Characterizing mixed mode oscillations shaped by noise and bifurcation structure

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and reset and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.Comment: 22 page

Experimental realization of an achromatic magnetic mirror based on metamaterials

Our work relates to the use of metamaterials engineered to realize a meta-surface approaching the exotic properties of an ideal object not observed in nature, a ‘magnetic mirror’. Previous realizations were based on resonant structures which implied narrow bandwidths and large losses. The working principle of our device is ideally frequency-independent, it does not involve resonances and it does not rely on a specific technology. The performance of our prototype, working at millimetre wavelengths, has never been achieved before and it is superior to any other device reported in the literature, both in the microwave and optical regions. The device inherently has large bandwidth (144%), low losses (<1 %) and is almost independent of incidence-angle and polarization-state and thus approaches the behaviour of an ideal magnetic mirror. Applications of magnetic mirrors range from low-profile antennas, absorbers to optoelectronic devices. Our device can be realised using different technologies to operate in other spectral regions

Orbital Dimer Model for Spin-Glass State in Y2_2Mo2_2O7_7

The formation of a spin glass usually requires both structural disorder and frustrated magnetic interactions. Consequently, the origin of spin-glass behaviour in Y$_2$Mo$_2$O$_7$ $-$ in which magnetic Mo$^{4+}$ ions occupy a frustrated pyrochlore lattice with minimal compositional disorder $-$ has been a longstanding question. Here, we use neutron and X-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously-reported PDF, EXAFS and NMR studies and provides a new and physical mechanism for spin-glass formation. We show that Mo$^{4+}$ ions displace according to a local "2-in/2-out" rule on each Mo$_4$ tetrahedron, driven by orbital dimerisation of Jahn-Teller active Mo$^{4+}$ ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O$^{2-}$ displacements yield a distribution of Mo$-$O$-$Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.Comment: 6 pages, 3 figure

Expression and functional analysis of TaASY1 during meiosis of bread wheat (Triticum aestivum)

Background: Pairing and synapsis of homologous chromosomes is required for normal chromosome segregation and the exchange of genetic material via recombination during meiosis. Synapsis is complete at pachytene following the formation of a tri-partite proteinaceous structure known as the synaptonemal complex (SC). In yeast, HOP1 is essential for formation of the SC, and localises along chromosome axes during prophase I. Homologues in Arabidopsis (AtASY1), Brassica (BoASY1) and rice (OsPAIR2) have been isolated through analysis of mutants that display decreased fertility due to severely reduced synapsis of homologous chromosomes. Analysis of these genes has indicated that they play a similar role to HOP1 in pairing and formation of the SC through localisation to axial/lateral elements of the SC. Results: The full length wheat cDNA and genomic clone, TaASY1, has been isolated, sequenced and characterised. TaASY1 is located on chromosome Group 5 and the open reading frame displays significant nucleotide sequence identity to OsPAIR2 (84%) and AtASY1 (63%). Transcript and protein analysis showed that expression is largely restricted to meiotic tissue, with elevated levels during the stages of prophase I when pairing and synapsis of homologous chromosomes occur. Immunolocalisation using transmission electron microscopy showed TaASY1 interacts with chromatin that is associated with both axial elements before SC formation as well as lateral elements of formed SCs. Conclusion: TaASY1 is a homologue of ScHOP1, AtASY1 and OsPAIR2 and is the first gene to be isolated from bread wheat that is involved in pairing and synapsis of homologous chromosomes.Scott A Boden, Nadim Shadiac, Elise J Tucker, Peter Langridge and Jason A Abl

A Career Preparation Course for Students in Mathematics and Computer Science

As professors, we all want our students to succeed, and to be motivated to study. We all get questions from students that can be boiled down to, What can I do with X degree? Certainly, a quick answer is to point students to career websites, or to send them to the career services department on campus. However, we want to do better than that. We want students to learn how to investigate these future directions, and to have them think about their future more holistically--not just an effort to find a job. To that end, we have developed a course at Whitworth University to help students in mathematics and computer science in their investigations. We help students to learn more carefully about their own strengths and values, and to find careers that match those strengths and values. We provide students with opportunities to consider many kinds of vocational options: industry, graduate school, and mission work. We push students to investigate how their life is affected and influenced doe to these various career directions, and to think further than just how to get their first job. Finally, we encourage students to think more holistically about vocation, and how their own faith and ethical values play an important role in their vocation. In this paper, we discuss the course and its components. When appropriate, we will also discuss how faith and ethics were considered in components

Transmission Properties of Subwavelength Planar Fractals for THz Wavelengths

We investigate the transmission properties of planar H fractal structures in THz range. 3D EM simulations using HFSS are used to design the parameters of the fractals and to evaluate the optical properties. We observe the transmission spectra with pass bands and stop bands, which show the subwavelength transmission through the non-metallic gaps. This unique transmission property through subwavelength apertures makes it potentially useful frequency selective components in THz region. We experimentally demonstrate its behavior by designing and fabricating four prototype planar fractals in the range of 0-1.5THz and characterize using a polarizing Fourier transform spectrometer. We find good agreement between the models and measurements

Structure–property insights into nanostructured electrodes for Li-ion batteries from local structural and diffusional probes

Microwave heating presents a faster, lower energy synthetic methodology for the realization of functional materials. Here, we demonstrate for the first time that employing this method also leads to a decrease in the occurrence of defects in olivine structured LiFe1−xMnxPO4. For example, the presence of antisite defects in this structure precludes Li+ diffusion along the b-axis leading to a significant decrease in reversible capacities. Total scattering measurements, in combination with Li+ diffusion studies using muon spin relaxation (μ+SR) spectroscopy, reveal that this synthetic method generates fewer defects in the nanostructures compared to traditional solvothermal routes. Our interest in developing these routes to mixed-metal phosphate LiFe1−xMnxPO4 olivines is due to the higher Mn2+/3+ redox potential in comparison to the Fe2+/3+ pair. Here, single-phase LiFe1−xMnxPO4 (x = 0, 0.25, 0.5, 0.75 and 1) olivines have been prepared following a microwave-assisted approach which allows for up to 4 times faster reaction times compared to traditional solvothermal methods. Interestingly, the resulting particle morphology is dependent on the Mn content. We also examine their electrochemical performance as active electrodes in Li-ion batteries. These results present microwave routes as highly attractive for reproducible, gram-scale syntheses of high quality nanostructured electrodes which display close to theoretical capacity for the full iron phase

Testing fluvial erosion models using the transient response of bedrock rivers to tectonic forcing in the Apennines, Italy

The transient response of bedrock rivers to a drop in base level can be used to discriminate between competing fluvial erosion models. However, some recent studies of bedrock erosion conclude that transient river long profiles can be approximately characterized by a transport‐limited erosion model, while other authors suggest that a detachment‐limited model best explains their field data. The difference is thought to be due to the relative volume of sediment being fluxed through the fluvial system. Using a pragmatic approach, we address this debate by testing the ability of end‐member fluvial erosion models to reproduce the well‐documented evolution of three catchments in the central Apennines (Italy) which have been perturbed to various extents by an independently constrained increase in relative uplift rate. The transport‐limited model is unable to account for the catchments’response to the increase in uplift rate, consistent with the observed low rates of sediment supply to the channels. Instead, a detachment‐limited model with a threshold corresponding to the field‐derived median grain size of the sediment plus a slope‐dependent channel width satisfactorily reproduces the overall convex long profiles along the studied rivers. Importantly, we find that the prefactor in the hydraulic scaling relationship is uplift dependent, leading to landscapes responding faster the higher the uplift rate, consistent with field observations. We conclude that a slope‐ dependent channel width and an entrainment/erosion threshold are necessary ingredients when modeling landscape evolution or mapping the distribution of fluvial erosion rates in areas where the rate of sediment supply to channels is low

A Bright Submillimeter Source in the Bullet Cluster (1E0657--56) Field Detected with BLAST

We present the 250, 350, and 500 micron detection of bright submillimeter emission in the direction of the Bullet Cluster measured by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). The 500 micron centroid is coincident with an AzTEC 1.1 mm point-source detection at a position close to the peak lensing magnification produced by the cluster. However, the 250 micron and 350 micron centroids are elongated and shifted toward the south with a differential shift between bands that cannot be explained by pointing uncertainties. We therefore conclude that the BLAST detection is likely contaminated by emission from foreground galaxies associated with the Bullet Cluster. The submillimeter redshift estimate based on 250-1100 micron photometry at the position of the AzTEC source is z_phot = 2.9 (+0.6 -0.3), consistent with the infrared color redshift estimation of the most likely IRAC counterpart. These flux densities indicate an apparent far-infrared luminosity of L_FIR = 2E13 Lsun. When the amplification due to the gravitational lensing of the cluster is removed, the intrinsic far-infrared luminosity of the source is found to be L_FIR <= 10^12 Lsun, consistent with typical luminous infrared galaxies.Comment: Accepted for publication in the Astrophysical Journal. Maps are available at http://blastexperiment.info