Student and expert perceptions of the role of mathematics within physics

Students’ perceptions of the role of mathematics within physics were examined. I propose that the identification of physics as a science based ultimately on experiment is a threshold concept: transformation from a naïve view that physics is based upon mathematics to an expert view that physics is based on experiment is difficult for students. Seven students taking first-year university physics were interviewed in two focus groups; nine practising physicists from academia and industry (considered as experts) were interviewed as six individuals plus one focus group of three participants. Of particular interest was the ‘expert’ view emphasizing the conceptual nature of physics. This was a threshold in understanding that had not been crossed by students. Rather, students viewed mathematics and physics as being more strongly connected than did practising physicists; specifically that “maths explains physics”. Experts consider this view as holding back a student’s understanding of the subject and preventing them from becoming effective physicists. It is troublesome to students because they are less able to identify the relevant concepts before trying to tackle a problem with mathematics, making their approach less likely to be effective, however, both groups (physicists and students) identified physics as belonging to ‘the real world’ and that mathematics shows how physical entities can be combined or related, indicating student responses are not completely naïve. Opinions on how best to teach mathematical concepts in physics varied considerably across participants

Subthreshold dynamics of a single neuron from a Hamiltonian perspective

We use Hamilton's equations of classical mechanics to investigate the behavior of a cortical neuron on the approach to an action potential. We use a two-component dynamic model of a single neuron, due to Wilson, with added noise inputs. We derive a Lagrangian for the system, from which we construct Hamilton's equations. The conjugate momenta are found to be linear combinations of the noise input to the system. We use this approach to consider theoretically and computationally the most likely manner in which such a modeled neuron approaches a firing event. We find that the firing of a neuron is a result of a drop in inhibition, due to a temporary increase in negative bias of the mean noise input to the inhibitory control equation. Moreover, we demonstrate through theory and simulation that, on average, the bias in the noise increases in an exponential manner on the approach to an action potential. In the Hamiltonian description, an action potential can therefore be considered a result of the exponential growth of the conjugate momenta variables pulling the system away from its equilibrium state, into a nonlinear regime

Surge pricing on a service platform under spatial spillovers: evidence from Uber

Ride-sharing platforms employ surge pricing to match anticipated capacity spillover with demand. We develop an optimization model to characterize the relationship between surge price and spillover. We test predicted relationships using a spatial panel model on a dataset from Ubers operation. Results reveal that Ubers pricing accounts for both capacity and price spillover. There is a debate in the management community on the ecacy of labor welfare mechanisms associated with shared capacity. We conduct counterfactual analysis to provide guidance in regards to the debate, for managing congestion, while accounting for consumer and labor welfare through this online platform.First author draf

Comparison of modelling approaches to transcranial magnetic stimulation.

This paper describes a comparison of modelling approaches to transcranial magnetic stimulation

Pancasila: Roadblock or Pathway to Economic Development

When Sukarno (1901-1970) led Indonesia towards independence from the Dutch, he rallied his supporters behind the vision of Pancasila (five principles). And although Sukarno used different wordings on different occasions and ranked the five principles differently in different speeches, Pancasila entered Indonesia’s constitution as follows: (1) Belief in one God, (2) Just and civilized humanity, (3) Indonesian unity, (4) Democracy under the wise guidance of representative consultations, (5) Social justice for all the peoples of Indonesia (Pancasila, 2013). Pancasila is a normative value system. This requires that a Pancasila economic framework must be the means towards the realization of this normative end. McCawley (1982, p. 102) poses the question: “What, precisely, is meant by ‘Pancasila Economics’?” and laments that “[a]s soon as we ask this question, there are difficulties because, as most contributors to the discussion admit, it is all rather vague.” A discussion of the nature of Pancasila economics is therefore as relevant today as it was back then. As far as the history of Pancasila economic thought is concerned, McCawley (1982, p. 103ff.) points at the importance of the writings of Mubyarto (1938-2005) and Boediono (1943-present). Both have stressed five major characteristics of Pancasila economics. These characteristics must be seen in the context of Indonesia as a geographically and socially diverse developing country after independence. They are discussed in the following five sub-sections

Numerical modelling of plasticity induced by transcranial magnetic stimulation

We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short (∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual’s electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes

Dense gap-junction connections support dynamic Turing structures in the cortex

The recent report by Fukuda et al [1] provides convincing evidence for dense gap-junction connectivity between inhibitory neurons in the cat visual cortex, each neuron making 60 +/- 12 gap-junction dendritic connections with neurons in both the same and adjoining orientation columns. These resistive connections provide a source of diffusive current to the receiving neuron, supplementing the chemical-synaptic currents generated by incoming action-potential spike activity. Fukuda et al describe how the gap junctions form a dense and homogeneous electrical coupling of interneurons, and propose that this diffusion-coupled network provides the substrate for synchronization of neuronal populations. To date, large-scale population-based mathematical models of the cortex have ignored diffusive communication between neurons. Here we augment a well-established mean-field cortical model [2] by incorporating gap-junction-mediated diffusion currents, and we investigate the implications of strong diffusive coupling. The significant result is the model prediction that the 2D cortex can spontaneously generate centimetre-scale Turing structures (spatial patterns), in which regions of high-firing activity are intermixed with regions of low-firing activity (see Fig. 1). Since coupling strength decreases with increases in firing rate, these patterns are expected to exchange contrast on a slow time-scale, with low-firing patches increasing their activity at the expense of high-firing patches. These theoretical predictions are consistent with the slowly fluctuating large-scale brain-activity images detected from the BOLD (blood oxygen-level-dependent) signal [3]