Stabilization of an arbitrary profile for an ensemble of half-spin systems

We consider the feedback stabilization of a variable profile for an ensemble of non interacting half spins described by the Bloch equations. We propose an explicit feedback law that stabilizes asymptotically the system around a given arbitrary target profile. The convergence proof is done when the target profile is entirely in the south hemisphere or in the north hemisphere of the Bloch sphere. The convergence holds for initial conditions in a H^1 neighborhood of this target profile. This convergence is shown for the weak H^1 topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the target profile.Comment: 6 pages, 2 figure

Towards a Generic Trace for Rule Based Constraint Reasoning

CHR is a very versatile programming language that allows programmers to declaratively specify constraint solvers. An important part of the development of such solvers is in their testing and debugging phases. Current CHR implementations support those phases by offering tracing facilities with limited information. In this report, we propose a new trace for CHR which contains enough information to analyze any aspects of \CHRv\ execution at some useful abstract level, common to several implementations. %a large family of rule based solvers. This approach is based on the idea of generic trace. Such a trace is formally defined as an extension of the $\omega_r^\lor$ semantics of CHR. We show that it can be derived form the SWI Prolog CHR trace

Cyclical effects of bank capital requirements with imperfect credit markets

This paper analyzes the cyclical effects of bank capital requirements in a simple model with credit market imperfections. Lending rates are set as a premium over the cost of borrowing from the central bank, with the premium itself depending on firms’ effective collateral. Basel I- and Basel II-type regulatory regimes are defined and a capital channel is introduced through a signaling effect of capital buffers on the cost of bank deposits. The macroeconomic effects of various shocks (a drop in output, an increase in the refinance rate, and a rise in the capital adequacy ratio) are analyzed, under both binding and nonbinding capital requirements. Factors affecting the procyclicality of each regime (defined in terms of the behavior of the risk premium) are also identified and policy implications are discussed.Banks&Banking Reform,Access to Finance,Economic Theory&Research,Currencies and Exchange Rates,Debt Markets

Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up

This paper presents a first mathematical convergence analysis of a Fock states feedback stabilization scheme via single-photon corrections. This measurement-based feedback has been developed and experimentally tested in 2012 by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel Raimond. Here, we consider the infinite-dimensional Markov model corresponding to the ideal set-up where detection errors and feedback delays have been disregarded. In this ideal context, we show that any goal Fock state can be stabilized by a Lyapunov-based feedback for any initial quantum state belonging to the dense subset of finite rank density operators with support in a finite photon-number sub-space. Closed-loop simulations illustrate the performance of the feedback law.Comment: 2 figures, extended version of the IEEE CDC2015 conference pape

On gender and growth : the role of intergenerational health externalities and women's occupational constraints

This paper studies the growth effects of externalities associated with intergenerational health transmission, health persistence, and women's occupational constraints-- with particular emphasis on the role of access to infrastructure. The first part provides a review of the evidence on these issues. The second and third parts present an overlapping generations model of endogenous growth that captures these interactions, and characterize its properties. The model is then used to perform several gender-based or gender-related experiments -- a reduction in the cost of child rearing, improved wage equality in the market place, and better access to infrastructure. The last part draws together the implications of the analysis for promoting the role of women in growth strategies.Health Monitoring&Evaluation,Population Policies,Gender and Health,Gender and Law,Rural Development Knowledge&Information Systems

Sudden Floods, Prudential Regulation and Stability in an Open Economy

We develop a dynamic stochastic model of a middle-income, small open economy with a two-level banking intermediation structure, a risk-sensitive regulatory capital regime, and imperfect capital mobility. Firms borrow from a domestic bank and the bank borrows on world capital markets, in both cases subject to an endogenous premium. A sudden flood in capital flows generates an expansion in credit and activity, and asset price pressures. Countercyclical regulation, in the form of a Basel III-type rule based on real credit gaps, is effective at promoting macroeconomic stability (defined in terms of the volatility of a weighted average of inflation and the output gap) and financial stability (defined in terms of the volatility of a composite index of the nominal exchange rate and house prices). However, because the gain in terms of reduced volatility may exhibit diminishing returns, a countercyclical regulatory rule may need to be supplemented by other, more targeted, macroprudential instruments.

Rank-1 Tensor Approximation Methods and Application to Deflation

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on successive rank-1 approximations can be used to perform this task, since the latter are rather easy to compute. We first present an algebraic rank-1 approximation method that performs better than the standard higher-order singular value decomposition (HOSVD) for three-way tensors. Second, we propose a new iterative rank-1 approximation algorithm that improves any other rank-1 approximation method. Third, we describe a probabilistic framework allowing to study the convergence of deflation CP decomposition (DCPD) algorithms based on successive rank-1 approximations. A set of computer experiments then validates theoretical results and demonstrates the efficiency of DCPD algorithms compared to other ones