A modified averaging operator with some applications

The paper presents a new approach to the conventional averaging in which the role of boundary values is considered in a more detailed way. It results in a new weighted local averaging operator (WLAO) taking into account the particular role of boundary values. A remarkable feature of WLAO is that this operator contains a parameter of boundary regulation p and depends on a local value $h$ of the integration domain. By varying these two parameters one can regulate the obtained approximate solutions in order to get more accurate ones. It has been shown that the combination of WLAO with Galerkin method can lead to an effective approximate tool for the buckling problem of columns and for the frequency analysis of free vibration of strongly nonlinear systems.

Spindle scaling is governed by cell boundary regulation of microtubule nucleation

Cellular organelles such as the mitotic spindle adjust their size to the dimensions of the cell. It is widely understood that spindle scaling is governed by regulation of microtubule polymerization. Here we use quantitative microscopy in living zebrafish embryos and Xenopus egg extracts in combination with theory to show that microtubule polymerization dynamics are insufficient to scale spindles and only contribute below a critical cell size. In contrast, microtubule nucleation governs spindle scaling for all cell sizes. We show that this hierarchical regulation arises from the partitioning of a nucleation inhibitor to the cell membrane. Our results reveal that cells differentially regulate microtubule number and length using distinct geometric cues to maintain a functional spindle architecture over a large range of cell sizes.

Statistical reprogramming of macroscopic self-assembly with dynamic boundaries

Self-assembly is a ubiquitous process that can generate complex and functional structures via local interactions among a large set of simpler components. The ability to program the self-assembly pathway of component sets elucidates fundamental physics and enables alternative competitive fabrication technologies. Reprogrammability offers further opportunities for tuning structural and material properties but requires reversible selection from multistable self-assembling patterns, which remains a challenge. Here, we show statistical reprogramming of two-dimensional (2D), noncompact self-assembled structures by the dynamic confinement of orbitally shaken and magnetically repulsive millimeter-scale particles. Under a constant shaking regime, we control the rate of radius change of an assembly arena via moving hard boundaries and select among a finite set of self-assembled patterns repeatably and reversibly. By temporarily trapping particles in topologically identified stable states, we also demonstrate 2D reprogrammable stiffness and three-dimensional (3D) magnetic clutching of the self-assembled structures. Our reprogrammable system has prospective implications for the design of granular materials in a multitude of physical scales where out-of-equilibrium self-assembly can be realized with different numbers or types of particles. Our dynamic boundary regulation may also enable robust bottom-up control strategies for novel robotic assembly applications by designing more complex spatiotemporal interactions using mobile robots.

“The Living God” and the Provenance of Joseph and Aseneth

Chapter 1 addresses the disputed date and provenance of Joseph and Aseneth. The question of whether the tale is “Jewish or Christian?” is the central frame in which its provenance has traditionally been sought. Yet, this formulation assumes that “Judaism” and “Christianity” were distinct entities without overlap, when it is now widely acknowledged that they were not easily separable in antiquity. This chapter suggests that the question of whether Joseph and Aseneth is Jewish or gentile is more profitable for contextualizing Aseneth’s tale and offers fresh evidence for historicizing its origins in Judaism of Greco-Roman Egypt. Placing the narrative’s concerns for boundary-regulation alongside the discursive projects of other ancient writers who engaged the story of the patriarch Joseph suggests that the author of Joseph and Aseneth was a participant in an ongoing Hellenistic Jewish interpretive tradition in Egypt that used Joseph’s tale as a platform for marking and maintaining boundaries.

Aseneth between Judaism and Christianity: Reframing the Debate

The question of whether Joseph and Aseneth is “Jewish or Christian?” is the central frame in which the provenance of this tale has traditionally been sought. Yet, such a formulation assumes that “Judaism” and “Christianity” were distinct entities without overlap, when it is now widely acknowledged that they were not easily separable in antiquity for quite some time. I suggest that the question of whether Joseph and Aseneth is Jewish or gentile is more profitable for contextualizing Aseneth’s tale. This article offers fresh evidence for historicizing its origins in Judaism of Greco-Roman Egypt. Placing the narrative’s concerns for boundary-regulation alongside the discursive projects of other ancient writers (both Jewish and gentile Christian) who engaged the story of Joseph suggests that the author of Joseph and Aseneth was likely a participant in a Hellenistic Jewish interpretive tradition in Egypt that used Joseph’s tale as a platform for marking and maintaining boundaries.

Organizational Boundary Regulation Through Social Media Policies

Digital ubiquity and penetration across spatio-temporal boundaries have exacerbated the need for a clearer understanding of where the boundaries of personal, professional, and public communication begin and end. Indeed, boundary specifications have become an iconic problematic for organizational control and employee communication in the age of social media. In response, corporations increasingly issue policies that aim to regulate when, where, how, and what employees communicate in online environments. We argue that these policies are forms of organizational boundary regulation. Drawing on a content analysis of 112 social media policies from the world’s largest corporations, we examine the boundary logics articulated in these policies to delineate corporate spheres of influence. Next, we show how boundary logics relate to directives for employee speech, self-expression, and relational engagement. We discuss how the boundary logic framework contributes to our understanding of the expansion of corporate control across multiple life domains in the digital age.