Synchronization of electrically coupled resonate-and-fire neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs

Semi-regular masas of transfinite length

In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each $n\in\mathbb N$, finding masas for which this procedure terminates at the $n$-th stage. Such masas are said to have length $n$. In this paper we consider a transfinite version of this idea, giving rise to a notion of ordinal valued length. We show that all countable ordinals arise as lengths of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalising tower.Comment: 14 page

Valence Quark Distribution in A=3 Nuclei

We calculate the quark distribution function for 3He/3H in a relativistic quark model of nuclear structure which adequately reproduces the nucleon approximation, nuclear binding energies, and nuclear sizes for small nuclei. The results show a clear distortion from the quark distribution function for individual nucleons (EMC effect) arising dominantly from a combination of recoil and quark tunneling effects. Antisymmetrization (Pauli) effects are found to be small due to limited spatial overlaps. We compare our predictions with a published parameterization of the nuclear valence quark distributions and find significant agreement.Comment: 18pp., revtex4, 4 fig

Effects of Extreme Obliquity Variations on the Habitability of Exoplanets

We explore the impact of obliquity variations on planetary habitability in hypothetical systems with high mutual inclination. We show that large amplitude, high frequency obliquity oscillations on Earth-like exoplanets can suppress the ice-albedo feedback, increasing the outer edge of the habitable zone. We restrict our exploration to hypothetical systems consisting of a solar-mass star, an Earth-mass planet at 1 AU, and 1 or 2 larger planets. We verify that these systems are stable for $10^8$ years with N-body simulations, and calculate the obliquity variations induced by the orbital evolution of the Earth-mass planet and a torque from the host star. We run a simplified energy balance model on the terrestrial planet to assess surface temperature and ice coverage on the planet's surface, and we calculate differences in the outer edge of the habitable zone for planets with rapid obliquity variations. For each hypothetical system, we calculate the outer edge of habitability for two conditions: 1) the full evolution of the planetary spin and orbit, and 2) the eccentricity and obliquity fixed at their average values. We recover previous results that higher values of fixed obliquity and eccentricity expand the habitable zone, but also find that obliquity oscillations further expand habitable orbits in all cases. Terrestrial planets near the outer edge of the habitable zone may be more likely to support life in systems that induce rapid obliquity oscillations as opposed to fixed-spin planets. Such planets may be the easiest to directly characterize with space-borne telescopes.Comment: 46 pages, 12 Figures, 5 Table

Energetics of Quantum Antidot States in Quantum Hall Regime

We report experiments on the energy structure of antidot-bound states. By measuring resonant tunneling line widths as function of temperature, we determine the coupling to the remote global gate voltage and find that the effects of interelectron interaction dominate. Within a simple model, we also determine the energy spacing of the antidot bound states, self consistent edge electric field, and edge excitation drift velocity.Comment: 4 pages, RevTex, 5 Postscript figure

Current-induced spin polarization in InGaAs and GaAs epilayers with varying doping densities

The current-induced spin polarization and momentum-dependent spin-orbit field were measured in In$_{x}$Ga$_{1-x}$As epilayers with varying indium concentrations and silicon doping densities. Samples with higher indium concentrations and carrier concentrations and lower mobilities were found to have larger electrical spin generation efficiencies. Furthermore, current-induced spin polarization was detected in GaAs epilayers despite the absence of measurable spin-orbit fields, indicating that the extrinsic contributions to the spin polarization mechanism must be considered. Theoretical calculations based on a model that includes extrinsic contributions to the spin dephasing and the spin Hall effect, in addition to the intrinsic Rashba and Dresselhaus spin-orbit coupling, are found to qualitatively agree with the experimental results.Comment: 16 pages, 8 figure

Positive regulation of meiotic DNA double-strand break formation by activation of the DNA damage checkpoint kinase Mec1(ATR)

During meiosis, formation and repair of programmed DNA double-strand breaks (DSBs) create genetic exchange between homologous chromosomes-a process that is critical for reductional meiotic chromosome segregation and the production of genetically diverse sexually reproducing populations. Meiotic DSB formation is a complex process, requiring numerous proteins, of which Spo11 is the evolutionarily conserved catalytic subunit. Precisely how Spo11 and its accessory proteins function or are regulated is unclear. Here, we use Saccharomyces cerevisiae to reveal that meiotic DSB formation is modulated by the Mec1(ATR) branch of the DNA damage signalling cascade, promoting DSB formation when Spo11-mediated catalysis is compromised. Activation of the positive feedback pathway correlates with the formation of single-stranded DNA (ssDNA) recombination intermediates and activation of the downstream kinase, Mek1. We show that the requirement for checkpoint activation can be rescued by prolonging meiotic prophase by deleting the NDT80 transcription factor, and that even transient prophase arrest caused by Ndt80 depletion is sufficient to restore meiotic spore viability in checkpoint mutants. Our observations are unexpected given recent reports that the complementary kinase pathway Tel1(ATM) acts to inhibit DSB formation. We propose that such antagonistic regulation of DSB formation by Mec1 and Tel1 creates a regulatory mechanism, where the absolute frequency of DSBs is maintained at a level optimal for genetic exchange and efficient chromosome segregation