Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds

For a compact set A in Euclidean space we consider the asymptotic behavior of optimal (and near optimal) N-point configurations that minimize the Riesz s-energy (corresponding to the potential 1/t^s) over all N-point subsets of A, where s>0. For a large class of manifolds A having finite, positive d-dimensional Hausdorff measure, we show that such minimizing configurations have asymptotic limit distribution (as N tends to infinity with s fixed) equal to d-dimensional Hausdorff measure whenever s>d or s=d. In the latter case we obtain an explicit formula for the dominant term in the minimum energy. Our results are new even for the case of the d-dimensional sphere.Comment: paper: 29 pages and addendum: 4 page

Semi-Informed Multi-Agent Patrol Strategies

The adversarial multi-agent patrol problem is an active research topic with many real-world applications such as physical robots guarding an area and software agents protecting a computer network. In it, agents patrol a graph looking for so-called critical vertices that are subject to attack by adversaries. The agents are unaware of which vertices are subject to attack by adversaries and when they encounter such a vertex they attempt to protect it from being compromised (an adversary must occupy the vertex it targets a certain amount of time for the attack to succeed). Even though the terms adversary and attack are used, the problem domain extends to patrolling a graph for other interesting noncompetitive contexts such as search and rescue. The problem statement adopted in this work is formulated such that agents obtain knowledge of local graph topology and critical vertices over the course of their travels via an API ; there is no global knowledge of the graph or communication between agents. The challenge is to balance exploration, necessary to discover critical vertices, with exploitation, necessary to protect critical vertices from attack. Four types of adversaries were used for experiments, three from previous research – waiting, random, and statistical - and the fourth, a hybrid of those three. Agent strategies for countering each of these adversaries are designed and evaluated. Benchmark graphs and parameter settings from related research will be employed. The proposed research culminates in the design and evaluation of agents to counter these various types of adversaries under a range of conditions. The results of this work are agent strategies in which each agent becomes solely responsible for protecting those critical vertices it discovers. The agents use emergent behavior to minimize successful attacks and maximize the discovery of new critical vertices. A set of seven edge choosing primitives (ECPs) are defined that are combined in different ways to yield a range of agent strategies using the chain of responsibility OOP design pattern. Every permutation of them were tested and measured in order to identify those strategies that perform well. One strategy performed particularly well against all adversaries, graph topology, and other experimental variables. This particular strategy combines ECPs of: A hard-deadline return to covered vertices to counter the random adversary, efficiently checking vertices to see if they are being attacked by the waiting adversary, and random movement to impede the statistical adversary

A COMPARISON OF THE CHARACTERISTICS OF CHILDREN IN FOSTER CARE IN A SELECTED SAMPLE OF MONTANA COUNTIES

Foster care placement, also known as substitute care, is defined as 24 hour care of a child provided outside of his own home as ah alternative to parental care (Social Services Manual, 301-1, 1979). The Community Services Division of the Montana Department of Social and Rehabilitative Services is responsible for licensing facilities which provide foster care, for the payment of foster care providers, and, along with juvenile probation officers, aftercare workers and private social service agencies under contract to the State, for the placement of children and youth in foster care

The Manchurian Candidate Narrative: The Need for Balance and a Counter Narrative

Contemporary American media commonly misrepresents violence committed by veterans suffering from Post-Traumatic Stress Disorder (PTSD) as common place. The reasons for PTSD-related violence are complex, and representations of it in popular media contribute to the stigmatization and fear of veterans with PTSD in both the civilian and military populations. This project rationale is the presentation of a counter narrative to these dominant cultural narratives in the form of a web comic, titled Binary. Binary is the story of Derek Anderson which shows how deeply PTSD changes the lives of sufferers. Despite his disabled status and less-than-ideal living circumstances, Derek is able to overcome immense challenges due to his profound life experiences, and subverts the traditional ‘dangerous veteran’ trope. Binary changes the dominant culture narrative into something that actively combats it

Reflections On Contributing To “Big Discoveries” About The Fly Clock: Our Fortunate Paths As Post-Docs With 2017 Nobel Laureates Jeff Hall, Michael Rosbash, And Mike Young

In the early 1980s Jeff Hall and Michael Rosbash at Brandeis University and Mike Young at Rockefeller University set out to isolate the period (per) gene, which was recovered in a revolutionary genetic screen by Ron Konopka and Seymour Benzer for mutants that altered circadian behavioral rhythms. Over the next 15 years the Hall, Rosbash and Young labs made a series of groundbreaking discoveries that defined the molecular timekeeping mechanism and formed the basis for them being awarded the 2017 Nobel Prize in Physiology or Medicine. Here the authors recount their experiences as post-docs in the Hall, Rosbash and Young labs from the mid-1980s to the mid-1990s, and provide a perspective of how basic research conducted on a simple model system during that era profoundly influenced the direction of the clocks field and established novel approaches that are now standard operating procedure for studying complex behavior