Search

We present an improved semi-analytic model for calculation of the broad optical emission-line signatures from sub-parsec supermassive black hole binaries (SBHBs) in circumbinary disks. The second-generation model improves upon the treatment of radiative transfer by taking into account the effect of the radiation driven accretion disk wind on the properties of the emission-line profiles. Analysis of 42.5 million modeled emission-line profiles shows that correlations between the profile properties and SBHB parameters identified in the first-generation model are preserved, indicating that their diagnostic power is not diminished. The profile shapes are a more sensitive measure of the binary orbital separation and the degree of alignment of the black hole mini-disks, and are less sensitive to the SBHB mass ratio and orbital eccentricity. We also find that modeled profile shapes are more compatible with the observed sample of SBHB candidates than with our control sample of regular AGNs. Furthermore, if the observed sample of SBHBs is made up of genuine binaries, it must include compact systems with comparable masses, and misaligned mini-disks. We note that the model described in this paper can be used to interpret the observed emission-line profiles once a sample of confirmed SBHBs is available but cannot be used to prove that the observed SBHB candidates are true binaries., Comment: Accepted to ApJ (25 pages, 16 figures), includes referee's comments

Semantic labeling for numerical values is a task of assigning semantic labels to unknown numerical attributes. The semantic labels could be numerical properties in ontologies, instances in knowledge bases, or labeled data that are manually annotated by domain experts. In this paper, we refer to semantic labeling as a retrieval setting where the label of an unknown attribute is assigned by the label of the most relevant attribute in labeled data. One of the greatest challenges is that an unknown attribute rarely has the same set of values with the similar one in the labeled data. To overcome the issue, statistical interpretation of value distribution is taken into account. However, the existing studies assume a specific form of distribution. It is not appropriate in particular to apply open data where there is no knowledge of data in advance. To address these problems, we propose a neural numerical embedding model (EmbNum) to learn useful representation vectors for numerical attributes without prior assumptions on the distribution of data. Then, the "semantic similarities" between the attributes are measured on these representation vectors by the Euclidean distance. Our empirical experiments on City Data and Open Data show that EmbNum significantly outperforms state-of-the-art methods for the task of numerical attribute semantic labeling regarding effectiveness and efficiency., Comment: 16 pages

In the case of scalar conservation laws $$ u_{t} + f(u)_{x}~=~0,\qquad t\geq 0, x\in\mathbb{R}, $$ with uniformly strictly convex flux $f$, quantitative compactness estimates - in terms of Kolmogorov entropy in ${\bf L}^{1}_{loc}$ - were established in~\cite{DLG,AON1} for sets of entropy weak solutions evaluated at a fixed time $t>0$, whose initial data have a uniformly bounded support and vary in a bounded subset of ${\bf L}^\infty$. These estimates reflect the irreversibility features of entropy weak discontinuous solutions of these nonlinear equations. We provide here an extension of such estimates to the case of scalar conservation laws with a smooth flux function $f$ that either is strictly (but not necessarily uniformly) convex or has a single inflection point with a polynomial degeneracy., Comment: 33 pages

In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to ${\bf L}^1$-distance., Comment: 14 pages

We consider a controlled evolution problem for a set $\Omega(t)\in\mathbb{R}^d$, originally motivated by a model where a dog controls a flock of sheep. Necessary conditions and sufficient conditions are given, in order that the evolution be completely controllable. Similar techniques are then applied to the approximation of a sweeping process. Under suitable assumptions, we prove that there exists a control function such that the corresponding evolution of the set $\Omega(t)$ is arbitrarily close to the one determined by the sweeping process., Comment: 28 pages, 3 figures

Lyapunov's theorem is a classical result in convex analysis, concerning the convexity of the range of nonatomic measures. Given a family of integrable vector functions on a compact set, this theorem allows to prove the equivalence between the range of integral values obtained considering all possible set decompositions and all possible convex combinations of the elements of the family. Lyapunov type results have several applications in optimal control theory: they are used to prove bang-bang properties and existence results without convexity assumptions. Here, we use the dual approach to the Baire category method in order to provide a "quantitative" version of such kind of results applied to a countable family of integrable functions., Comment: 13 pages

We consider a model of debt management, where a sovereign state trade some bonds to service the debt with a pool of risk-neutral competitive foreign investors. At each time, the government decides which fraction of the gross domestic product (GDP) must be used to repay the debt, and how much to devaluate its currency. Both these operations have the effect to reduce the actual size of the debt but have a social cost in terms of welfare sustainability. Moreover, at any time the sovereign state can declare bankruptcy by paying a correspondent bankruptcy cost. We show that these optimization problems admits an equilibrium solution, leading to bankruptcy or to a stationary state, depending on the initial conditions., Comment: 46

Motivated by observational searches for sub-parsec supermassive black hole binaries (SBHBs) we develop a modular analytic model to determine the likelihood for detection of SBHBs by ongoing spectroscopic surveys. The model combines the parametrized rate of orbital evolution of SBHBs in circumbinary disks with the selection effects of spectroscopic surveys and returns a multivariate likelihood for SBHB detection. Based on this model we find that in order to evolve into the detection window of the spectroscopic searches from larger separations in less than a Hubble time, $10^8M_\odot$ SBHBs must, on average, experience angular momentum transport faster than that provided by a disk with accretion rate $0.06\,\dot{M}_E$. Spectroscopic searches with yearly cadence of observations are in principle sensitive to binaries with orbital separations $< {\rm few}\times 10^4\, r_g$ ($r_g = GM/c^2$ and $M$ is the binary mass), and for every one SBHB in this range there should be over 200 more gravitationally bound systems with similar properties, at larger separations. Furthermore, if spectra of all SBHBs in this separation range exhibit the AGN-like emission lines utilized by spectroscopic searches, the projection factors imply five undetected binaries for each observed $10^8M_\odot$ SBHB with mass ratio $0.3$ and orbital separation $10^4\,r_g$ (and more if some fraction of SBHBs is inactive). This model can be used to infer the most likely orbital parameters for observed SBHB candidates and to provide constraints on the rate of orbital evolution of SBHBs, if observed candidates are shown to be genuine binaries., Comment: Accepted to ApJ (16 pages, 11 figures). Revised version includes referee's comments

A problem of optimal debt management is modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio $x(t)$ reaches a given size $x^*$, bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold $x^*$, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of $x^*$, changes, depending on different values of $x^*$?., Comment: 29 pages, 3 figures

Motivated by advances in observational searches for sub-parsec supermassive black hole binaries (SBHBs) made in the past few years we develop a semi-analytic model to describe spectral emission line signatures of these systems. The goal of this study is to aid the interpretation of spectroscopic searches for binaries and help test one of the leading models of binary accretion flows in the literature: SBHB in a circumbinary disk. In this work we present the methodology and a comparison of the preliminary model with the data. We model SBHB accretion flows as a set of three accretion disks: two mini-disks that are gravitationally bound to the individual black holes and a circumbinary disk. Given a physically motivated parameter space occupied by sub-parsec SBHBs, we calculate a synthetic database of nearly 15 million broad optical emission line profiles and explore the dependence of the profile shapes on characteristic properties of SBHBs. We find that the modeled profiles show distinct statistical properties as a function of the semi-major axis, mass ratio, eccentricity of the binary, and the degree of alignment of the triple disk system. This suggests that the broad emission line profiles from SBHB systems can in principle be used to infer the distribution of these parameters and as such merit further investigation. Calculated profiles are more morphologically heterogeneous than the broad emission lines in observed SBHB candidates and we discuss improved treatment of radiative transfer effects which will allow direct statistical comparison of the two groups., Comment: 27 pages, 20 figures, accepted to ApJ

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L^1(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided., Comment: 22 pages

We study quantitative estimates of compactness in $\mathbf{W}^{1,1}_{loc}$ for the map $S_t$, $t>0$ that associates to every given initial data $u_0\in \mathrm{Lip}(\mathbb{R}^N)$ the corresponding solution $S_t u_0$ of a Hamilton-Jacobi equation $$ u_t+H\big(x, \nabla_{\!x} u\big)=0\,, \qquad t\geq 0,\quad x\in \mathbb{R}^N, $$ with a convex and coercive Hamiltonian $H=H(x,p)$. We provide upper and lower bounds of order $1/\varepsilon^N$ on the the Kolmogorov $\varepsilon$-entropy in $\mathbf{W}^{1,1}$ of the image through the map $S_t$ of sets of bounded, compactly supported initial data. Quantitative estimates of compactness, as suggested by P.D. Lax, could provide a measure of the order of "resolution" and of "complexity" of a numerical method implemented for this equation. We establish these estimates deriving accurate a-priori bounds on the Lipschitz, semiconcavity and semiconvexity constant of a viscosity solution when the initial data is semiconvex. The derivation of a small time controllability result is also fundamental to establish the lower bounds on the $\varepsilon$-entropy., Comment: 36 pages. arXiv admin note: text overlap with arXiv:1403.4556