Optimal Non-Linear Income Tax when Highly Skilled Individuals Vote with their Feet

This paper examines how allowing individuals to emigrate to pay lower taxes changes the optimal non-linear income tax scheme in a Mirrleesian economy. Type dependent participation constraints are borrowed from contract theory. An individual emigrates if his domestic utility is less than his utility abroad net of migration costs, utilities and costs both depending on productivity. Three social criteria are distinguished according to the agents whose welfare matters. Mobility significantly alters the closed-economy results qualitatively, but also quantitatively as verified by simulations. A curse of the middle-skilled occurs in the first-best. In the second-best, the middle skilled can support the highest average tax rates and the marginal tax rates can be negative. Moveover, preventing emigration of the highly skilled is not necessarily optimal

Spectral Properties of Quantum Walks on Rooted Binary Trees

We define coined Quantum Walks on the infinite rooted binary tree given by unitary operators $U(C)$ on an associated infinite dimensional Hilbert space, depending on a unitary coin matrix $C\in U(3)$, and study their spectral properties. For circulant unitary coin matrices $C$, we derive an equation for the Carath\'eodory function associated to the spectral measure of a cyclic vector for $U(C)$. This allows us to show that for all circulant unitary coin matrices, the spectrum of the Quantum Walk has no singular continuous component. Furthermore, for coin matrices $C$ which are orthogonal circulant matrices, we show that the spectrum of the Quantum Walk is absolutely continuous, except for four coin matrices for which the spectrum of $U(C)$ is pure point

Shall we Keep the Highly Skilled at Home? The Optimal Income Tax Perspective

We examine how allowing individuals to emigrate to pay lower taxes abroad changes the optimal non-linear income tax scheme in a Mirrleesian economy. An individual emigrates if his domestic utility is less than his utility abroad net of migration costs, utilities and costs both depending on productivity. Three average social criteria are distinguished – national, citizen and resident – according to the agents whose welfare matters. A curse of the middle-skilled occurs in the first-best, and it may be optimal to let some highly skilled leave the country under the resident criterion. In the second-best, under the Citizen and Resident criteria, preventing emigration of the highly skilled is not necessarily optimal because the interaction between the incentive-compatibility and participations constraints may cause countervailing incentives. In important cases, a Rawlsian policymaker should decrease top marginal tax rates to keep everyone at home.optimal income tax, top-income earners, migration, incentive constraints, participation constraints

Asymptotics of repeated interaction quantum systems

A quantum system \s interacts in a successive way with elements \ee of a chain of identical independent quantum subsystems. Each interaction lasts for a duration $\tau$ and is governed by a fixed coupling between \s and \ee. We show that the system, initially in any state close to a reference state, approaches a {\it repeated interaction asymptotic state} in the limit of large times. This state is $\tau$--periodic in time and does not depend on the initial state. If the reference state is chosen so that \s and \ee are individually in equilibrium at positive temperatures, then the repeated interaction asymptotic state satisfies an average second law of thermodynamics

Repeated and continuous interactions in open quantum systems

We consider a finite quantum system S coupled to two environments of different nature. One is a heat reservoir R (continuous interaction) and the other one is a chain C of independent quantum systems E (repeated interaction). The interactions of S with R and C lead to two simultaneous dynamical processes. We show that for generic such systems, any initial state approaches an asymptotic state in the limit of large times. We express the latter in terms of the resonance data of a reduced propagator of S+R and show that it satisfies a second law of thermodynamics. We analyze a model where both S and E are two-level systems and obtain the asymptotic state explicitly (lowest order in the interaction strength). Even though R and C are not direcly coupled, we show that they exchange energy, and we find the dependence of this exchange in terms of the thermodynamic parameters. We formulate the problem in the framework of W*-dynamical systems and base the analysis on a combination of spectral deformation methods and repeated interaction model techniques. We do not use master equation approximations

Efficient genetic algorithms for solving hard constrained optimization problems

This paper studies many Genetic Algorithm strategies to solve hard-constrained optimization problems. It investigates the role of various genetic operators to avoid premature convergence. In particular, an analysis of niching methods is carried out on a simple function to show advantages and drawbacks of each of them. Comparisons are also performed on an original benchmark based on an electrode shape optimization technique coupled with a charge simulation metho

Topological model for machining of parts with complex shapes

Complex shapes are widely used to design products in several industries such as aeronautics, automotive and domestic appliances. Several variations of their curvatures and orientations generate difficulties during their manufacturing or the machining of dies used in moulding, injection and forging. Analysis of several parts highlights two levels of difficulties between three types of shapes: prismatic parts with simple geometrical shapes, aeronautic structure parts composed of several shallow pockets and forging dies composed of several deep cavities which often contain protrusions. This paper mainly concerns High Speed Machining (HSM) of these dies which represent the highest complexity level because of the shapes' geometry and their topology. Five axes HSM is generally required for such complex shaped parts but 3 axes machining can be sufficient for dies. Evolutions in HSM CAM software and machine tools lead to an important increase in time for machining preparation. Analysis stages of the CAD model particularly induce this time increase which is required for a wise choice of cutting tools and machining strategies. Assistance modules for prismatic parts machining features identification in CAD models are widely implemented in CAM software. In spite of the last CAM evolutions, these kinds of CAM modules are undeveloped for aeronautical structure parts and forging dies. Development of new CAM modules for the extraction of relevant machining areas as well as the definition of the topological relations between these areas must make it possible for the machining assistant to reduce the machining preparation time. In this paper, a model developed for the description of complex shape parts topology is presented. It is based on machining areas extracted for the construction of geometrical features starting from CAD models of the parts. As topology is described in order to assist machining assistant during machining process generation, the difficulties associated with tasks he carried out are analyzed at first. The topological model presented after is based on the basic geometrical features extracted. Topological relations which represent the framework of the model are defined between the basic geometrical features which are gathered afterwards in macro-features. Approach used for the identification of these macro-features is also presented in this paper. Detailed application on the construction of the topological model of forging dies is presented in the last part of the paper