Active Sampling-based Binary Verification of Dynamical Systems

Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While analytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system's response at different operating conditions, they often produce conservative approximations due to restrictive assumptions and are difficult to construct in many applications. In contrast, popular statistical verification techniques relax the restrictions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into "safe" and "unsafe" subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction error. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.Comment: 23 page

The price of rapid exit in venture capital-backed IPOs

This paper proposes an explanation for two empirical puzzles surrounding initial public offerings (IPOs). Firstly, it is well documented that IPO underpricing increases during “hot issue” periods. Secondly, venture capital (VC) backed IPOs are less underpriced than non-venture capital backed IPOs during normal periods of activity, but the reverse is true during hot issue periods: VC backed IPOs are more underpriced than non-VC backed ones. This paper shows that when IPOs are driven by the initial investor’s desire to exit from an existing investment in order to finance a new venture, both the value of the new venture and the value of the existing firm to be sold in the IPO drive the investor’s choice of price and fraction of shares sold in the IPO. When this is the case, the availability of attractive new ventures increases equilibrium underpricing, which is what we observe during hot issue periods. Moreover, I show that underpricing is affected by the severity of the moral hazard problem between an investor and the firm’s manager. In the presence of a moral hazard problem the degree of equilibrium underpricing is more sensitive to changes in the value of the new venture. This can explain why venture capitalists, who often finance firms with more severe moral hazard problems, underprice IPOs less in normal periods, but underprice more strongly during hot issue periods. Further empirical implications relating the fraction of shares sold and the degree of underpricing are presented

The Politics of Race and Class and the Changing Spatial Fortunes of the McCarren Pool in Brooklyn, New York, 1936-2010

This paper explores the changing spatial properties of the McCarren Pool and connects them to the politics of race and class. The pool was a large liberal government project that sought to improve the leisure time of working class Brooklynites and between 1936 and the early 1970s it was a quasi-public functional space. In the 1970s and the early 1980s, the pool became a quasi-public dysfunctional space because the city government reduced its maintenance and staffing levels. Working class whites of the area engaged into neighborhood defense in order to prevent the influx of Latinos and African Americans into parts of Williamsburg and Greenpoint and this included the environs of the McCarren Pool. The pool was shut down in 1983 because of a mechanical failure. Its restoration did not take place because residents and storekeepers near the vicinity of the pool complained that by the 1970s, it was only African Americans and Latinos who patronized the pool and that their presence in the neighborhood undermined white exclusivity. For two decades, the McCarren Pool became a multi-use alternative space frequented by homeless people, graffiti artists, heroin users, teenagers, and drug dealers. Unlike previous decades, during this period, people of various racial and ethnic backgrounds frequented the pool area in a relatively harmonious manner. In the early part of the twenty-first century, a neoliberal city administration allowed a corporation to organize music concerts in the pool premises and promised to restore the facility into an operable swimming pool. The problem with this restoration project is that the history of the pool between the early 1970s and the early 2000s is downplayed and this does not serve well former or future users of the poo