Filling loops at infinity in the mapping class group

We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angled Artin groups.Comment: 7 pages, 2 figures; this note presents a result which was contained in an earlier version of "Pushing fillings in right-angled Artin groups" (arXiv:1004.4253) but is independent of the techniques in that pape

Pushing fillings in right-angled Artin groups

We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use radial pushing to obtain upper bounds on higher divergence functions, finding that the k-dimensional divergence of a RAAG is bounded by r^{2k+2}. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties "at infinity," are defined here as a family of quasi-isometry invariants of groups; thus, these results give new information about the QI classification of RAAGs. By pushing along the height gradient, we also show that the k-th order Dehn function of a Bestvina-Brady group is bounded by V^{(2k+2)/k}. We construct a class of RAAGs called "orthoplex groups" which show that each of these upper bounds is sharp.Comment: The result on the Dehn function at infinity in mapping class groups has been moved to the note "Filling loops at infinity in the mapping class group.

Autophagy occurs upstream or parallel to the apoptosome during histolytic cell death

Histolysis refers to a widespread disintegration of tissues that is morphologically distinct from apoptosis and often associated with the stimulation of autophagy. Here, we establish that a component of the apoptosome, and pivotal regulator of apoptosis, is also required for histolytic cell death. Using in vivo and ex vivo assays, we demonstrate a global apoptogenic requirement for dark, the fly ortholog of Apaf1, and show that a required focus of dark– organismal lethality maps to the central nervous system. We further demonstrate that the Dark protein itself is a caspase substrate and find that alterations of this cleavage site produced the first hypermorphic point mutation within the Apaf1/Ced-4 gene family. In a model of ‘autophagic cell death’, dark was essential for histolysis but dispensable for characteristic features of the autophagic program, indicating that the induction of autophagy occurs upstream or parallel to histolytic cell death. These results demonstrate that stimulation of autophagy per se is not a ‘killing event’ and, at the same time, establish that common effector pathways, regulated by the apoptosome, can underlie morphologically distinct forms of programmed cell death

Combating social differences within institutions: The need for a curriculum based on social awareness in our schools

To combat social, economic and racial inequality in the United States, the author advocates for \u27social awareness\u27 education to be built into the curriculum of the public school system. The purpose of the curriculum is to create a society that respects people and recognizes each individual\u27s worth regardless of gender, socio-economic status, race, ethnicity, age, cultural confines, or religious beliefs. The author suggests a course of action on how to institute a social awareness course into the public school curriculum

Does the Doctrine of Equitable Apportionment Apply to Conflicts between States over Groundwater Resources When Such Resources Are Derived from an Aquifer That Lies beneath More than One State?

The Middle Claiborne Aquifer is a large sand formation that contains groundwater within its sand’s porous spaces. The Aquifer spans beneath Mississippi, Tennessee, and at least six other neighboring states. Since 1886, the City of Memphis has withdrawn water from the aquifer to supply drinking water. Memphis also has withdrawn water for irrigation and industrial purposes. Due to increased water pumping, water levels in the aquifer have dropped, lowering the piezometric head (water pressure) in different locations, including between the two states’ borders. In 2005, Mississippi filed suit against the City of Memphis and the Memphis Light, Gas and Water Division (MLGW) on territorial property rights theory, claiming that the city and MLGW were stealing Mississippi’s groundwater resources. The District Court for the Northern District of Mississippi dismissed the case on a procedural ground. Mississippi subsequently filed a new complaint within the Supreme Court’s original jurisdiction, this time including Tennessee. Mississippi is seeking declaratory and injunctive relief as well as more than $600 million in damages for conversion of the groundwater. Mississippi argues its territorial property rights are being invaded. The suit explicitly disclaims reliance on equitable apportionment, which is the typical remedy supplied by the Supreme Court for disputes between states involving interstate water resources. The Court appointed a Special Master who found that the water of the aquifer was not “owned” by Mississippi and was, instead, an interstate resource subject to equitable apportionment. Both states objected to aspects of the Special Master’s Report

Under the Pecos River Compact, Can Texas\u27s Allocation of Water Be Charged for Evaporation of Floodwater Stored in an Upstream Reservoir Located in New Mexico?

The 1949 Pecos River Compact allocates the river’s water between Texas and New Mexico. In an earlier phase of this original jurisdiction litigation, concluded roughly 30 years ago, the Supreme Court resolved issues regarding how the states’ obligations were to be calculated. The Compact allocation involves a highly technical formula that depends on measurements of the river’s inflow and outflow in each water year. To effectuate its decision going forward, the Court retained jurisdiction and appointed a River Master to oversee the annual quantification of New Mexico’s delivery obligation. The current dispute arose when in fall of 2014, Tropical Storm Odile caused heavy and widespread rainfall in the Pecos River Basin. Texas requested that water be stored in the Brantley Reservoir in New Mexico because the Red Bluff Reservoir in Texas was already full. When the flood risk abated in 2015, the Bureau of Reclamation (the operator of the Brantley Reservoir) began releases that continued throughout 2015 even though Texas remained unable to store that water in the Red Bluff Reservoir. As a result, more than 40,000 acre-feet of water released from Brantley flowed downstream without any benefit to Texas. This case involves the claim by New Mexico, eventually agreed to by the River Master, that New Mexico should be given a credit toward the calculation of its 2014 and 2015 delivery obligations for evaporative losses from the Brantley Reservoir associated with the extra stored floodwater. Eventually, in the 2018 and 2019 Water Year Reports, the Water Master recognized the credits and began to apply them retroactively to lower the amount of New Mexico’s delivery obligations