An offline/online procedure for dual norm calculations of parameterized functionals: empirical quadrature and empirical test spaces

We present an offline/online computational procedure for computing the dual norm of parameterized linear functionals. The key elements of the approach are (i) an empirical test space for the manifold of Riesz elements associated with the parameterized functional, and (ii) an empirical quadrature procedure to efficiently deal with parametrically non-affine terms. We present a number of theoretical results to identify the different sources of error and to motivate the technique. Finally, we show the effectiveness of our approach to reduce both offline and online costs associated with the computation of the time-averaged residual indicator proposed in [Fick, Maday, Patera, Taddei, Journal of Computational Physics, 2018 (accepted)]

Collateral, Financial Arrangements and Pareto Optimality

The existence of collateral requirements to guarantee repayment on issued securities reduces in general the efficiency of competitive equilibria. The general equilibrium analysis is presented in a world where reputation plays no role, and the lender always expects a future payment equal to the future market value of provided collateral. In this context I show that collateral requirements result in two distinct problems for efficiency. I argue that two financial arrangements, tranching and financial pyramiding, arise in developed capital markets in response to the challenges posed by collateral requirements. If these arrangements are sufficiently developed, then the pareto efficiency of competitive equilibria is restored, even in the presence of collateral requirements.Collateral, Pareto Optimality, Financial Arrangements, Tranching, Financial Pyramiding.

Equity Premium: Interaction of Belief Heterogeneity and Distribution of Wealth?

Introducing heterogeneity of beliefs across different agents builds a link between wealth distribution and the equity premium. We demonstrate that an economy populated only by risk neutral agents may nonetheless display a strictly positive equity premium. We then place our notion of belief heterogeneity within the popular representative agent construct. We show that any level of belief heterogeneity in the multi agent economy can be mapped into some specific degree of risk aversion of the representative agent economy that keeps equilibrium prices constant. A fully dynamic model follows. Finally, we suggest an explanation for the recent behavior of the equity premium: a story of "heterogeneous optimism" versus "homogeneous pessimism" is presented.Belief Heterogeneity, Equity Premium Puzzle, Representative Agent, Risk Aversion, Wealth Distribution.

Liquidity and Economic Fluctuations

This paper shows that private information may be crucial in explaining the relationship between liquidity, investment and economic fluctuations. First, it defines liquidity in a way that is clearly connected to investment and output. Second, it models economies where privately informed entrepreneurs issue debt to fund their investment opportunities and identifies a theoretically based, empirically usable, and macroeconomic relevant measure of liquidity of the economy: the cross-firm dispersion in debt yields. Finally, it rationalizes one novel stylized fact regarding the US corporate bond market: the positive relationship between the proposed meaure of liquidity - the cross-firm dispersion in the "yields to maturity" on newly issued publicly traded debt - and subsequent aggregate economic activity.Liquidity; private information; robust pooling equilibrium; bond yield

Nonlocal superconducting correlations in graphene in the quantum Hall regime

We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-B\"{u}ttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance

Properties of Mesoscopic Hybrid Superconducting Systems

In this paper we review several aspects of mesoscopic hybrid superconducting systems. In particular we consider charge and heat transport properties in hybrid superconducting-metal structures and the effect of charging energy in superconducting nanostructures.Comment: 27 pages, 8 figure

Spherical collapse and halo mass function in the symmetron model

We study the gravitational clustering of spherically symmetric overdensities and the statistics of the resulting dark matter halos in the "symmetron model", in which a new long range force is mediated by a $Z_2$ symmetric scalar field. Depending on the initial radius of the overdensity, we identify two distinct regimes: for small initial radii the symmetron mediated force affects the spherical collapse at all redshifts; for initial radii larger than some critical size this force vanishes before collapse because of the symmetron screening mechanism. In both cases overdensities collapse earlier than in the $\Lambda$CDM and statistically tend to form more massive dark matter halos. Regarding the halo-mass function of these objects, we observe order one departures from standard $\Lambda$CDM predictions. The formalism developed here can be easily applied to other models where fifth-forces participate to the dynamics of the gravitational collapse.Comment: 17 pages, 5 figures. Minor revisions to match published versio