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We study of the connection between operator valued central limits for monotone, Boolean and free probability theory, which we shall call the arcsine, Bernoulli and semicircle distributions, respectively. In scalar-valued non-commutative probability these measures are known to satisfy certain arithmetic relations with respect to Boolean and free convolutions. We show that generally the corresponding operator-valued distributions satisfy the same relations only when we consider them in the fully matricial sense introduced by Voiculescu. In addition, we provide a combinatorial description in terms of moments of the operator valued arcsine distribution and we show that its reciprocal Cauchy transform satisfies a version of the Abel equation similar to the one satisfied in the scalar-valued case.

This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each agent should receive a plot of a usable geometric shape, and (2) plots of different agents must be physically separated. With these requirements, the classic fairness notion of \emph{proportionality} is impractical, since it may be impossible to attain any multiplicative approximation of it. In contrast, the \emph{ordinal maximin share approximation}, introduced by Budish in 2011, provides meaningful fairness guarantees. We prove upper and lower bounds on achievable maximin share guarantees when the usable shapes are squares, fat rectangles, or arbitrary axis-aligned rectangles, and explore the algorithmic and query complexity of finding fair partitions in this setting. Our work makes use of tools and concepts from computational geometry such as independent sets of rectangles and guillotine partitions. Appears in the 30th International Joint Conference on Artificial Intelligence (IJCAI), 2021

Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor $\beta$: When an object $o$ of size $s(o)$ arrives, the decisions for objects of total size at most $\beta\cdot s(o)$ may be revoked. Usually $\beta$ should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classic problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective. In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small $\eps$). We therefore resolve the competitiveness of the bin covering problem with migration.

We investigate the firm level investment responses to narrative shocks to average personal and corporate tax rates using a universal micro dataset of publicly traded U.S firms for the post- 1962 period. By allowing for heterogeneous effects over the business cycle and accompanying monetary policy regime, as well as over firm-level characteristics, we show that : (i) corporate tax multipliers are negative overall, but this result is driven by smaller firms who face larger borrowing constraints, especially during high-unemployment periods or when the accompanying monetary policy is contractionary; (ii) while the magnitude and the significance of personal income tax multipliers are smaller on the aggregate, there is some evidence of positive personal tax multipliers in high-unemployment state by large (dividend-paying) firms, which is consistent with the recent literature.

Throughout the female menstrual cycle, physiological changes occur that affect the biodistribution of nanoparticles within the reproductive system. We demonstrate a 2-fold increase in nanoparticle accumulation in murine ovaries and uterus during ovulation, compared to the nonovulatory stage, following intravenous administration. This biodistribution pattern had positive or negative effects when drug-loaded nanoparticles, sized 100 nm or smaller, were used to treat different cancers. For example, treating ovarian cancer with nanomedicines during mouse ovulation resulted in higher drug accumulation in the ovaries, improving therapeutic efficacy. Conversely, treating breast cancer during ovulation, led to reduced therapeutic efficacy, due to enhanced nanoparticle accumulation in the reproductive system rather than at the tumor site. Moreover, chemotherapeutic nanoparticles administered during ovulation increased ovarian toxicity and decreased fertility compared to the free drug. The menstrual cycle should be accounted for when designing and implementing nanomedicines for females.

Circadian clocks are synchronized by external timing cues to align with one another and the environment. Various signaling pathways have been shown to independently reset the phase of the clock. However, in the body, circadian clocks are exposed to a multitude of potential timing cues with complex temporal dynamics, raising the question of how clocks integrate information in response to multiple signals. To investigate different modes of signal integration by the circadian clock, we used Circa-SCOPE, a method we recently developed for high-throughput phase resetting analysis. We found that simultaneous exposure to different combinations of known pharmacological resetting agents elicits a diverse range of responses. Often, the response was nonadditive and could not be readily predicted by the response to the individual signals. For instance, we observed that dexamethasone is dominant over other tested inputs. In the case of signals administered sequentially, the background levels of a signal attenuated subsequent resetting by the same signal, but not by signals acting through a different pathway. This led us to examine whether the circadian clock is sensitive to relative rather than absolute levels of the signal. Importantly, our analysis revealed the involvement of a signal-specific fold-change detection mechanism in the clock response. This mechanism likely stems from properties of the signaling pathway that are upstream to the clock. Overall, our findings elucidate modes of input integration by the circadian clock, with potential relevance to clock resetting under both physiological and pathological conditions.

We map the available scientific literature on how and why victims of sexual violence use digital platforms in the aftermath of victimization. Twenty-four empirical studies on sexual victimization and online disclosure were identified by systematically searching Web of Science and PsycINFO, checking reference lists, and consulting authors about relevant publications. The literature on online disclosure of sexual victimization does not yield a coherent picture. International literature pays limited attention to the various components of online disclosure like the characteristics of victims who disclosure online and the characteristics of the disclosure messages. Most studies focused on motivations for and reactions to online disclosure. Victims of sexual violence disclose sexual victimization online to seek support for clarification and validation, unburdening, documenting, seeking justice, informing others, or commercial goals (individual-oriented disclosure) and to provide support, educate, and as a form of activism (other-oriented disclosure). Responses to online disclosure are predominantly positive. Negative responses are rare. This review provides a comprehensive overview of multidisciplinary empirical information and displays knowledge gaps in victimological research. Future research should use robust quantitative and/or qualitative designs with substantial sample sizes, comparing victims who do disclose their sexual victimization online to victims who do not and comparing disclosure on different online platforms to increase generalizability. Potential for online support is identified, in which online disclosure can serve as a relatively safe alternative to off-line disclosure. This offers points of intervention for assistance and victim support in facilitating the use of the internet for support for victims of sexual violence.

Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is completed and a machine becomes idle. Robust optimization is the natural methodology to cope with the first characteristic of duration uncertainty, yet the existing literature on robust scheduling does not explicitly consider the second characteristic - the possibility to adjust decisions as more information about the tasks' duration becomes available, despite that re-optimizing the schedule every time new information emerges is standard practice. In this paper, we develop a scheduling approach that takes into account, at the beginning of the planning horizon, the possibility that scheduling decisions can be adjusted. We demonstrate that the suggested approach can lead to better here-and-now decisions and better makespan guarantees. To that end, we develop the first mixed integer linear programming model for adjustable robust scheduling, and a scalable two-stage approximation heuristic, where we minimize the worst-case makespan. Using this model, we show via a numerical study that adjustable scheduling leads to solutions with better and more stable makespan realizations compared to static approaches.