The relative detectability for mice of gaps having different ramp durations at their onset and offset boundaries

The effect on gap detectability of varying noise fall time (FT) and rise time (RT) of the gap boundary ramps was examined in mice using reflex modification audiometry, measuring inhibition of acoustic startle reflexes by variously shaped gaps just preceding reflex expression. In experiment 1 (n = 12) inhibition increased up to near-asymptotic values with longer FT (0, 1, 2, 3, 5, or 10 ms) and QT (quiet time, 0 to 13 ms), with a 2:1 trade-off between FT and QT. In experiment 2 (n = 24) inhibition increased for any RT above 0 ms (2, 3, 5, or 7 ms) if QT= 1 ms, but diminished with increased RT when QT = 3 or 8 ms. Enhanced detectability for subthreshold gaps by longer ramps results from their extending the apparent gap duration. The negative effect of increased RT for threshold gaps suggests the importance for gap detection of the stronger neural responses to sharp edges at the end of the gap shown previously in the mouse inferior colliculus. These effects are specific to gaps: inhibition for fixed (70-dB SPL) or varied level pulses (30 to 60 dB) was unaffected by varying the ramped edges (experiments 3 and 4, n = 9).     

Collisions between optical spatial solitons propagating in opposite directions

We formulate the theory describing the evolution and interactions between optical spatial solitons that propagate in opposite directions. We show that coherent collisions between counterpropagating solitons give rise to a new focusing mechanism resulting from the interference between the beams, and that interactions between such solitons are insensitive to the relative phase between the beams.     

The RATIO method for time‐resolved Laue crystallography

A RATIO method for analysis of intensity changes in time‐resolved pump–probe Laue diffraction experiments is described. The method eliminates the need for scaling the data with a wavelength curve representing the spectral distribution of the source and removes the effect of possible anisotropic absorption. It does not require relative scaling of series of frames and removes errors due to all but very short term fluctuations in the synchrotron beam.     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.     

Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide

We experimentally demonstrate the first integrated temporal Fourier transformer based on a linearly chirped Bragg grating waveguide written in silica glass with a femtosecond laser. The operation is based on mapping the energy spectrum of the input optical signal to the output temporal waveform by making use of first-order chromatic dispersion. The device operates in reflection, has a bandwidth of 10 nm, and can be used for incident temporal waveforms as long as 20 ps. Experimental results, obtained through both temporal oscilloscope traces and Fourier transform spectral interferometry, display a successful Fourier transformation of in-phase and out-of-phase pairs of input optical pulses, and demonstrate the correct functionality of the device for both amplitude and phase of the temporal output.     

Generation of low-timing-jitter femtosecond pulse trains with 2 GHz repetition rate via external repetition rate multiplication

Generation of low-timing-jitter 150 fs pulse trains at 1560 nm with 2 GHz repetition rate is demonstrated by locking a 200 MHz fundamental polarization additive-pulse mode-locked erbium fiber laser to high-finesse external Fabry-Perot cavities. The timing jitter and relative intensity noise of the repetition-rate multiplied pulse train are investigated.     

Spectral- and frequency-encoded fluorescence imaging

A method for obtaining fluorescence images with a high number of resolvable points by using spectral and frequency encoding is presented. Broadband excitation light is encoded with a wavelength-dependent frequency modulation and dispersed onto the sample with a grating to simultaneously illuminate an entire image line. The Fourier transform of the frequency-encoded fluorescence emission provides one line of the image. Mechanical scanning along a direction orthogonal to the wavelength-encoded axis allows creation of the two-dimensional fluorescent image. This method is applicable for developing submillimeter diameter endoscopes. The principles of the technique are validated by imaging indocyanine green fluorescence in microfluidic channels.     

The twenty-fourth Fermat number is composite

We have shown by machine proof that is composite. The rigorous Pépin primality test was performed using independently developed programs running simultaneously on two different, physically separated processors. Each program employed a floating-point, FFT-based discrete weighted transform (DWT) to effect multiplication modulo . The final, respective Pépin residues obtained by these two machines were in complete agreement. Using intermediate residues stored periodically during one of the floating-point runs, a separate algorithm for pure-integer negacyclic convolution verified the result in a ``wavefront' paradigm, by running simultaneously on numerous additional machines, to effect piecewise verification of a saturating set of deterministic links for the Pépin chain. We deposited a final Pépin residue for possible use by future investigators in the event that a proper factor of should be discovered; herein we report the more compact, traditional Selfridge-Hurwitz residues. For the sake of completeness, we also generated a Pépin residue for , and via the Suyama test determined that the known cofactor of this number is composite.