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Despite repeated promises by Democratic presidents to address environmental justice (EJ), meaningful federal action on the issue remains elusive. The EJ obligations that have been imposed on federal agencies are all purely procedural, not substantive. Such procedural obligations-like filing environmental impact statements and providing forums for community feedback-may facilitate greater transparency and accountability from industry and government agencies. But in the absence of more substantive obligations-like stricter emissions caps in highly burdened communities of color-these procedural requirements are often satisfied through mere box-checking. Meanwhile, litigants pursuing relief through the U.S. Constitution's Equal Protection Clause face closed courthouse doors unless they can show \"discriminatory intent\"-a nearly impossible task. And despite Title VI's promises of anti-discrimination, litigants' Title VI claims are subject to long delays, industry-friendly settlements, and looming existential threats by a federal judiciary and a new presidential administration increasingly skeptical of-if not even outright hostile to-both environmental remediation and race-conscious policymaking. But with the federal government on the sidelines, there is enormous opportunity at the state level. A recent fight over an asphalt plant outside Flint, Michigan, demonstrates that state environmental agencies may have expansive-though largely untapped-power to address environmental injustice through the permitting process. This Note analyzes state and federal administrative law to provide a case study on how state agencies can fill the massive gap in EJ enforcement and fulfill the unkept promises of past federal administrations.

Advances in intelligent robotic systems and brain-machine interfaces (BMI) have helped restore functionality and independence to individuals living with sensorimotor deficits; however, tasks requiring bimanual coordination and fine manipulation continue to remain unsolved given the technical complexity of controlling multiple degrees of freedom across multiple limbs in a coordinated way through a user input. To address this challenge, we implemented a collaborative shared control strategy to manipulate and coordinate two Modular Prosthetic Limbs (MPL) for performing a bimanual self-feeding task. A human participant with microelectrode arrays in sensorimotor brain regions provided commands to both MPLs to perform the self-feeding task, which included bimanual cutting. Motor commands were decoded from bilateral neural signals to control up to two degrees of freedom (DOF) on each MPL at a time. The shared control strategy enabled the participant to map his four-DOF control inputs, two per hand, to as many as 12 degrees of freedom for specifying robot end effector position and orientation. Using neurally-driven shared control, the participant successfully and simultaneously controlled movements of both robotic limbs to cut and eat food in a complex bimanual self-feeding task. This demonstration of bimanual robotic system control via a BMI in collaboration with intelligent robot behavior has major implications for restoring complex movement behaviors for those living with sensorimotor deficits.

By previous work of Giordano and the author, ergodic actions of $\\mathbf{Z}$ (and other discrete groups) are completely classified measure-theoretically by their dimension space, a construction analogous to the dimension group used in $\\text{C}^{\\ast }$ -algebras and topological dynamics. Here we investigate how far from approximately transitive (AT) actions can be that derive from circulant (and related) matrices. It turns out not very: although non-AT actions can arise from this method of construction, under very modest additional conditions, approximate transitivity arises. KIn addition, if we drop the positivity requirement in the isomorphism of dimension spaces, then all these ergodic actions satisfy an analogue of AT. Many examples are provided.

We translate Akin’s notion of good (and related concepts) from measures on Cantor sets to traces on dimension groups, and particularly for invariant measures of minimal homeomorphisms (and their corresponding simple dimension groups). This yields characterizations and examples, which translate back to the original context. Good traces on a simple dimension group are characterized by their kernel having dense image in their annihilating set of affine functions on the trace space; this makes it possible to construct many examples with seemingly paradoxical properties. In order to study the related property of refinability, we consider goodness for sets of measures (traces on dimension groups), and obtain partial characterizations in terms of (special) convex subsets of Choquet simplices. These notions are also very closely related to unperforation of quotients of dimension groups by convex subgroups (that are not order ideals), and we give partial characterizations. Numerous examples illustrate the results.

We answer affirmatively a question of Goodearl on the existence of simple archimedean dimension groups with arbitrary Choquet simplex as a trace space—at least when the Choquet simplex is metrizable.

Despite repeated promises by Democratic presidents to address environmental justice (EJ), meaningful federal action on the issue remains elusive. The EJ obligations that have been imposed on federal agencies are all purely procedural, not substantive. Such procedural obligations—like filing environmental impact statements and providing forums for community feedback—may facilitate greater transparency and accountability from industry and government agencies. But in the absence of more substantive obligations—like stricter emissions caps in highly burdened communities of color—these procedural requirements are often satisfied through mere box-checking. Meanwhile, litigants pursuing relief through the U.S. Constitution’s Equal Protection Clause face closed courthouse doors unless they can show “discriminatory intent”—a nearly impossible task. And despite Title VI’s promises of anti-discrimination, litigants’ Title VI claims are subject to long delays, industry-friendly settlements, and looming existential threats by a federal judiciary and a new presidential administration increasingly skeptical of—if not even outright hostile to—both environmental remediation and race-conscious policymaking. But with the federal government on the sidelines, there is enormous opportunity at the state level. A recent fight over an asphalt plant outside Flint, Michigan, demonstrates that state environmental agencies may have expansive—though largely untapped—power to address environmental injustice through the permitting process. This Note analyzes state and federal administrative law to provide a case study on how state agencies can fill the massive gap in EJ enforcement and fulfill the unkept promises of past federal administrations.

There exist simple dimension groups that cannot be expressed as a direct limit of simple, or even approximately divisible, dimension groups, each with finitely many pure traces. Every infinite-dimensional Choquet simplex can be realized as the trace space of such dimension groups. Simple initial objects (in the category of dimension groups) in the sense of Elliott and Rørdam [6] satisfy this. Related to this is a drastic property, defined in terms of non-existence of positive homomorphisms from simple dimension groups with finite pure trace space. We also enlarge the class of weakly initial objects for AF (and slightly more general) C*-algebras. On the other hand, if G is a p-divisible simple dimension group (for some integer p > 1), then it can be expressed as such a direct limit.