Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size

Some infinite permutation groups and related finite linear groups

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy min-n, the minimal condition on normal subgroups. The groups G are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal non-trivial normal subgroups, or they have a regular normal subgroup M which is a divisible abelian p-group of finite rank. In the latter case the point stabilisers are finite and act irreducibly on a p-adic vector space associated with M. This leads to our second variation, which is a study of the finite linear groups that can arise

Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling allows for steady-state hump profiles at different flow rates and tube heights to be scaled onto a single similarity profile. I show that the scaling behavior is independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl

Instrument Design and In Orbit Performance of Planetary L1dars at NASA GSFC

Space lidars provides a unique and powerful tool in earth environment monitoring and planetary exploration. Lidars operate at a much shorter wavelength than radars and can have a much narrower beam and much smaller transmitter and receiver. Lidars carry their own light sources and can continue measurement day and night, and over polar regions, where the passive instruments cannot observe. NASA Goddard Space Flight Center (GSFC) has developed several space lidars, three of them on planetary missions. These were the Mars Orbiter Laser Altimeter (MOLA) on the Mars Observer and Mars Global Surveyor missions, the Mercury Laser Altimeter (MLA) on the MErcury Surface Space ENvironment, GEochemistry and Ranging (MESSENGER) mission and the Lunar Orbital Laser Altimeter (LOLA) on the Lunar Reconnaissance (LRO) mission. These lidars all use similar technologies but with major improvement from one instrument In the next in size, power, measurement capability and operating environment

Permutation symmetry for the tomographic probability distribution of a system of identical particles

The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution. Explicit calculations are performed in the case of the two-dimensional harmonic oscillator.Comment: 13 pages, latex, no figure

Rasch Analysis, Dimensionality, and Scoring of the Neuropsychiatric Inventory Irritability and Aggression Subscales in Individuals With Traumatic Brain Injury

Objectives To develop, for versions completed by individuals with traumatic brain injury (TBI) and an observer, a more precise metric for the Neuropsychiatric Inventory (NPI) Irritability and Aggression subscales using all behavioral item ratings for use with individuals with TBI and to address the dimensionality of the represented behavioral domains. Design Rasch and confirmatory factor analyses of retrospective baseline NPI data from 3 treatment studies. Setting Postacute rehabilitation clinic. Participants NPI records (N = 525) consisting of observer ratings (n = 287) and self-ratings (n = 238) by participants with complicated mild, moderate, or severe TBI at least 6 months postinjury. Interventions Not applicable. Main Outcome Measures Frequency and severity ratings from NPI Irritability/Lability and Agitation/Aggression subscales. Results Confirmatory factor analyses of both observer and participant ratings showed good fit for either a 1-factor or a 2-factor solution. Consistent with this, the Rasch model also fit the data well with aggression items indicating the more severe end of the construct and irritability items populating the milder end. Conclusions Irritability and aggression appear to represent different levels of severity of a single construct. The derived Rasch metric offers a measure of this construct based on responses to all specific items that is appropriate for parametric statistical analysis and may be useful in research and clinical assessments of individuals with TBI

Joint effects of storm surge and sea-level rise on US Coasts: new economic estimates of impacts, adaptation, and benefits of mitigation policy

Recent literature, the US Global Change Research Program’s National Climate Assessment, and recent events, such as Hurricane Sandy, highlight the need to take better account of both storm surge and sea-level rise (SLR) in assessing coastal risks of climate change. This study combines three models—a tropical cyclone simulation model; a storm surge model; and a model for economic impact and adaptation—to estimate the joint effects of storm surge and SLR for the US coast through 2100. The model is tested using multiple SLR scenarios, including those incorporating estimates of dynamic ice-sheet melting, two global greenhouse gas (GHG) mitigation policy scenarios, and multiple general circulation model climate sensitivities. The results illustrate that a large area of coastal land and property is at risk of damage from storm surge today; that land area and economic value at risk expands over time as seas rise and as storms become more intense; that adaptation is a cost-effective response to this risk, but residual impacts remain after adaptation measures are in place; that incorporating site-specific episodic storm surge increases national damage estimates by a factor of two relative to SLR-only estimates, with greater impact on the East and Gulf coasts; and that mitigation of GHGs contributes to significant lessening of damages. For a mid-range climate-sensitivity scenario that incorporates dynamic ice sheet melting, the approach yields national estimates of the impacts of storm surge and SLR of $990 billion through 2100 (net of adaptation, cumulative undiscounted 2005$); GHG mitigation policy reduces the impacts of the mid-range climate-sensitivity estimates by $84 to$100 billion.United States. Environmental Protection Agency. Climate Change Division (Contract EP-D-09-054)United States. Environmental Protection Agency. Climate Change Division (Contract EP-BPA-12-H-0024

Coherent Population Trapping of Single Spins in Diamond Under Optical Excitation

Coherent population trapping is demonstrated in single nitrogen-vacancy centers in diamond under optical excitation. For sufficient excitation power, the fluorescence intensity drops almost to the background level when the laser modulation frequency matches the 2.88 GHz splitting of the ground states. The results are well described theoretically by a four-level model, allowing the relative transition strengths to be determined for individual centers. The results show that all-optical control of single spins is possible in diamond.Comment: minor correction

Topographic Rise in the Northern Smooth Plains of Mercury: Characteristics from Messenger Image and Altimetry Data and Candidate Modes of Origin

MESSENGER observations from orbit around Mercury have revealed that a large contiguous area of smooth plains occupies much of the high northern latitudes and covers an area in excess of approx.6% of the surface of the planet [1] (Fig. 1). Smooth surface morphology, embayment relationships, color data, candidate flow fronts, and a population of partly to wholly buried craters provide evidence for the volcanic origin of these plains and their emplacement in a flood lava mode to depths at least locally in excess of 1 km. The age of these plains is similar to that of plains associated with and postdating the Caloris impact basin, confirming that volcanism was a globally extensive process in the post-heavy bombardment history of Mercury [1]. No specific effusive vent structures, constructional volcanic edifices, or lava distributary features (leveed flow fronts or sinuous rilles) have been identified in the contiguous plains, although vent structures and evidence of high-effusion-rate flood eruptions are seen in adjacent areas [1]. Subsequent to the identification and mapping of the extensive north polar smooth plains, data from the Mercury Laser Altimeter (MLA) on MESSENGER revealed the presence of a broad topographic rise in the northern smooth plains that is ~1,000 km across and rises more than 1.5 km above the surrounding smooth plains [2] (Fig. 2). The purpose of this contribution is to characterize the northern plains rise and to outline a range of hypotheses for its origin