Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments

Tunable Oscillations in the Purkinje Neuron

In this paper, we study the dynamics of slow oscillations in Purkinje neurons in vitro, and derive a strong association with a forced parametric oscillator model. We demonstrate the precise rhythmicity of the oscillations in Purkinje neurons, as well as a dynamic tunability of this oscillation using a photo-switchable compound. We show that this slow oscillation can be induced in every Purkinje neuron, having periods ranging between 10-25 seconds. Starting from a Hodgkin-Huxley model, we also demonstrate that this oscillation can be externally modulated, and that the neurons will return to their intrinsic firing frequency after the forced oscillation is concluded. These results signify an additional functional role of tunable oscillations within the cerebellum, as well as a dynamic control of a time scale in the brain in the range of seconds.Comment: 12 pages, 5 figure

Commutator Leavitt path algebras

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.Comment: 24 page

Carrying the World with the Grace of a Lady and the Grit of a Warrior: Deepening Our Understanding of the “Strong Black Woman” Schema

Across varied disciplines, attempts have been made to capture the multidimensionality of Black womanhood under a unifying framework illustrative of Black women’s perceived roles, responsibilities, and experiences of intersectional oppression. The result has been the emergence of a number of divergent but overlapping constructs (e.g., Superwoman Schema, Sojourner Truth Syndrome, Sisterella Complex, and Strong Black Woman [SBW] Schema). The goal of our study is to integrate overlapping attributes of existing constructs beneath a single term while also expounding upon the defining characteristics of the SBW Schema. Thematic analyses were conducted with data gathered from eight focus groups with 44 Black women from the Mid-Atlantic region of the United States. Women ranged in age from 18 to 91 and were diverse in religious and educational backgrounds. Data analysis involved iterative processes (i.e., continuous development of new codes and constant comparison of themes). Prominent themes identified as characteristics of the SBW Schema were (a) Embodies and Displays Multiple Forms of Strength, (b) Possesses Self/Ethnic Pride in Spite of Intersectional Oppression, (c) Embraces Being Every Woman, and (d) Anchored by Religion/Spirituality. Mental and physical health outcomes (e.g., psychological distress, depressive symptomology, obesity, and cardiovascular disease risk) associated with characteristics of the SBW Schema underscore the importance of the construct and its exploration

The B→Xsl+l−B\to X_sl^+l^- and B→XsγB\to X_s \gamma decays with the fourth generation

If the fourth generation fermions exist, the new quarks could influence the branching ratios of the decays of $B\to X_s \gamma$ and $B\to X_sl^+l^-$. We obtain two solutions of the fourth generation CKM factor $V^{*}_{t^{'}s}V_{t^{'}b}$ from the decay of $B\to X_s \gamma$. We use these two solutions to calculate the new contributions of the fourth generation quark to Wilson coefficients of the decay of $B\to X_sl^+l^-$. The branching ratio and the forward-backward asymmetry of the decay of $B\to X_sl^+l^-$ in the two cases are calculated. Our results are quite different from that of SM in one case, almost same in another case. If Nature chooses the formmer, the $B$ meson decays could provide a possible test of the forth generation existence.Comment: 10 pages, 5 figure