Sound educational policy recommendations require valid estimates of causal effects, but observational studies in physics education research sometimes have loosely specified causal hypotheses. The connections between the observational data and the exp
licit or implicit causal conclusions are sometimes misstated. The link between the causal conclusions reached and the policy recommendations made is also sometimes loose. Causal graphs are used to illustrate these issues in several papers from Physical Review Physics Education Research. For example, the core causal conclusion of one paper rests entirely on the choice of a causal direction although an unstated plausible alternative gives an exactly equal fit to the data.
A recent paper by Salehi et al. claims that the differences found between major demographic groups on scores in introductory college physics tests are due to differences in pre-college preparation. No evidence is produced, however, to show that prepa
ration differences are more causally important than any other differences. In one case, the male/female difference, the paper actually provides evidence that preparation gaps are unimportant.
Though the Boltzmann-Gibbs framework of equilibrium statistical mechanics has been successful in many arenas, it is clearly inadequate for describing many interesting natural phenomena driven far from equilibrium. The simplest step towards that goal
is a better understanding of nonequilibrium steady-states (NESS). Here we focus on one of the distinctive features of NESS, persistent probability currents, and their manifestations in our climate system. We consider the natural variability of the steady-state climate system, which can be approximated as a NESS. These currents must form closed loops, which are odd under time reversal, providing the crucial difference between systems in thermal equilibrium and NESS. Seeking manifestations of such current loops leads us naturally to the notion of probability angular momentum and oscillations in the space of observables. Specifically, we will relate this concept to the asymmetric part of certain time-dependent correlation functions. Applying this approach, we propose that these current loops give rise to preferred spatio-temporal patterns of natural climate variability that take the form of climate oscillations such as the El-Ni~{n}o Southern Oscillation (ENSO) and the Madden-Julien Oscillation (MJO). In the space of climate indices, we observe persistent currents and define a new diagnostic for these currents: the probability angular momentum. Using the observed climatic time series of ENSO and MJO, we compute both the averages and the distributions of the probability angular momentum. These results are in good agreement with the analysis from a linear Gaussian model. We propose that, in addition to being a new quantification of climate oscillations across models and observations, the probability angular momentum provides a meaningful characterization for all statistical systems in NESS.
A recent paper in Sci. Adv. by Miller et al. concludes that GREs do not help predict whether physics grad students will get Ph.D.s. The paper makes numerous elementary statistics errors, including introduction of unnecessary collider-like stratificat
ion bias, variance inflation by collinearity and range restriction, omission of needed data (some subsequently provided), a peculiar choice of null hypothesis on subgroups, blurring the distinction between failure to reject a null and accepting a null, and an extraordinary procedure for radically inflating confidence intervals in a figure. Release of results of simpler models, e.g. without unnecessary stratification, would fix some key problems. The paper exhibits exactly the sort of research techniques which we should be teaching students to avoid.
The famous two-fold cost of sex is really the cost of anisogamy -- why should females mate with males who do not contribute resources to offspring, rather than isogamous partners who contribute equally? In typical anisogamous populations, a single ve
ry fit male can have an enormous number of offspring, far larger than is possible for any female or isogamous individual. If the sexual selection on males aligns with the natural selection on females, anisogamy thus allows much more rapid adaptation via super-successful males. We show via simulations that this effect can be sufficient to overcome the two-fold cost and maintain anisogamy against isogamy in populations adapting to environmental change. The key quantity is the variance in male fitness -- if this exceeds what is possible in an isogamous population, anisogamous populations can win out in direct competition by adapting faster.
In this paper we prove local existence of solutions to the nonlinear heat equation $u_t = Delta u +a |u|^alpha u, ; tin(0,T),; x=(x_1,,cdots,, x_N)in {mathbb R}^N,; a = pm 1,; alpha>0;$ with initial value $u(0)in L^1_{rm{loc}}left({mathbb R}^Nsetminu
s{0}right)$, anti-symmetric with respect to $x_1,; x_2,; cdots,; x_m$ and $|u(0)|leq C(-1)^mpartial_{1}partial_{2}cdot cdot cdot partial_{m}(|x|^{-gamma})$ for $x_1>0,; cdots,; x_m>0,$ where $C>0$ is a constant, $min {1,; 2,; cdots,; N},$ $0<gamma<N$ and $0<alpha<2/(gamma+m).$ This gives a local existence result with highly singular initial values. As an application, for $a=1,$ we establish new blowup criteria for $0<alphaleq 2/(gamma+m)$, including the case $m=0.$ Moreover, if $(N-4)alpha<2,$ we prove the existence of initial values $u_0 = lambda f,$ for which the resulting solution blows up in finite time $T_{max}(lambda f),$ if $lambda>0$ is sufficiently small. We also construct blowing up solutions with initial data $lambda_n f$ such that $lambda_n^{[({1over alpha}-{gamma+mover 2})^{-1}]}T_{max}(lambda_n f)$ has different finite limits along different sequences $lambda_nto 0$. Our result extends the known small lambda blow up results for new values of $alpha$ and a new class of initial data.
An unusual noise component is found near and below about 250 K in the normal state of underdoped YBCO and Ca-YBCO films. This noise regime, unlike the more typical noise above 250 K, has features expected for a symmetry-breaking collective electronic
state. These include large individual fluctuators, a magnetic sensitivity, and aging effects. A possible interpretation in terms of fluctuating charge nematic order is presented.
The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through the work o
f D. Bailey that no universal estimator for $textbf{P}(X_{n+1}|X_0,X_1,...X_n)$ can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of these flu
ctuations. The properties of the fluctuations which are unconstrained by the fluctuation theorem are investigated and related to the model parameters. The irreversibility of trajectory segments, which satisfies a fluctuation theorem, is used as a measure of nonequilibrium fluctuations. The moments of the irreversibility probability density function (pdf) are found and the pdf is seen to be non-Gaussian. The average irreversibility goes to zero for short and long trajectory segments and has a maximum for some finite segment length, which defines a characteristic timescale of the fluctuations. The initial average irreversibility growth rate is equal to the average entropy production and is related to noise-amplification. For systems with a separation of deterministic timescales, modes with timescales much shorter than the trajectory timespan and whose noise amplitudes are not asymptotically large, do not, to first order, contribute to the irreversibility statistics, providing a potential basis for dimensional reduction.
We describe estimators $chi_n(X_0,X_1,...,X_n)$, which when applied to an unknown stationary process taking values from a countable alphabet ${cal X}$, converge almost surely to $k$ in case the process is a $k$-th order Markov chain and to infinity otherwise.
