Model Comparison in the Introductory Physics Laboratory

Model comparison is at the heart of all scientific methodologies. Progress is made in science by constructing many models (possibly of different complexities), testing them against measurements, and determining which of them explain the data the best. It is my observation, however, that in many introductory physics labs we provide students with the materials and methods to verify the “correct” model of the experiment they are performing, e.g. measuring “g” or verifying the period of a pendulum. In this way, we do our students a disservice and don’t allow them to experience the richness and creativity that constitutes the scientific enterprise. Limiting the lab to the “correct” model can have its uses—for example, getting the students to practice the proper methods to measure lengths and times or to support the specific theory covered in the lecture portion of the class. However, when students perform these labs, they come to view these activities as repetitive and mechanical, reinforcing the notion that science concerns not the true exploration of nature but simply the verification of what we already know. By verifying what we already know, the laboratory experience does not improve overall understanding and can mislead students about the methods of science overall

Using Python to Program LEGO MINDSTORMS Robots: The PyNXC Project

LEGO MINDSTORMS® NXT (Lego Group, 2006) is a perfect platform for introducing programming concepts, and is generally targeted toward children from age 8-14. The language which ships with the MINDSTORMS®, called NXTg, is a graphical language based on LabVIEW (Jeff Kodosky, 2010). Although there is much value in graphical languages, such as LabVIEW, a text-based alternative can be targeted at an older audiences and serve as part of a more general introduction to modern computing. Other languages, such as NXC (Not Exactly C) (Hansen, 2010) and PbLua (Hempel, 2010), fit this description. Here we introduce PyNXC, a subset of the Python language which can be used to program the NXT MINDSTORMS®. We present results using PyNXC, comparisons with other languages, and some challenges and future possible extensions

Teaching Bayesian Model Comparision with the Three-Sided Coin

In the present work we introduce the problem of determining the probability that a rotating and bouncing cylinder (i.e. flipped coin) will land and come to rest on its edge. We present this problem and analysis as a practical, nontrivial example to introduce the reader to Bayesian model comparison. Several models are presented, each of which take into consideration different physical aspects of the problem and the relative effects on the edge landing probability. The Bayesian formulation of model comparison is then used to compare the models and their predictive agreement with data from hand-flipped cylinders of several sizes

Statistical Inference for Everyone (sie)

In the field of statistical inference, there are two primary schools of thought. Each has its proponents, but it is generally accepted that on all problems covered in an introductory course, that both approaches are valid and lead to the same numerical values when applied to actual problems. Only one of these approaches is covered in a traditional course, which denies the students access to an entire field of statistical inference. The traditional approach, also called the frequentist or orthodox perspective, leads almost directly to problem above. The other approach, also called Probability Theory as Logic, derives all statistical inference from probability theory directly. It is this approach that I hope to expose students to in an introductory course

Effect of Correlated Lateral Geniculate Nucleus Firing Rates on Predictions for Monocular Eye Closure Versus Monocular Retinal Inactivation

Monocular deprivation experiments can be used to distinguish between different ideas concerning properties of cortical synaptic plasticity. Monocular deprivation by lid suture causes a rapid disconnection of the deprived eye connected to cortical neurons whereas total inactivation of the deprived eye produces much less of an ocular dominance shift. In order to understand these results one needs to know how lid suture and retinal inactivation affect neurons in the lateral geniculate nucleus (LGN) that provide the cortical input. Recent experimental results by Linden et al. showed that monocular lid suture and monocular inactivation do not change the mean firing rates of LGN neurons but that lid suture reduces correlations between adjacent neurons whereas monocular inactivation leads to correlated firing. These, somewhat surprising, results contradict assumptions that have been made to explain the outcomes of different monocular deprivation protocols. Based on these experimental results we modify our assumptions about inputs to cortex during different deprivation protocols and show their implications when combined with different cortical plasticity rules. Using theoretical analysis, random matrix theory and simulations we show that high levels of correlations reduce the ocular dominance shift in learning rules that depend on homosynaptic depression (i.e., Bienenstock-Cooper-Munro type rules), consistent with experimental results, but have the opposite effect in rules that depend on heterosynaptic depression (i.e., Hebbian/principal component analysis type rules)

Selectivity and Metaplasticity in a Unified Calcium-Dependent Model

A unified, biophysically motivated Calcium-Dependent Learning model has been shown to account for various rate-based and spike time-dependent paradigms for inducing synaptic plasticity. Here, we investigate the properties of this model for a multi-synapse neuron that receives inputs with different spike-train statistics. In addition, we present a physiological form of metaplasticity, an activity-driven regulation mechanism, that is essential for the robustness of the model. A neuron thus implemented develops stable and selective receptive fields, given various input statistic

Recovery From Monocular Deprivation Using Binocular Deprivation: Experimental Observations and Theoretical Analysis

Ocular dominance (OD) plasticity is a robust paradigm for examining the functional consequences of synaptic plasticity. Previous experimental and theoretical results have shown that OD plasticity can be accounted for by known synaptic plasticity mechanisms, using the assumption that deprivation by lid suture eliminates spatial structure in the deprived channel. Here we show that in the mouse, recovery from monocular lid suture can be obtained by subsequent binocular lid suture but not by dark rearing. This poses a significant challenge to previous theoretical results. We therefore performed simulations with a natural input environment appropriate for mouse visual cortex. In contrast to previous work we assume that lid suture causes degradation but not elimination of spatial structure, whereas dark rearing produces elimination of spatial structure. We present experimental evidence that supports this assumption, measuring responses through sutured lids in the mouse. The change in assumptions about the input environment is sufficient to account for new experimental observations, while still accounting for previous experimental results

Algal biomarkers as a proxy for pCO2: Constraints from late Quaternary sapropels in the eastern Mediterranean

Records of carbon dioxide concentrations (partial pressure expressed as pCO2) over Earth’s history provide trends that are critical to understand our changing world. To better constrain pCO2 estimations, here we test organic pCO2 proxies against the direct measurements of pCO2 recorded in ice cores. Based on the concept of stable carbon isotopic fractionation due to photosynthetic CO2 fixation (Ɛp), we use the stable carbon isotopic composition (δ13C) of the recently proposed biomarker phytol (from all photoautotrophs), as well as the conventionally used alkenone biomarkers (from specific species) for comparison, to reconstruct pCO2 over several Quaternary sapropel formation periods (S1, S3, S4, and S5) in the eastern Mediterranean Sea. The reconstructed pCO2 values are within error of the ice core values but consistently exceed the ice core values by ca. 100 µatm. This offset corresponds with atmospheric disequilibrium of present day CO2[aq] concentrations in the Mediterranean Sea from global pCO2, equivalent to ca. 100 µatm, although pCO2 estimates derived from individual horizons within each sapropel do not covary with the ice core values. This may possibly be due to greater variability in local CO2[aq] concentration changes in the Mediterranean, as compared with the global average pCO2, or possibly due to biases in the proxy, such as variable growth rate or carbon-concentrating mechanisms. Thus, the offset is likely a combination of physiological or environmental factors. Nevertheless, our results demonstrate that alkenone- and phytol-based pCO2 proxies yield statistically similar estimations (P-value = 0.02, Pearson’s r-value = 0.56), and yield reasonable absolute estimations although with relatively large uncertainties (± 100 µatm)