5,683 research outputs found
3nj Morphogenesis and Semiclassical Disentangling
Recoupling coefficients (3nj symbols) are unitary transformations between
binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum
operators. They have been used in a variety of applications in spectroscopy,
quantum chemistry and nuclear physics and quite recently also in quantum
gravity and quantum computing. These coefficients, naturally associated to
cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and
analytical features that make them fashinating objects to be studied on their
own. In this paper we develop a bottom--up, systematic procedure for the
generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and
algebraic methods. We provide also a novel approach to the problem of
classifying various regimes of semiclassical expansions of 3nj coefficients
(asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial,
analytical and numerical tools
A randomized trial in a massive online open course shows people don't know what a statistically significant relationship looks like, but they can learn
Scatterplots are the most common way for statisticians, scientists, and the
public to visually detect relationships between measured variables. At the same
time, and despite widely publicized controversy, P-values remain the most
commonly used measure to statistically justify relationships identified between
variables. Here we measure the ability to detect statistically significant
relationships from scatterplots in a randomized trial of 2,039 students in a
statistics massive open online course (MOOC). Each subject was shown a random
set of scatterplots and asked to visually determine if the underlying
relationships were statistically significant at the P < 0.05 level. Subjects
correctly classified only 47.4% (95% CI: 45.1%-49.7%) of statistically
significant relationships, and 74.6% (95% CI: 72.5%-76.6%) of non-significant
relationships. Adding visual aids such as a best fit line or scatterplot smooth
increased the probability a relationship was called significant, regardless of
whether the relationship was actually significant. Classification of
statistically significant relationships improved on repeat attempts of the
survey, although classification of non-significant relationships did not. Our
results suggest: (1) that evidence-based data analysis can be used to identify
weaknesses in theoretical procedures in the hands of average users, (2) data
analysts can be trained to improve detection of statistically significant
results with practice, but (3) data analysts have incorrect intuition about
what statistically significant relationships look like, particularly for small
effects. We have built a web tool for people to compare scatterplots with their
corresponding p-values which is available here:
http://glimmer.rstudio.com/afisher/EDA/.Comment: 7 pages, including 2 figures and 1 tabl
The role of Bacterial-based Protist Communities in Aquatic and Soil Ecosystems and the Carbon Biogeochemical Cycle, with Emphasis on Naked Amoebae
Current research is reviewed on aquatic and soil microbial ecology with attention to the fate of organic carbon in bacterial-based protist food webs, including some new data. Particular attention is given to the effects of pulsed sources of low-molecular weight organic sources of carbon on soil respiration, changes in bacterial, nanoflagellate, and naked amoeba C-biomass, and evidence for throughput of carbon in microbial food webs in Arctic and some low-latitude, temperate soil environments. The proportion of pulsed sources of glucose-C that is sequestered in microbial biomass relative to loss as CO2 is examined in laboratory experimental studies, and implications of the research for microbial community dynamics and global warming due to terrestrial sources of respiratory CO2 are discussed
Defender-assisted Evasion and Pursuit Maneuvers
Motivated by the possibilities afforded by active target defense, a 3-agent pursuit-evasion differential game involving an Attacker/Pursuer, a Target/Evader, and a Defender is considered. The Defender strives to assist the Target by intercepting the Attacker before the latter reaches the Target. A barrier surface in a reduced state space separates the winning regions of the Attacker and Target-Defender team. In this thesis, attention focuses primarily on the Attacker\u27s region of win where, under optimal Attacker play, the Defender cannot preclude the Attacker from capturing the Target. Both optimal and suboptimal strategies are investigated. This thesis uses several methods to breakdown and analyze the 3-player differential game
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