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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.

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.

We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such methods using a quasi-Monte Carlo (QMC) approach. We consider cases where the time-frequency representation is redundant, having feature axes in addition to the time and frequency axes. The proposed QMC method allows sampling both efficiently and evenly such redundant time-frequency representations. Indeed, 1) the number of samples required for a certain accuracy is log-linear in the resolution of the signal space, and depends only weakly on the dimension of the redundant time-frequency space, and 2) the quasi-random samples have low discrepancy, so they are spread evenly in the redundant time-frequency space. One example of such redundant representation is the localizing time-frequency transform (LTFT), where the time-frequency plane is enhanced by a third axis. This higher dimensional time-frequency space improves the quality of some time-frequency signal processing tasks, like the phase vocoder (an audio signal processing effect). Since the computational complexity of the QMC is log-linear in the resolution of the signal space, this higher dimensional time-frequency space does not degrade the computation complexity of the proposed QMC method. The proposed QMC method is more efficient than standard Monte Carlo methods, since the deterministic QMC sample points are optimally spread in the time-frequency space, while random samples are not.

Financialization and rising income inequality are two of the most pronounced economic developments of recent decades, and there is increasing evidence that these trends are somehow related. However, explanations of this link are still limited, and pay little attention to workers themselves. As a result, the impact of financialization on income inequality appears at most as an unfortunate side-effect. This article takes a different approach by investigating both financialization and income inequality from within the historical development of the class struggle in the United States economy. It shows that the economic problems of the 1970s that provided the impetus for financialization were closely related to the escalating conflicts between labor and capital, in which the state served as an increasingly important terrain of struggle. Viewed from this perspective, rising income inequality appears less as an unexpected outcome of financialization and more as its very raison d’etre.

Background: Becoming a parent is viewed as one of the most important transitions in one’s life. However, a history of childhood maltreatment may affect the adjustment to parenthood. Objective: The objective of this review was to synthesize the current evidence base to further our understanding of prospective and new parents’ experiences in the transition to parenthood (pregnancy to 2 years post-birth), in the context of having a childhood maltreatment history. Method: A scoping review of the literature was conducted using the following online databases: PubMed, PsycINFO, PsycNET, and Published International Literature of Traumatic Stress. Results: The findings were synthesized into a four-component theoretical framework, which included mental health of the parent, physical changes, parental view of the child, and view of the self as a parent. A total of 69 papers, including 181,537 participants (of whom 30,482 mothers and 235 fathers had maltreatment histories), investigated the transition to parenthood. The majority of the studies showed that parents with a maltreatment history may suffer from a range of mental health problems during the transition to parenthood, experience more negative physical changes, and have more negative views of their child (or children). However, they reported both positive and negative experiences regarding their identity as a parent. Conclusions: The findings suggest that maltreatment is a risk factor for a more challenging transition to parenthood. Experiences of fathers with maltreatment histories merit more attention, as do those of parents in low- and middle-income countries. Future directions should include predictors of positive experiences and the development of early interventions to improve outcomes for this population.

Stateful logic is a digital processing-in-memory technique that could address von Neumann memory bottleneck challenges while maintaining backward compatibility with standard von Neumann architectures. In stateful logic, memory cells are used to perform the logic operations without reading or moving any data outside the memory array. Stateful logic has been previously demonstrated using several resistive memory types, mostly by resistive RAM (RRAM). Here we present a new method to design stateful logic using a different resistive memory - phase change memory (PCM). We propose and experimentally demonstrate four logic gate types (NOR, IMPLY, OR, NIMP) using commonly used PCM materials. Our stateful logic circuits are different than previously proposed circuits due to the different switching mechanism and functionality of PCM compared to RRAM. Since the proposed stateful logic form a functionally complete set, these gates enable sequential execution of any logic function within the memory, paving the way to PCM-based digital processing-in-memory systems.

Inscriptions on medieval buildings provide information such as the date or circumstances of the structuresʼ foundation. At the same time, we suggest, they may reveal their founders’ ideals and priorities. This article looks at a lengthy Hebrew inscription from the city of Worms, commemorating the foundation of the town’smikve (ritual bath). The inscription, from 1185/6, was situated on a wall perpendicular to the entrance of the medieval synagogue and adjacent to an older inscription commemorating the foundation of the synagogue in 1034. A close analysis of the biblical references in both inscriptions, we propose, yields insights about the hopes and values of the Jewish community. These inscriptions are studded with biblical quotations that invite many layers of reading, depending on the readers’ erudition. At a basic level, they provide chronological information about donations to the Worms mikve and synagogue. Through their intentional use of speci􏰀c biblical contexts and quotes, the authors of the inscriptions also added ideological content such as symbolic connections between the Worms community buildings and the Jerusalem Temple. Other quotations underscore the community’s hope for its salvation in the End of Days, as well as its wish to see the wicked receive their due. While the inscriptions commemorating the synagogue may be understood without reference to the biblical contexts of the quotations, the mikve inscription is extremely enigmatic. By delving into the biblical contexts, our reading demonstrates the ways in which the inscribers connected the architecture of the buildings in Worms, the community’s self-identi􏰀cation as a holy congregation, and the encoded name of the mikve’s donor.

This article explores the Pisan Cathedral (1063), Baptistery (1153) and Camposanto, 1278 as buildings used to express spiritual and political associations of the city with the Levant in the Middle Ages, in order to strengthen Pisa’s self-identity and express its civic pride. The paper analyses the three major monuments as commemoratory buildings, designed to mark in stone the valor of the major ideological military campaigns in which Pisa participated between the eleventh and the thirteenth centuries in the East. These are the Battle of Palermo – commemorated through the Cathedral; the First Crusade – commemorated by the Baptistery; and the Third Crusade – commemorated by the Camposanto.