No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions: The circular results.

Page and Wooders (1996) prove that the no-unbounded-arbitrage (NUBA) condition introduced by Page (1987) is equivalent to the existence of a no arbitrage price (NAPS) when no agent has non-null useless vectors. Al- louch, Le Van and Page (2002) show that their generalized NAPS condition is actually equivalent to the weak-no-market-arbitrage (WNMA) condition introduced by Hart (1974). They mention that this result implies the one given by Page andWooders (1996). In this note, we show that these results are actually circular.Arbitrage, Equilibrium, Recession cone.

Exploring Historically Black College and Universities\u27 Ethos of Racial Uplift: Stem Students\u27 Challenges and Institutions\u27 Practices for Cultivating Learning and Persistence in Stem

Achievement in STEM (Science, Technology, Engineering and Mathematics) is a marker of racial inequality. Despite making up 13 percent of the U.S. populace, Black representation in STEM education and the STEM workforce is far from equitable. A reversal of this trend, however, exists at Historically Black Colleges and Universities (HBCUs), where HBCU graduates represent nearly 18 percent of STEM baccalaureate degrees awarded to Black students. Through a multi-site case study of STEM education at four HBCUs, I interviewed students, faculty and administrators involved in services and programs (i.e. undergraduate research, mentoring) specific to supporting students in the gateway courses. Validation Theory and Science Identity Theory were used to inform the overall design--collection and analysis of data--of the study. I found that these services make a meaningful difference in the achievement of students in STEM by providing them with sound relationships and effective study skills, embedded within a culture of family, that help them overcome the challenges associated with the gateway courses. This difference can also be attributed to the multiple roles that faculty plays outside the classroom to address the challenges that externally bear on their students\u27 achievement. By understanding how these four HBCUs have helped their students overcome this critical stage in the STEM educational pipeline, findings help identify salient practices and strategies that encourage minority student learning and persistence that could be informative to other minority serving institutions and majority institutions struggling to support these student populations. Lastly, this study also demonstrates the ongoing importance of HBCUs in improving minority access to opportunities in the STEM workforce

Historically Black Colleges and Universities (HBCUs): Leading Our Nation's Effort to Improve the Science, Technology, Engineering, and Mathematics (STEM) Pipeline

This article examines the contributions of Historically Black Colleges and Universities in improving the achievement of Black students in STEM (Science, Technology, Engineering, and Mathematics) fields. We couple recent descriptive statistics with an extensive review of the literature to elucidate the conditions and best practices, which exist at many HBCUs and characterize these institutions as models for majority institutions for the support of all Black and other racial minority students. We conclude with a discussion and recommendations.Educatio

Savage's theorem with atoms

The famous theorem of Savage is based on the richness of the states space, by assuming a \textit{continuum} nature for this set. In order to fill the gap, this article considers Savage's theorem with discrete state space. The article points out the importance the existence of pair event in the existence of utility function and the subjective probability. Under the discrete states space, this can be ensured by the intuitive \textit{atom swarming} condition. Applications for the establishment of an inter-temporal evaluation \emph{\`a la } Koopman \cite{K60}, \cite{K72}, and for the configuration under \textit{unlikely atoms} of Mackenzie \cite{Mackenzie2018} are provided

A tale of two Rawlsian criteria

This work considers optimization problems under Rawls and maximin with multiple discount factors criteria. It proves that though these criteria are different, they have the same optimal value and solution

EMaP: Explainable AI with Manifold-based Perturbations

In the last few years, many explanation methods based on the perturbations of input data have been introduced to improve our understanding of decisions made by black-box models. The goal of this work is to introduce a novel perturbation scheme so that more faithful and robust explanations can be obtained. Our study focuses on the impact of perturbing directions on the data topology. We show that perturbing along the orthogonal directions of the input manifold better preserves the data topology, both in the worst-case analysis of the discrete Gromov-Hausdorff distance and in the average-case analysis via persistent homology. From those results, we introduce EMaP algorithm, realizing the orthogonal perturbation scheme. Our experiments show that EMaP not only improves the explainers' performance but also helps them overcome a recently-developed attack against perturbation-based methods.Comment: 29 page

Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities

We consider a model with an infinite numbers of states of nature, von Neumann - Morgenstern utilities and where agents have different prob- ability beliefs. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. How- ever, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold