Student understanding of the Boltzmann factor

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions

SIMPEL: Circuit model for photonic spike processing laser neurons

We propose an equivalent circuit model for photonic spike processing laser neurons with an embedded saturable absorber---a simulation model for photonic excitable lasers (SIMPEL). We show that by mapping the laser neuron rate equations into a circuit model, SPICE analysis can be used as an efficient and accurate engine for numerical calculations, capable of generalization to a variety of different laser neuron types found in literature. The development of this model parallels the Hodgkin--Huxley model of neuron biophysics, a circuit framework which brought efficiency, modularity, and generalizability to the study of neural dynamics. We employ the model to study various signal-processing effects such as excitability with excitatory and inhibitory pulses, binary all-or-nothing response, and bistable dynamics.Comment: 16 pages, 7 figure

Representing uncertainty on model analysis plots

Model analysis provides a mechanism for representing student learning as measured by standard multiple-choice surveys. The model plot contains information regarding both how likely students in a particular class are to choose the correct answer and how likely they are to choose an answer consistent with a well-documented conceptual model. Unfortunately Bao's original presentation of the model plot did not include a way to represent uncertainty in these measurements. I present details of a method to add error bars to model plots by expanding the work of Sommer and Lindell. I also provide a template for generating model plots with error bars.Comment: Accepted for publication in Phys. Rev. Phys. Edu. Res. Published version will include supplementary file

Professor Walks into a Bar: Using Humor and Q-Score to Determine Instructor and Department Appeal

Building on existing research on humor in the classroom, the authors propose a research design that examines the effect of humor on a professor\u27s effectiveness in the classroom. The concept of Q-Score is applied to academia, which is a popular rating used by advertisers to measure source attractiveness and determine celebrity appeal. Several factors leading to teaching effectiveness and “favorite prof” status are explored in addition to overall effects of humor in the classroom. This study combines evaluations from popular student-viewed websites, student evaluations, and a Humor Orientation scale. An awareness and application of this metric can assist professors in marketing themselves, the discipline, and the major

Identifying Student Difficulties with Entropy, Heat Engines, and the Carnot Cycle

We report on several specific student difficulties regarding the Second Law of Thermodynamics in the context of heat engines within upper-division undergraduates thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the Second Law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students' struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices

Dynamical laser spike processing

Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the excitable dynamics also found in the time-resolved "spiking" of neurons. Spiking reconciles the expressiveness and efficiency of analog processing with the robustness and scalability of digital processing. We demonstrate that graphene-coupled laser systems offer a unified low-level spike optical processing paradigm that goes well beyond previously studied laser dynamics. We show that this platform can simultaneously exhibit logic-level restoration, cascadability and input-output isolation---fundamental challenges in optical information processing. We also implement low-level spike-processing tasks that are critical for higher level processing: temporal pattern detection and stable recurrent memory. We study these properties in the context of a fiber laser system, but the addition of graphene leads to a number of advantages which stem from its unique properties, including high absorption and fast carrier relaxation. These could lead to significant speed and efficiency improvements in unconventional laser processing devices, and ongoing research on graphene microfabrication promises compatibility with integrated laser platforms.Comment: 13 pages, 7 figure

Mindfulness meditation targets transdiagnostic symptoms implicated in stress-related disorders: Understanding relationships between changes in mindfulness, sleep quality, and physical symptoms

Mindfulness-Based Stress Reduction (MBSR) is an 8-week meditation program known to improve anxiety, depression, and psychological well-being. Other health-related effects, such as sleep quality, are less well established, as are the psychological processes associated with therapeutic change. This prospective, observational study (n=213) aimed to determine whether perseverative cognition, indicated by rumination and intrusive thoughts, and emotion regulation, measured by avoidance, thought suppression, emotion suppression, and cognitive reappraisal, partly accounted for the hypothesized relationship between changes in mindfulness and two health-related outcomes: sleep quality and stress-related physical symptoms. As expected, increased mindfulness following the MBSR program was directly correlated with decreased sleep disturbance (r=-0.21, p=0.004) and decreased stress-related physical symptoms (r=-0.38, p<0.001). Partial correlations revealed that pre-post changes in rumination, unwanted intrusive thoughts, thought suppression, experiential avoidance, emotion suppression, and cognitive reappraisal each uniquely accounted for up to 32% of the correlation between the change in mindfulness and change in sleep disturbance and up to 30% of the correlation between the change in mindfulness and change in stress-related physical symptoms. Results suggest that the stress-reducing effects of MBSR are due, in part, to improvements in perseverative cognition and emotion regulation, two “transdiagnostic” mental processes that cut across stress-related disorders

A framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects--both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebra contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond

Decreased symptoms of depression after mindfulness-based stress reduction: potential moderating effects of religiosity, spirituality, trait mindfulness, sex, and age

Objective: mindfulness-based stress reduction (MBSR) is a secular meditation training program that reduces depressive symptoms. Little is known, however, about the degree to which a participant's spiritual and religious background, or other demographic characteristics associated with risk for depression, may affect the effectiveness of MBSR. Therefore, this study tested whether individual differences in religiosity, spirituality, motivation for spiritual growth, trait mindfulness, sex, and age affect MBSR effectiveness.Methods: as part of an open trial, multiple regression was used to analyze variation in depressive symptom outcomes among 322 adults who enrolled in an 8-week, community-based MBSR program.Results: as hypothesized, depressive symptom severity decreased significantly in the full study sample (d=0.57; p&lt;0.01). After adjustment for baseline symptom severity, moderation analyses revealed no significant differences in the change in depressive symptoms following MBSR as a function of spirituality, religiosity, trait mindfulness, or demographic variables. Paired t tests found consistent, statistically significant (p&lt;0.01) reductions in depressive symptoms across all subgroups by religious affiliation, intention for spiritual growth, sex, and baseline symptom severity. After adjustment for baseline symptom scores, age, sex, and religious affiliation, a significant proportion of variance in post-MBSR depressive symptoms was uniquely explained by changes in both spirituality (?=?0.15; p=0.006) and mindfulness (?=?0.17; p&lt;0.001).Conclusions: these findings suggest that MBSR, a secular meditation training program, is associated with improved depressive symptoms regardless of affiliation with a religion, sense of spirituality, trait level of mindfulness before MBSR training, sex, or age. Increases in both mindfulness and daily spiritual experiences uniquely explained improvement in depressive symptom

Locus ceruleus regulates sensory encoding by neurons and networks in waking animals

Substantial evidence indicates that the locus ceruleus (LC)–norepinephrine (NE) projection system regulates behavioral state and state-dependent processing of sensory information. Tonic LC discharge (0.1–5.0 Hz) is correlated with levels of arousal and demonstrates an optimal firing rate during good performance in a sustained attention task. In addition, studies have shown that locally applied NE or LC stimulation can modulate the responsiveness of neurons, including those in the thalamus, to nonmonoaminergic synaptic inputs. Many recent investigations further indicate that within sensory relay circuits of the thalamus both general and specific features of sensory information are represented within the collective firing patterns of like-modality neurons. However, no studies have examined the impact of NE or LC output on the discharge properties of ensembles of functionally related cells in intact, conscious animals. Here, we provide evidence linking LC neuronal discharge and NE efflux with LC-mediated modulation of single-neuron and neuronal ensemble representations of sensory stimuli in the ventral posteriomedial thalamus of waking rats. As such, the current study provides evidence that output from the LC across a physiologic range modulates single thalamic neuron responsiveness to synaptic input and representation of sensory information across ensembles of thalamic neurons in a manner that is consistent with the well documented actions of LC output on cognition