminosity of luminous infrared galaxies (LIRGs), and 6^{+1}_{-1}% of M_V < -19 cluster members show 24-micron emission at or above this level. We compare with a large sample of coeval field galaxies and find that while the fraction of cluster LIRGs lies significantly below that of the field, the IR luminosities of the field and cluster galaxies are consistent. However, the stellar masses of the EDisCS LIRGs are systematically higher than those of the field LIRGs. A comparison with optical data reveals that ~80% of cluster LIRGs are blue and the remaining 20% lie on the red sequence. Of LIRGs with optical spectra, 88^{+4}_{-5}% show [O II] emission with EW([O II])>5A, and ~75% exhibit optical signatures of dusty starbursts. On average, the fraction of cluster LIRGs increases with projected cluster-centric radius but remains systematically lower than the field fraction over the area probed (< 1.5xR200). The amount of obscured star formation declines significantly over the 2.4 Gyr interval spanned by the EDisCS sample, and the rate of decline is the same for the cluster and field populations. Our results are consistent with an exponentially declining LIRG fraction, with the decline in the field delayed by ~1 Gyr relative to the clusters.
The spatial clustering properties of HI galaxies can be studied using the formalism of the halo occupation distribution (HOD). The resulting parameter constraints describe properties like gas richness verses environment. Unfortunately, clustering studies based on individual HI galaxies will be restricted to the local Universe for the foreseeable future, even with the deepest HI surveys. Here we discuss how clustering studies of the HI HOD could be extended to moderate redshift, through observations of fluctuations in the combined 21cm intensity of unresolved galaxies. In particular we make an analytic estimate for the clustering of HI in the HOD. Our joint goals are to estimate i) the amplitude of the signal, and ii) the sensitivity of telescopes like the Australian SKA Pathfinder to HOD parameters. We find that the power spectrum of redshifted 21cm intensity could be used to study the distribution of HI within dark matter halos at z>0.5 where individual galaxies cannot be detected. In addition to the HOD of HI, the amplitude of the 21cm power spectrum would also yield estimates of the cosmic HI content at epochs between the local Universe, and redshifts probed by damped Ly-alpha absorbers.
We suggest that neutron star mergers eject an ultra-relativistic envelope of mass $m\sim 10^{-7}M_\odot$, which helps explain the gamma-ray burst from GW170817. One ejection mechanism is the ablation of the neutron star surface by the burst of neutrinos in the first $30\,\mu$s of the merger. Another, more efficient, mechanism for inflating the ultra-relativistic envelope is an internal shock in the massive ejecta from the merger. A strong shock is expected if the merger product is a magnetar, which emits a centrifugally accelerated wind. The shock propagates outward through the ejecta and accelerates in its outer layers at radii $r\sim 10^9-10^{10}$cm, launching an ultra-relativistic opaque envelope filled with $\sim 10^4$ photons per nucleon. The Lorentz factor profile of the envelope rises outward and determines its homologous expansion, which adiabatically cools the trapped photons. Once the magnetar loses its differential rotation and collapses into a black hole, a powerful jet forms. It drives a blast wave into the envelope, chasing its outer layers and eventually catching up with the envelope photosphere at $r\sim 10^{12}$cm. The ultra-relativistic photospheric breakout of the delayed blast wave emits a gamma-ray burst in a broad solid angle around the merger axis. This model explains the gamma-ray pulse from merger GW170817 with luminosity $L_\gamma\sim 10^{47}$erg/s, duration $\Delta t_{\rm obs}\sim 0.5$s, and characteristic photon energy $\sim 100$keV. The blast wave Lorentz factor at the envelope photosphere is consistent with $\Gamma\geq 5$ that we derive from the observed light curve of the burst. We suggest future tests of the model.
Sparse-representation-based classification (SRC) has been widely studied and developed for various practical signal classification applications. However, the performance of a SRC-based method is degraded when both the training and test data are corrupted. To counteract this problem, we propose an approach that learns Representation with Block-Diagonal Structure (RBDS) for robust image recognition. To be more specific, we first introduce a regularization term that captures the block-diagonal structure of the target representation matrix of the training data. The resulting problem is then solved by an optimizer. Last, based on the learned representation, a simple yet effective linear classifier is used for the classification task. The experimental results obtained on several benchmarking datasets demonstrate the efficacy of the proposed RBDS method.
We consider the following elliptic system with fractional laplacian $$ -(-\Delta)^su=uv^2,\ \ -(-\Delta)^sv=vu^2,\ \ u,v>0 \ \mbox{on}\ \R^n,$$ where $s\in(0,1)$ and $(-\Delta)^s$ is the $s$-Lapalcian. We first prove that all positive solutions must have polynomial bound. Then we use the Almgren monotonicity formula to perform a blown-down analysis to $s$-harmonic functions. Finally we use the method of moving planes to prove the uniqueness of the one dimensional profile, up to translation and scaling.
X-ray and mid-infrared emission are signposts of the accretion of matter onto the supermassive black holes that reside at the centres of most galaxies. As a major step towards understanding accreting supermassive black holes and their role in the evolution of galaxies, we will use the 4MOST multi-object spectrograph to provide a highly complete census of active galactic nuclei over a large fraction of the extragalactic sky observed in X-rays by eROSITA that is visible to 4MOST. We will systematically follow up all eROSITA point-like extragalactic X-ray sources (mostly active galactic nuclei), and complement them with a heavily obscured active galactic nuclei selection approach using mid-infrared data from the Wide-field Infrared Survey Explorer (WISE). The X-ray and mid-infrared flux limits of eROSITA and WISE are well matched to the spectroscopic capabilities of a 4-metre-class telescope, allowing us to reach completeness levels of ~80-90% for all X-ray selected active galactic nuclei with fluxes $f_{0.5-2\ {\rm keV}} > 10^{-14}$ erg s$^{-1}$ cm$^{-2}$; this is about a factor of 30 deeper than the ROSAT all-sky survey. With these data we will determine the physical properties (redshift, luminosity, line emission strength, masses, etc.) of up to one million supermassive black holes, constrain their cosmic evolution and clustering properties, and explore the connection between active galactic nuclei and large-scale structure over redshifts $0 \le z \le 6$.
We prove some functional equations involving the (classical) matching polynomials of path and cycle graphs and the $d$-matching polynomial of a cycle graph. A matching in a (finite) graph $G$ is a subset of edges no two of which share a vertex, and the matching polynomial of $G$ is a generating function encoding the numbers of matchings in $G$ of each size. The $d$-matching polynomial is a weighted average of matching polynomials of degree-$d$ covers, and was introduced in a paper of Hall, Puder, and Sawin. Let $\mathcal{C}_n$ and $\mathcal{P}_n$ denote the respective matching polynomials of the cycle and path graphs on $n$ vertices, and let $\mathcal{C}_{n,d}$ denote the $d$-matching polynomial of the cycle $C_n$. We give a purely combinatorial proof that $\mathcal{C}_k (\mathcal{C}_n (x)) = \mathcal{C}_{kn} (x)$ en route to proving a conjecture made by Hall: that $\mathcal{C}_{n,d} (x) = \mathcal{P}_d (\mathcal{C}_n (x))$.
In this note, we present the closed form solution for the joint distribution of the range and terminal value of a Brownian motion. Based on this distribution we build a range scaled terminal value distribution and show the derivation steps of its density, further s-density. Finally, we sample the s-density from different groups of currency pairs and compare them with theoretical result.
We employ an all-sky map of the anomalous microwave emission (AME) produced by component separation of the microwave sky to study correlations between the AME and Galactic dust properties. We find that while the AME is highly correlated with all tracers of dust emission, the best predictor of the AME strength is the dust radiance. Fluctuations in the AME intensity per dust radiance are uncorrelated with fluctuations in the emission from polycyclic aromatic hydrocarbons (PAHs), casting doubt on the association between AME and PAHs. The PAH abundance is strongly correlated with the dust optical depth and dust radiance, consistent with PAH destruction in low density regions. We find that the AME intensity increases with increasing radiation field strength, at variance with predictions from the spinning dust hypothesis. Finally, the temperature-dependence of the AME per dust radiance disfavors the interpretation of the AME as thermal emission. A reconsideration of other AME carriers, such as ultrasmall silicates, and other emission mechanisms, such as magnetic dipole emission, is warranted.
The localization of stellar-mass binary black hole mergers using gravitational waves is critical in understanding the properties of the binaries' host galaxies, observing possible electromagnetic emission from the mergers, or using them as a cosmological distance ladder. The precision of this localization can be substantially increased with prior astrophysical information about the binary system. In particular, constraining the inclination of the binary can reduce the distance uncertainty of the source. Here we present the first realistic set of localizations for binary black hole mergers, including different prior constraints on the binaries' inclinations. We find that prior information on the inclination can reduce the localization volume by a factor of 3. We discuss two astrophysical scenarios of interest: (i) follow-up searches for beamed electromagnetic/neutrino counterparts and (ii) mergers in the accretion disks of active galactic nuclei.
In this paper we answer a question posed by C. A. Athanasiadis. Namely, we prove that the local $h$-polynomial of the $r$th edgewise subdivision of the $(n-1)$-dimensional simplex $2^V$ has only real zeros. In doing so we find a tool, using compatible polynomials, that can be used to check if polynomials in certain types of families of polynomials have only real zeros.
A new dynamical approach that combines covariant parton transport theory with hadronization channels via parton coalescence and fragmentation is applied to Au+Au at RHIC. Basic consequences of the simple coalescence formulas, such as elliptic flow scaling and enhanced proton/pion ratio, turn out to be rather sensitive to the spacetime aspects of coalescence dynamics.
We construct examples of surfaces of general type with $p_g=1$, $q=0$ and $K^2=6$. We use as key varieties Fano fourfolds and Calabi-Yau threefolds that are zero section of some special homogeneous vector bundle on Grassmannians. We link as well our construction to a classical Campedelli surface, using the Pfaffian-Grassmannian correspondence.
We give some examples of isomorphisms of moduli of sheaves induced by Fourier-Mukai functor. As applications, we give another proof on deformation type of some moduli spaces of sheaves on abelian and K3 surfaces.
We present an efficient algorithm for computing certain special values of Rankin triple product $p$-adic L-functions and give an application of this to the explicit construction of rational points on elliptic curves.
Let $\mathcal{C}$ be a plane curve defined over the algebraic closure $K$ of a prime finite field $\mathbb{F}_p$ by a separated polynomial, that is $\mathcal{C}: A(y)=B(x)$, where $A(y)$ is an additive polynomial of degree $p^n$ and the degree $m$ of $B(X)$ is coprime with $p$. Plane curves given by separated polynomials are well-known and studied in the literature. However just few informations are known on their automorphism groups. In this paper we compute the full automorphism group of $\mathcal{C}$ when $m \not\equiv 1 \pmod {p^n}$ and $B(X)$ has just one root in $K$, that is $B(X)=b_m(X+b_{m-1}/mb_m)^m$ for some $b_m,b_{m-1} \in K$. Moreover, some sufficient conditions for the automorphism group of $\mathcal{C}$ to imply that $B(X)=b_m(X+b_{m-1}/mb_m)^m$ are provided. As a byproduct, the full automorphism group of the Norm-Trace curve $\mathcal{C}: x^{(q^r-1)/(q-1)}=y^{q^{r-1}}+y^{q^{r-2}}+\ldots+y$ is computed. Finally, these results are used to construct multi point AG codes with many automorphisms.
It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain a systematic scheme to classify bosonic SPT phases with any finite Abelian symmetry group. We point out that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the current Chern-Simons theory framework. We also apply the theory to fermionic SPT phases with $\mathbb{Z}_m$ symmetry and find the classification of SPT phases depends on the parity of $m$: for even $m$ there are $2m$ classes, $m$ out of which is intrinsically fermionic SPT phases and can not be realized in any bosonic system. Finally we propose a classification scheme of fermionic SPT phases for any finite, Abelian symmetry.