Discrete models of force chain networks

A fundamental property of any material is its response to a localized stress applied at a boundary. For granular materials consisting of hard, cohesionless particles, not even the general form of the stress response is known. Directed force chain networks (DFCNs) provide a theoretical framework for addressing this issue, and analysis of simplified DFCN models reveal both rich mathematical structure and surprising properties. We review some basic elements of DFCN models and present a class of homogeneous solutions for cases in which force chains are restricted to lie on a discrete set of directions.Comment: 17 pages, 6 figures, dcds-B.cls; Minor corrections to version 2, but including an important factor of 2; Submitted to Discrete and Continuous Dynamical Systems B for special issue honoring David Schaeffe

Intersectional Cohorts, Dis/ability, and Class Actions

This Article occupies the junction of dis/abilities studies and critical race theory. It joins the growing commentary analyzing the groundbreaking lawsuit by Compton, California students and teachers against the Compton school district under federal disability law and seeking class certification and injunctive relief in the form of teacher training, provision of counselors, and changed disciplinary practices. The federal district court denied the defendants’ motion to dismiss but also denied the plaintiffs’ motion for a preliminary injunction and class certification, resulting in prolonged settlement talks. The suit is controversial because it seeks to address the trauma suffered by Black and Latinx students in poor, violence-torn inner-city communities by characterizing the students as disabled.The Article disagrees with legal scholarship thus far, which posits that using disability law to help these students both stigmatizes them and ignores current disability law’s focus on individual claims. It asserts that concerns about stigma are outweighed by the potential to assist distressed students. Doctrinally, it contends the concern for individual claims is overstated because one major goal of disability law is to remove social barriers to the flourishing of people with dis/abilities. By analyzing the social construction model of dis/abilities implicit within current law, this Article shows that group-based claims like those of the Compton students are a valid use of the class certification power.This Article’s key contribution to the dis/abilities studies and critical race literatures is the creation of a theory of “intersectional cohorts.” The members of intersectional cohorts share similar self-identities, attributed identities, and identity performances to such extent that it is appropriate to think of them as a discrete and cohesive group in relation to a particular issue. This is a way to explore the meso-level of discrete and cohesive social groups who share multiple identities without devolving into a micro-level theory of each individual or essentializing identities through a macro-level theory of broad social groups.Understanding poor Black and Latinx students in violence-torn neighborhoods as an intersectional cohort shows they have sufficiently shared experiences and responses to their environment to presume they constitute a class that should be certified in the Compton suit and in other similar lawsuits. This approach is supported by the scientific research on Adverse Childhood Experiences (ACEs) and their relationship to complex trauma and disability. We hope this analysis will serve as a model for future theoretical and applied analysis of intersectional cohorts, especially with respect to dis/abilities

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Factory of realities: on the emergence of virtual spatiotemporal structures

The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realities. To what extent are these "realities" real? Which "physics" should be applied to quantitatively describe them? In this essay I dwell on few examples. The first is Adaptive neural networks, which are not networks and not neural, but still provide service similar to classical ANNs in extended fashion. The second is the emergence of objects looking like Einsteinian spacetime, which describe the behavior of an Internet surfer like geodesic motion. The third is the demonstration of nonclassical and even stronger-than-quantum probabilities in Information Retrieval, their use. Immense operable datasets provide new operationalistic environments, which become to greater and greater extent "realities". In this essay, I consider the overall Information Retrieval process as an objective physical process, representing it according to Melucci metaphor in terms of physical-like experiments. Various semantic environments are treated as analogs of various realities. The readers' attention is drawn to topos approach to physical theories, which provides a natural conceptual and technical framework to cope with the new emerging realities.Comment: 21 p