An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for application to some non-compact Shimura varieties with their bundles of cusp forms. As an application, we treat the case of Hilbert modular surfaces, establishing an arithmetic analogue of the classical result expressing the dimensions of spaces of cusp forms in terms of special values of Dedekind zeta functions

Full vs Partial Market Coverage with Minimum Quality Standards

The consequences of the adoption of quality standards on the extent of market coverage is investigated by modelling a game between regulator and low-quality firm in a vertically differentiated duopoly. The game has a unique equilibrium in the most part of the parameter range. There exists a non-negligible range where the game has no equilibrium in pure strategies. This result questions the feasibility of MQS regulation when firms endogenously determine market coverage

An equivalent formulation for the Shapley value

The final authenticated version is available online at: https://doi.org/10.1007/978-3-662-58464-4_1.An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.Peer ReviewedPostprint (published version

Clearing algorithms and network centrality

I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results which showed that Katz-type centrality measures are closely related to contagiousness. It also allows assessing the assumptions that one is making when using such centrality measures as systemic risk indicators. I conclude that these assumptions should be considered too strong and that, from a theoretical perspective, clearing models should be given preference over centrality measures in systemic risk analyses

Nearly optimal solutions for the Chow Parameters Problem and low-weight approximation of halfspaces

The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$ are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of any linear threshold function $f$ uniquely specify $f$ within the space of all Boolean functions, but until recently (O'Donnell and Servedio) nothing was known about efficient algorithms for \emph{reconstructing} $f$ (exactly or approximately) from exact or approximate values of its Chow parameters. We refer to this reconstruction problem as the \emph{Chow Parameters Problem.} Our main result is a new algorithm for the Chow Parameters Problem which, given (sufficiently accurate approximations to) the Chow parameters of any linear threshold function $f$, runs in time \tilde{O}(n^2)\cdot (1/\eps)^{O(\log^2(1/\eps))} and with high probability outputs a representation of an LTF $f'$ that is \eps-close to $f$. The only previous algorithm (O'Donnell and Servedio) had running time \poly(n) \cdot 2^{2^{\tilde{O}(1/\eps^2)}}. As a byproduct of our approach, we show that for any linear threshold function $f$ over $\{-1,1\}^n$, there is a linear threshold function $f'$ which is \eps-close to $f$ and has all weights that are integers at most \sqrt{n} \cdot (1/\eps)^{O(\log^2(1/\eps))}. This significantly improves the best previous result of Diakonikolas and Servedio which gave a \poly(n) \cdot 2^{\tilde{O}(1/\eps^{2/3})} weight bound, and is close to the known lower bound of $\max\{\sqrt{n},$ (1/\eps)^{\Omega(\log \log (1/\eps))}\} (Goldberg, Servedio). Our techniques also yield improved algorithms for related problems in learning theory

Impact of a training program on the surveillance of Clostridioides difficile infection

A high degree of vigilance and appropriate diagnostic methods are required to detect Clostridioides difficile infection (CDI). We studied the effectiveness of a multimodal training program for improving CDI surveillance and prevention. Between 2011 and 2016, this program was made available to healthcare staff of acute care hospitals in Catalonia. The program included an online course, two face-to-face workshops and dissemination of recommendations on prevention and diagnosis. Adherence to the recommendations was evaluated through surveys administered to the infection control teams at the 38 participating hospitals. The incidence of CDI increased from 2.20 cases/10 000 patient-days in 2011 to 3.41 in 2016 (P < 0.001). The number of hospitals that applied an optimal diagnostic algorithm rose from 32.0% to 71.1% (P = 0.002). Hospitals that applied an optimal diagnostic algorithm reported a higher overall incidence of CDI (3.62 vs. 1.92, P < 0.001), and hospitals that were more active in searching for cases reported higher rates of hospital-acquired CDI (1.76 vs. 0.84, P < 0.001). The results suggest that the application of a multimodal training strategy was associated with a significant rise in the reporting of CDI, as well as with an increase in the application of the optimal diagnostic algorithm