Purely infinite crossed products by endomorphisms

We study the crossed product $C^*$-algebra associated to injective endomorphisms, which turns out to be equivalent to study the crossed product by the dilated autormorphism. We prove that the dilation of the Bernoulli $p$-shift endomorphism is topologically free. As a consequence, we have a way to twist any endomorphism of a \D-absorbing $C^*$-algebra into one whose dilated automorphism is essentially free and have the same $K$-theory map than the original one. This allows us to construct purely infinite crossed products $C^*$-algebras with diverse ideal structures.Comment: Corrected misprints. Clarified some points in Section 3. Added a reference. Re-submitted to JMA

Proportional Topology Optimization: A new non-gradient method for solving stress constrained and minimum compliance problems and its implementation in MATLAB

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing gradient optimality criteria method. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.Comment: 18 pages, 8 figures, and 2 appendices (MATLAB codes

Virtual to Real Reinforcement Learning for Autonomous Driving

Reinforcement learning is considered as a promising direction for driving policy learning. However, training autonomous driving vehicle with reinforcement learning in real environment involves non-affordable trial-and-error. It is more desirable to first train in a virtual environment and then transfer to the real environment. In this paper, we propose a novel realistic translation network to make model trained in virtual environment be workable in real world. The proposed network can convert non-realistic virtual image input into a realistic one with similar scene structure. Given realistic frames as input, driving policy trained by reinforcement learning can nicely adapt to real world driving. Experiments show that our proposed virtual to real (VR) reinforcement learning (RL) works pretty well. To our knowledge, this is the first successful case of driving policy trained by reinforcement learning that can adapt to real world driving data

Barriers to saving

When the poor succeed in building up a few assets, they often find themselves disqualified from badly needed government programs. Confusing rules about IRAs and 401(k)s plus conflicting state regulations make retirement saving particularly challenging.Saving and investment ; Poverty ; Medicaid ; Social security

Linking institutional investors to communities

Public pension funds, insurance companies, foundations, and universities increasingly pursue community investments because they deliver on twin goals: high financial returns and economic growth in underserved areas. Since 2000, mission-related investments have grown at a 19.5 percent compound annual rate.Investments ; Community development ; Community development - New England

Introduction to Islamic finance

An increasing number of individuals and banks have become curious about Islamic finance and how it is conducted in America. The author provides helpful background and tells where services can be found in New England.Finance (Islamic law)

Connecting public schools to community development

In neighborhoods across the country, public schools and community groups are beginning to work together in new and innovative ways. Connie Chung explores the wide variety of roles that public schools can play in community development efforts.Community development ; Public schools

The storm clouds begin to depart

Economic indicators