Normal transversality and uniform bounds

For two ideals $I$ and $J$ of a noetherian ring, we characterize, in terms of the vanishing of Tor modules, when the associated graded ring of the sum $I+J$ is isomorphic to the tensor product of the associated graded ring of $I$ and the associated graded ring of $J$. It is shown that the relation type of the tensor product of two standard algebras is bounded above by the maximum of the relation type of each algebra. As a consequence, we deduce a uniform bound for the relation type of maximal ideals of an excellent ring and a classical result of Duncan and O'Carroll on the strong uniform Artin-Rees property.Comment: 12 pages, Late

The relation type of affine algebras and algebraic varieties

We introduce the notion of relation type of an affine algebra and prove that it is well defined by using the Jacobi-Zariski exact sequence of Andr\'e-Quillen homology. In particular, the relation type is an invariant of an affine algebraic variety. Also as a consequence of the invariance, we show that in order to calculate the relation type of an ideal in a polynomial ring one can reduce the problem to trinomial ideals. When the relation type is at least two, the extreme equidimensional components play no role. This leads to the non existence of affine algebras of embedding dimension three and relation type two

Consensus stabilizability and exact consensus controllability of multi-agent linear systems

A goal in engineering systems is to try to control them. Control theory offers mathematical tools for steering engineered systems towards a desired state. Stabilizability and controllability can be studied under different points of view, in particular, we focus on measure of controllability in the sense of the minimum set of controls that need for to steer the multiagent system toward any desired state. In this paper, we study the consensus stabilizability and exact consensus controllability of multi-agent linear systems, in which all agents have a same linear dynamic mode that can be in any orderPostprint (published version

Analyzing controllability of neural networks

In recent years, due to the relation between cognitive control and mathematical concept of control dynamical systems, there has been growing interest in the descriptive analysis of complex networks with linear dynamics, permeating many aspects from everyday life, obtaining considerable advances in the description of their structural and dynamical properties. Nevertheless, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems is of interest to study the exact controllability, this measure is defined as the minimum set of controls that are needed to steer the whole system toward any desired state. In this paper, a revision of controllability concepts is presented and provides conditions for exact controllability for the multiagent systemsPostprint (author's final draft

Mentoring, Educational Services, and Incentives to Learn: What Do We Know About Them?

This paper reviews recent studies on the effectiveness of services and incentives offered to disadvantaged youth. We focus our analysis on three types of interventions: mentoring, educational services, and financial rewards. The objective of this article is threefold. First, we explain alternative theoretical points of view in favor (or against – when applicable) each of these interventions. Then, we discuss how recent empirical work has affected that view, and we summarize the latest findings. We conclude with a discussion on what questions remain to be examined. Our hope is that this article will serve as a resource for those seeking to understand what educational interventions work and for whom, and to use as a starting point to illuminate the debate on where to go next.cognitive and non-cognitive skills, intrinsic and extrinsic motivation, at-risk youth, resilience, deviancy training, deterrence, primary- and high-school, post-secondary education, remedial programs, incentives on inputs and outputs

A model of credit limits and bankruptcy with applications to welfare and indebtedness

This paper presents a macroeconomic model of unsecured consumer debt and default where credit conditions consist of pre-approved interest rates and borrowing limits, a feature of actual credit cards. All loans, irrespective of their size and risk, take place against the same type of credit line, and some borrowers are credit constrained. This type of situation is shown to arise in a free-entry competitive equilibrium if there are fixed costs in banking and the banks' decisions on interest rates and on credit limits are made separately. Numerical experiments are conducted to study, on one hand, the macroeconomic and welfare effects of the consumer bankruptcy code, and on the other hand, the consequences of various factors for both indebtedness and bankruptcy. Restricting bankruptcy filings - be it through a stricter Chapter 7 means testing or a longer period of credit exclusion - leads to sizable welfare loses. The recent rise in filing rates and debt is best explained by a combination of lower intermediation costs and more severe non-discretionary expenditures shocks. The endogenous response ofthe credit limit proves to be crucial for these findings Keywords; bankruptcy, unsecured credit, general equilibrium, default risk, credit limits