Local observers on linear Lie groups with linear estimation error dynamics

This paper proposes local exponential observers for systems on linear Lie groups. We study two different classes of systems. In the first class, the full state of the system evolves on a linear Lie group and is available for measurement. In the second class, only part of the system's state evolves on a linear Lie group and this portion of the state is available for measurement. In each case, we propose two different observer designs. We show that, depending on the observer chosen, local exponential stability of one of the two observation error dynamics, left- or right-invariant error dynamics, is obtained. For the first class of systems these results are developed by showing that the estimation error dynamics are differentially equivalent to a stable linear differential equation on a vector space. For the second class of system, the estimation error dynamics are almost linear. We illustrate these observer designs on an attitude estimation problem

Estimating the Effect of Student Aid on College Enrollment: Evidence from a Government Grant Policy Reform

In this paper, we investigate the responsiveness of the demand for college to changes in student aid arising from a Danish reform. We separately identify the effect of aid from that of other observed and unobserved variables such as parental income. We exploit the combination of a kinked aid scheme and a reform of the student aid scheme to identify the effect of direct costs on college enrollment. To allow for heterogeneous responses due to borrowing constraints, we use detailed information on parents' assets. We find that enrollment is less responsive than found in other studies and that the presence of borrowing constraints only deters college enrollment to a minor extent.college attendance, educational subsidies, reform, kink regression

Ibogaine offers an alternative approach for treating opiate addiction

Substance use disorders (SUDs) such as opioid addiction account for a large portion of the total global burden of disease. Nearly 5% of all disability-adjusted life years and 4% of overall mortality appear to be attributed to SUDs. An SUD, such as opioid use is often characterized by its addictiveness and frequent relapse among those who attempt quitting. Despite traditional methods of treatment, 5-year relapse rates are as high as 97% for opioid dependence. Alternative or novel forms of treating opioid addiction should be investigated and adopted, especially in countries which face an “epidemic” of opioid use and dependence, such as the United States. Ibogaine is a naturally occurring indole alkaloid that may be an effective alternative form of treatment for individuals struggling with opiate addiction and/or withdrawal. Preliminary research has found that iboga alkaloids such as ibogaine are effective at reducing morphine self-administration in rats. An elaborate history of human case reports has found ibogaine to be successful at reducing drug self-administration, withdrawal symptoms, and ceasing opioid cravings. The complex pharmacological profile of ibogaine is mediated by several classes of neurological receptors and transporters, including the sigma-2, kappa- and mu-opioid, 5HT2 and 5HT3 receptors, 34 nicotinic receptors, and the N-methyl-d-aspartic acid ion channel. Ibogaine’s combined interaction with all of these receptors has been suggested to reset or normalize neuroadaptation related to drug sensitization and tolerance. The resulting anti-addictive physiological and psychological properties appear to persist beyond pharmacokinetic elimination from serum or brain tissue, but may also cause unwanted side effects such as cardiovascular and neurologic toxicity. Developing a safe and effective standard dosing regimen has proven to be difficult in humans. The controversial therapeutic use of ibogaine in medical and nonmedical settings has been called a “vast uncontrolled experiment” or “medical subculture”, and ibogaine remains unscheduled in much of the world. However, ibogaine does not appear to have potential for recreational or other forms of abuse. During the 1995 Ibogaine Review Meeting, none of the consultants to NIDA were concerned about the abuse of ibogaine. Opiate users struggling with addiction and also interested in ibogaine therapy prompted the formation of “informal” treatment networks. Ibogaine therapy clinics catering to foreigners have also become more common in the Caribbean and Latin America. In order to clarify ibogaine’s clinical safety and therapeutic use against opiate dependence, the following thesis will investigate and analyze the ibogaine literature. Areas of focus for future ibogaine research will be identified, such as the invention of ibogaine congeners that retain efficacy against opioid dependence, but minimize unwanted toxic or psychological effects

Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, arXiv:quant-ph/0402005, accepted to appear in Phys. Rev. Lett.]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which non-deterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space.Comment: 31 pages, 54 figure

Global Stability of a Class of Difference Equations on Solvable Lie Algebras

Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference equation has three key properties that facilitate our analysis: 1) its power series expansion enjoys a type of strong convergence; 2) the origin is an equilibrium; 3) the algebraic ideals enumerated in the lower central series of the Lie algebra are dynamically invariant. We show that certain global stability properties are implied by stability of the Jacobian linearization of dynamics at the origin. In particular global asymptotic stability. If the Lie algebra is nilpotent, then the origin enjoys semiglobal exponential stability