Efficient data structures for masks on 2D grids

This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them between computers. While these considerations were originally motivated by the specific tasks of representing sky coverage and cross-matching catalogues of astronomical surveys, they can be profitably applied in many other situations as well.Comment: accepted by A&

Strategic Freedom, Constraint, and Symmetry in One-period Markets with Cash and Credit Payment

In order to explain in a systematic way why certain combinations of market, financial, and legal structures may be intrinsic to certain capabilities to exchange real goods, we introduce criteria for abstracting the qualitative functions of markets. The criteria involve the number of strategic freedoms the combined institutions, considered as formalized strategic games, present to traders, the constraints they impose, and the symmetry with which those constraints are applied to the traders. We pay particular attention to what is required to make these "strategic market games" well-defined, and to make various solutions computable by the agents within the bounds on information and control they are assumed to have. As an application of these criteria, we present a complete taxonomy of the minimal one-period exchange economies with symmetric information and inside money. A natural hierarchy of market forms is observed to emerge, in which institutionally simpler markets are often found to be more suitable to fewer and less-diversified traders, while the institutionally richer markets only become functional as the size and diversity of their users gets large.Strategic market games, Clearinghouses, Credit evaluation, Default

Commodity Money and the Valuation of Trade

In a previous essay we modeled the enforcement of contract, and through it the provision of money and markets, as a production function within the society, the scale of which is optimized endogenously by labor allocation away from primary production of goods. Government and a central bank provided fiat money and enforced repayment of loans, giving fiat a predictable value in trade, and also rationalizing the allocation of labor to government service, in return for a fiat salary. Here, for comparison, we consider the same trade problem without government or fiat money, using instead a durable good (gold) as a commodity money between the time it is produced and the time it is removed by manufacture to yield utilitarian services. We compare the monetary value of the two money systems themselves, by introducing a natural money-metric social welfare function. Because labor allocation both to production and potentially to government of the economy is endogenous, the only constraint in the society is its population, so that the natural money-metric is labor. Money systems, whether fiat or commodity, are valued in units of the labor that would produce an equivalent utility gain among competitive equilibria, if it were added to the primary production capacity of the society.Bureaucracy, Contract enforcement, Taxes, Money

Volume integral equations for electromagnetic scattering in two dimensions

We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the cylinder, which allows the reduction to two-dimensional problems. With this simplification, we can refine the analysis of the essential spectrum of the volume integral operator started in a previous paper (M. Costabel, E. Darrigrand, H. Sakly: The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body, Comptes Rendus Mathematique, 350 (2012), pp. 193-197) and obtain results for non-smooth domains that were previously available only for smooth domains. It turns out that in the TE case, the magnetic contrast has no influence on the Fredholm properties of the problem. As a byproduct of the choice that exists between a vectorial and a scalar volume integral equation, we discover new results about the symmetry of the spectrum of the double layer boundary integral operator on Lipschitz domains.Comment: 21 page

Ground-state and spectral properties of an asymmetric Hubbard ladder

We investigate a ladder system with two inequivalent legs, namely a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wavenumbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.Comment: published versio

Correlated atomic wires on substrates. II. Application to Hubbard wires

In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely paramagnetic Mott insulators, Luttinger liquids, and spin-$1/2$ Heisenberg chains. The validity of the effective ladder models is assessed by studying the convergence with the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate

The Square Root Velocity Framework for Curves in a Homogeneous Space

In this paper we study the shape space of curves with values in a homogeneous space $M = G/K$, where $G$ is a Lie group and $K$ is a compact Lie subgroup. We generalize the square root velocity framework to obtain a reparametrization invariant metric on the space of curves in $M$. By identifying curves in $M$ with their horizontal lifts in $G$, geodesics then can be computed. We can also mod out by reparametrizations and by rigid motions of $M$. In each of these quotient spaces, we can compute Karcher means, geodesics, and perform principal component analysis. We present numerical examples including the analysis of a set of hurricane paths.Comment: To appear in 3rd International Workshop on Diff-CVML Workshop, CVPR 201