The critical role of logarithmic transformation in Nernstian equilibrium potential calculations

The membrane potential, arising from uneven distribution of ions across cell membranes containing selectively permeable ion channels, is of fundamental importance to cell signaling. The necessity of maintaining the membrane potential may be appreciated by expressing Ohm’s law as current = voltage/resistance and recognizing that no current flows when voltage = 0, i.e., transmembrane voltage gradients, created by uneven transmembrane ion concentrations, are an absolute requirement for the generation of currents that precipitate the action and synaptic potentials that consume >80% of the brain’s energy budget and underlie the electrical activity that defines brain function. The concept of the equilibrium potential is vital to understanding the origins of the membrane potential. The equilibrium potential defines a potential at which there is no net transmembrane ion flux, where the work created by the concentration gradient is balanced by the transmembrane voltage difference, and derives from a relationship describing the work done by the diffusion of ions down a concentration gradient. The Nernst equation predicts the equilibrium potential and, as such, is fundamental to understanding the interplay between transmembrane ion concentrations and equilibrium potentials. Logarithmic transformation of the ratio of internal and external ion concentrations lies at the heart of the Nernst equation, but most undergraduate neuroscience students have little understanding of the logarithmic function. To compound this, no current undergraduate neuroscience textbooks describe the effect of logarithmic transformation in appreciable detail, leaving the majority of students with little insight into how ion concentrations determine, or how ion perturbations alter, the membrane potential

Search for sterile neutrino mixing in the MINOS long-baseline experiment

A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neutrino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated noninteracting sterile neutrinos, scenarios not ruled out by existing data. From an exposure of 3.18×1020 protons on target in which neutrinos of energies between ~500¿¿MeV and 120 GeV are produced predominantly as ¿µ, the visible energy spectrum of candidate neutral-current reactions in the MINOS far detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near-detector sample shows that of the portion of the ¿µ flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles ¿24 and ¿34 are constrained to be less than 11° and 56° at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscillations is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime t3/m3>2.1×10-12¿¿s/eV at 90% C.L

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

Measurements of atmospheric neutrinos and antineutrinos in the MINOS far detector

This paper reports measurements of atmospheric neutrino and antineutrino interactions in the MINOS Far Detector, based on 2553 live-days (37.9 kton-years) of data. A total of 2072 candidate events are observed. These are separated into 905 contained-vertex muons and 466 neutrino-induced rock-muons, both produced by charged-current v_µ and v¯_µ interactions, and 701 contained-vertex showers, composed mainly of charged-current v_e and v¯_e interactions and neutral-current interactions. The curvature of muon tracks in the magnetic field of the MINOS Far Detector is used to select separate samples of v_µ and v¯_µ events. The observed ration of v¯_µ to v_µ events is compared with the Monte Carlo (MC) simulation, giving a double ration of (R^(data)_(v¯/v))/(R^(MC)_(v¯/v)) = 1.03 ± 0.08(stat) ± 0.08(syst). The v_µ and v¯_µ data are separated into bins of L/E resolution, based on the reconstructed energy and direction of each event, and a maximum likelihood fit to the observed L/E distributions is used to determine the atmospheric neutrino oscillation parameters. This fit returns 90% confidence limits of |Δm^2| = (1.9 ± 0.4) x 10^(-3) eV^2 and sin^(2)2θ > 0.86. The fit is extended to incorporate separate v_µ and v¯_µ oscillation parameters, returning 90% confidence limits of |Δm^2|-|Δm¯^2| = 0.6^(2.4)_(-0.8) x 10^(-3) eV^2 on the difference between the squared-mass splittings for neutrinos and antineutrinos

Measurement of Neutrino and Antineutrino Oscillations Using Beam and Atmospheric Data in MINOS

We report measurements of oscillation parameters from νμ and ν̅ μ disappearance using beam and atmospheric data from MINOS. The data comprise exposures of 10.71×1020 protons on target in the νμ-dominated beam, 3.36×1020 protons on target in the ν̅ μ-enhanced beam, and 37.88 kton yr of atmospheric neutrinos. Assuming identical ν and ν̅ oscillation parameters, we measure |Δm2|=(2.41-0.10+0.09)×10-3  eV2 and sin⁡2(2θ)=0.950-0.036+0.035. Allowing independent ν and ν̅ oscillations, we measure antineutrino parameters of |Δm̅ 2|=(2.50-0.25+0.23)×10-3  eV2 and sin⁡2(2θ̅ )=0.97-0.08+0.03, with minimal change to the neutrino parameters

First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA

The NOvA experiment has seen a 4.4σ signal of ν̄e appearance in a 2 GeV ν̄μ beam at a distance of 810 km. Using 12.33×1020 protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 ν̄μ→ν̄e candidates with a background of 10.3 and 102 ν̄μ→ν̄μ candidates. This new antineutrino data are combined with neutrino data to measure the parameters |Δm322|=2.48-0.06+0.11×10-3 eV2/c4 and sin2θ23 in the ranges from (0.53-0.60) and (0.45-0.48) in the normal neutrino mass hierarchy. The data exclude most values near δCP=π/2 for the inverted mass hierarchy by more than 3σ and favor the normal neutrino mass hierarchy by 1.9σ and θ23 values in the upper octant by 1.6σ

First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA

The NOvA experiment has seen a 4.4 σ signal of ¯ ν e appearance in a 2 GeV ¯ ν μ beam at a distance of 810 km. Using 12.33 × 10 20 protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 ¯ ν μ → ¯ ν e candidates with a background of 10.3 and 102 ¯ ν μ → ¯ ν μ candidates. This new antineutrino data are combined with neutrino data to measure the parameters | Δ m 2 32 | = 2.4 8 + 0.11 − 0.06 × 10 − 3     eV 2 / c 4 and sin 2 θ 23 in the ranges from (0.53–0.60) and (0.45–0.48) in the normal neutrino mass hierarchy. The data exclude most values near δ C P = π / 2 for the inverted mass hierarchy by more than 3 σ and favor the normal neutrino mass hierarchy by 1.9 σ and θ 23 values in the upper octant by 1.6 σ

Measurement of neutrino-induced neutral-current coherent π0 production in the NOvA near detector

The cross section of neutrino-induced neutral-current coherent π0 production on a carbon-dominated target is measured in the NOvA near detector. This measurement uses a narrow-band neutrino beam with an average neutrino energy of 2.7 GeV, which is of interest to ongoing and future long-baseline neutrino oscillation experiments. The measured, flux-averaged cross section is σ=13.8±0.9(stat)±2.3(syst)×10−40cm2/nucleus, consistent with model prediction. This result is the most precise measurement of neutral-current coherent π0 production in the few-GeV neutrino energy region