Minimum Neighboring Degree Realization in Graphs and Trees

We study a graph realization problem that pertains to degrees in vertex neighborhoods. The classical problem of degree sequence realizability asks whether or not a given sequence of n positive integers is equal to the degree sequence of some n-vertex undirected simple graph. While the realizability problem of degree sequences has been well studied for different classes of graphs, there has been relatively little work concerning the realizability of other types of information profiles, such as the vertex neighborhood profiles. In this paper we introduce and explore the minimum degrees in vertex neighborhood profile as it is one of the most natural extensions of the classical degree profile to vertex neighboring degree profiles. Given a graph G = (V,E), the min-degree of a vertex v ? V, namely MinND(v), is given by min{deg(w) ? w ? N[v]}. Our input is a sequence ? = (d_?^{n_?}, ?d?^{n?}), where d_{i+1} > d_i and each n_i is a positive integer. We provide some necessary and sufficient conditions for ? to be realizable. Furthermore, under the restriction that the realization is acyclic, i.e., a tree or a forest, we provide a full characterization of realizable sequences, along with a corresponding constructive algorithm. We believe our results are a crucial step towards understanding extremal neighborhood degree relations in graphs

Lightweight Exoskeletons with Controllable Actuators

A proposed class of lightweight exoskeletal electromechanical systems would include electrically controllable actuators that would generate torques and forces that, depending on specific applications, would resist and/or assist wearers movements. The proposed systems would be successors to relatively heavy, bulky, and less capable human-strength-amplifying exoskeletal electromechanical systems that have been subjects of research during the past four decades. The proposed systems could be useful in diverse applications in which there are needs for systems that could be donned or doffed easily, that would exert little effect when idle, and that could be activated on demand: examples of such applications include (1) providing controlled movement and/or resistance to movement for physical exercise and (2) augmenting wearers strengths in the performance of military, law-enforcement, and industrial tasks. An exoskeleton according to the proposal would include adjustable lightweight graphite/epoxy struts and would be attached to the wearer's body by belts made of hook-and-pile material. At selected rotary and linear joints, the exoskeleton would be fitted, variously, with lightweight, low-power-consumption rotary and linear brakes, clutches, and motors. The exoskeleton would also be equipped with electronic circuitry for monitoring, control, and possibly communication with external electronic circuits that would perform additional monitoring and control functions

Housing Arrangement and Location Determine the Likelihood of Housing Loss Due to Wildfire

Surging wildfires across the globe are contributing to escalating residential losses and have major social, economic, and ecological consequences. The highest losses in the U.S. occur in southern California, where nearly 1000 homes per year have been destroyed by wildfires since 2000. Wildfire risk reduction efforts focus primarily on fuel reduction and, to a lesser degree, on house characteristics and homeowner responsibility. However, the extent to which land use planning could alleviate wildfire risk has been largely missing from the debate despite large numbers of homes being placed in the most hazardous parts of the landscape. Our goal was to examine how housing location and arrangement affects the likelihood that a home will be lost when a wildfire occurs. We developed an extensive geographic dataset of structure locations, including more than 5500 structures that were destroyed or damaged by wildfire since 2001, and identified the main contributors to property loss in two extensive, fire-prone regions in southern California. The arrangement and location of structures strongly affected their susceptibility to wildfire, with property loss most likely at low to intermediate structure densities and in areas with a history of frequent fire. Rates of structure loss were higher when structures were surrounded by wildland vegetation, but were generally higher in herbaceous fuel types than in higher fuel-volume woody types. Empirically based maps developed using housing pattern and location performed better in distinguishing hazardous from non-hazardous areas than maps based on fuel distribution. The strong importance of housing arrangement and location indicate that land use planning may be a critical tool for reducing fire risk, but it will require reliable delineations of the most hazardous locations

Dynamics of thyroid diseases and thyroid‐axis gland masses

Abstract Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid‐stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life‐years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto's thyroiditis and Graves' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders