A structure from motion inequality

We state an elementary inequality for the structure from motion problem for m cameras and n points. This structure from motion inequality relates space dimension, camera parameter dimension, the number of cameras and number points and global symmetry properties and provides a rigorous criterion for which reconstruction is not possible with probability 1. Mathematically the inequality is based on Frobenius theorem which is a geometric incarnation of the fundamental theorem of linear algebra. The paper also provides a general mathematical formalism for the structure from motion problem. It includes the situation the points can move while the camera takes the pictures.Comment: 15 pages, 22 figure

The Impact of Stochastic Convenience Yield on Long-term Forestry Investment Decisions

This paper investigates whether convenience yield is an important factor in determining optimal decisions for a forestry investment. The Kalman filter method is used to estimate three different models of lumber prices: a mean reverting model, a simple geometric Brownian motion and the two-factor price model due to Schwartz (1997). In the latter model there are two correlated stochastic factors: spot price and convenience yield. The two-factor model is shown to provide a reasonable fit of the term structure of lumber futures prices. The impact of convenience yield on a forestry investment decision is examined using the Schwartz (1997) long-term model which transforms the two-factor price model into a single factor model with a composite price. Using the long-term model an optimal harvesting problem is analyzed, which requires the numerical solution of an impulse control problem formulated as a Hamilton-Jacobi-Bellman Variational Inequality. We compare the results for the long-term model to those from single-factor mean reverting and geometric Brownian motion models. The inclusion of convenience yield through the long-term model is found to have a significant impact on land value and optimal harvesting decisions.

Modeling and control of impact in mechanical systems: theory and experimental results

International audienceThis paper considers the equations of motion of mechanical systems subject to inequality constraints, which can be obtained by looking for the stationary value of the action integral. Two different methods are used to take into account the inequality constraints in the computation of the stationary value of the action integral: the method of the Valentine variables and the method of the penalty functions. The equations of motion resulting from the application of the method of the Valentine variables, which introduces the concept of " nonsmooth " impacts, constitute the exact model of the constrained mechanical system; such a model is suitable to be employed when the impacting parts of the actual mechanical system are very stiff. The equations of motion resulting from the application of the method of the penalty functions, which introduces the concept of " smooth impacts, " constitute an approximate model of the constrained mechanical system; such a model is suitable to be employed when the impacting parts of the actual mechanical system show some flexibility. Various feedback control laws from the natural outputs and from their time derivatives are studied with reference to both models of impact; the closed-loop systems resulting from the application of the same control law to both models show pretty much the same global asymptotic stability properties. The proposed control laws are only concerned with regulation problems in the presence of possible contacts and impacts among parts of the mechanical system or with the external environment ; the problem of controlling these mechanical systems along time-varying trajectories is not considered in this paper. The effectiveness of the proposed control structure has been tested experimentally with reference to a single-link robot arm, showing a valuable behavior

Dynamic Factor Price Equalization & International Convergence

We offer a duality-based methodology for incorporating multi-sector effects of international trade into open economy macroeconomic models, developing the concepts of the dynamic factor price equalization set and the integrated intertemporal equilibrium. Under this approach, the aggregate production function depends on output prices and factor endowment stocks. It preserves all of the structure of a standard GDP function from the trade theory literature. In a two-country version of the model considered below, we examine the properties of the dynamic factor price equalization set. If the global economy is initially outside of this set, the equations of motion will pull the economy back into this set. Inside the dynamic FPE set, factor prices are equalized internationally, and with identical tastes and technology, the economy can be regarded as a fully integrated world equilibrium in a dynamic sense (the integrated intertemporal equilibrium). In this equilibrium, all of the standard properties of a closed economy one-sector neoclassical growth model hold, ruling out cycles and chaos, and allowing us to characterize the evolution of international inequality and the persistence of productivity and endowment shocks. Working from the integrated intertemporal equilibrium, we identify properties of persistence linked to inequality and real economic shocks. Cross-country differences in per capita incomes and wealth, and the factor content of trading patterns, may persist over time and even into the new steady state. This provides yet another reason why we might observe lack of income convergence internationally. In addition, real shocks in one country may be transmitted to the other country through factor markets and product prices, and may have persistent effects into the steady-state as well. The model can also generate an endogenous Balassa-Samuelson effect.Neoclassical Models of Trade, Economic Growth of Open Economies, Cross- Country Output Convergence