A hierarchy of LMI inner approximations of the set of stable polynomials

Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size $m$) of the nonconvex set of Schur stable polynomials of given degree $n < m$. It is shown that when $m$ tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in $n$) already studied in the technical literature

Frontier Capital: Early Stage Investing for Financial Returns and Social Impact in Emerging Markets

This report outlines the importance and promise of serving low- and lower-middle-income (LMI) populations -- essentially, the groups situated between the very bottom of the pyramid and the existing middle class. As we detail herein, LMI populations have huge unmet needs and face quite a bit of instability -- challenges that can be addressed by innovative business models. We believe companies serving this demographic represent an under-tapped opportunity, both for financial returns and for outsized impact. The LMI segment represents a major market opportunity. For example, in Latin America and the Caribbean, the purchasing power of the LMI population is estimated at $405B. In South Asia, it is estimated at$483B

The State of Knowledge on the Role and Impact of Labour Market Information: A Survey of the International Evidence

This report provides a critical examination of the international literature on the role and impact of labour market information (LMI). The purpose of this exercise is to assess the current state of knowledge on the role and impact of LMI and to identify gaps in our knowledge. The report finds that we know very little about the impact of LMI per se on labour market outcomes. What knowledge we do possess must be inferred from evaluations of labour market programs or technologies that are related to LMI, such as job-search assistance programs, career counseling, and internet-based LMI. The literature on each of these topics reveals some beneficial impacts on labour market outcomes, but the precise role of LMI in driving these relationships is never specified.labour market, international, labour market information, decision-making, labour market outcomes

Solar+Storage for Low-and Moderate-Income Communities: A Guide for States and Municipalities

The Clean Energy States Alliance (CESA) has produced a new report for states and municipalities on solar+storage for low- and moderate-income (LMI) communities. The report explains how solar+storage can benefit LMI residents and describes a variety of policy tools for doing so, including grants, rebates, utility procurement standards, financing support, opening markets, and soft cost reduction

Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier LtdThis Letter is concerned with the analysis problem of exponential stability for a class of discrete-time recurrent neural networks (DRNNs) with time delays. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strict monotonic. Furthermore, the description of the activation functions is more general than the recently commonly used Lipschitz conditions. Under such mild conditions, we first prove the existence of the equilibrium point. Then, by employing a Lyapunov–Krasovskii functional, a unified linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the DRNNs to be globally exponentially stable. It is shown that the delayed DRNNs are globally exponentially stable if a certain LMI is solvable, where the feasibility of such an LMI can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China (05KJB110154), the NSF of Jiangsu Province of China (BK2006064), and the National Natural Science Foundation of China (10471119)

Equipping communities to achieve equitable transit-oriented development

Though transit-oriented development (TOD) is uniquely positioned to benefit low- and moderate-income (LMI) communities, most TOD projects do not focus on the interests of LMI communities and in some cases have dramatically disrupted low-income neighborhoods. However, there are several tools and strategies that can help mitigate the potential negative impacts of TOD and maximize benefits for LMI communities. This article examines Denver's TOD fund, Oakland CA's Fruitvale Village, and Longfellow Station in Minneapolis, MN, highlighting the equity provisions built into each model.Community development ; Transportation

Affordable housing in the greater Boston area: what challenges are LMI households facing?

Traditional programs designed to assist low- and moderate-income (LMI) renters and prospective homebuyers may not be sufficient given the rapidly accelerating Greater Boston real-estate market. Kathleen Gill explores how a growing shortage of affordable housing impacts LMI households and what options may be available to them.Housing - Massachusetts ; Housing - Prices

The effect of credit scoring on small business lending in low- and moderate-income areas

This paper empirically examines the effect of the use of credit scoring by large banking organizations on small business lending in low- and moderate-income (LMI) areas. Using census tract level data for the southeastern United States, the authors estimate that credit scoring increases small business lending by $16.4 million per LMI area served. Furthermore, this effect is almost 2.5 times larger than that estimated for higher income census tracts ($6.8 million). The authors also find that credit scoring increases the probability that a large banking organization will make small business loans in a given census tract. The change in this probability is 3.8 percent for LMI areas and 1.7 percent for higher income areas. These findings suggest that credit scoring reduces asymmetric information problems for borrowers and lenders and that this is particularly important for LMI areas, which lenders may have historically bypassed because of their questionable economic health.Credit scoring systems ; Bank loans ; Commercial loans ; Small business