Politics and Integral Mission

Strong cultural and historical forces generate considerable challenges to American Christians seeking to become informed, meaningful and faithful political actors. Given the widespread lack of exposure to a number of the most basic elements of Christian Political Theology many are unfamiliar with rich historical (Augustine) and contemporary political thought (Oliver O\u27Donovan, Mark Noll, Ron Sider) within the Christian tradition. In the absence of a Christian political theology politics is often reduced to the decision of being either a Republican or Democrat. While Scripture calls all Christians to be subject to governing authorities (Rom 13:1), it sets this mandate within the broader context of the rule and kingdom of God. Christians, in short, properly engage in politics when they embody and seek the shalom and justice of the kingdom of God

Segregation of cortical head direction cell assemblies on alternating theta cycles

High-level cortical systems for spatial navigation, including entorhinal grid cells, critically depend on input from the head direction system. We examined spiking rhythms and modes of synchrony between neurons participating in head direction networks for evidence of internal processing, independent of direct sensory drive, which may be important for grid cell function. We found that head direction networks of rats were segregated into at least two populations of neurons firing on alternate theta cycles (theta cycle skipping) with fixed synchronous or anti-synchronous relationships. Pairs of anti-synchronous theta cycle skipping neurons exhibited larger differences in head direction tuning, with a minimum difference of 40 degrees of head direction. Septal inactivation preserved the head direction signal, but eliminated theta cycle skipping of head direction cells and grid cell spatial periodicity. We propose that internal mechanisms underlying cycle skipping in head direction networks may be critical for downstream spatial computation by grid cells.We kindly thank S. Gillet, J. Hinman, E. Newman and L. Ewell for their invaluable consultations and comments on previous versions of this manuscript, as well as M. Connerney, S. Eriksson, C. Libby and T. Ware for technical assistance and behavioral training. This work was supported by grants from the National Institute of Mental Health (R01 MH60013 and MH61492) and the Office of Naval Research Multidisciplinary University Research Initiative (N00014-10-1-0936). (R01 MH60013 - National Institute of Mental Health; MH61492 - National Institute of Mental Health; N00014-10-1-0936 - Office of Naval Research Multidisciplinary University Research Initiative)Accepted manuscrip

Parabolic pulse propagation in mean-zero, dispersion-managed transmission systems and mode-locked laser cavities

Self-similarity is a ubiquitous concept in the physical sciences used to explain a wide range of spatial- or temporalstructures observed in a broad range of applications and natural phenomena. Indeed, they have been predicted or observed in the context of Raman scattering, spatial soliton fractals, propagation in the normal dispersion regime with strong nonlinearity, optical amplifiers, and mode-locked lasers. These self-similar structures are typically long-time transients formed by the interplay, often nonlinear, of the underlying dominant physical effects in the system. A theoretical model shows that in the context of the universal Ginzburg-Landau equation with rapidly-varying, mean-zero dispersion, stable and attracting self-similar pulses are formed with parabolic profiles: the zero-dispersion similariton. The zero-dispersion similariton is the final solution state of the system, not a long-time, intermediate asymptotic behavior. An averaging analysis shows the self-similarity to be governed by a nonlinear diffusion equation with a rapidly-varying, mean-zero diffusion coefficient. Indeed, the leadingorder behavior is shown to be governed by the porous media (nonlinear diffusion) equation whose solution is the well-known Barenblatt similarity solution which has a parabolic, self-similar profile. The alternating sign of the diffusion coefficient, which is driven by the dispersion fluctuations, is critical to supporting the zero-dispersion similariton which is, to leading-order, of the Barenblatt form. This is the first analytic model proposing a mechanism for generating physically realizable temporal parabolic pulses in the Ginzburg-Landau model. Although the results are of restricted analytic validity, the findings are suggestive of the underlying physical mechanism responsible for parabolic (self-similar) pulse formation in lightwave transmission and observed in mode-locked laser cavities

The critical role of intracavity dynamics in high-power mode-locked fiber lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile

Application of waveguide arrays and spectral filtering for a multi-frequency picosecond mode-locked pulse source

Current optical fiber-communication networks increasingly rely on wavelength-division multiplexing (WDM) technologies in conjunction with optical time-division multiplexing (OTDM) of individual WDM channels. The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s, creating a demand for all-optical transmission sources that can generate pico-second modelocked pulses at various wavelengths. Through nonlinear mode-coupling in a wave-guide array and a periodically applied multi-notch frequency filter, robust multi-frequency mode-locking can be achieved in a laser cavity in both the normal and anomalous dispersion regimes. We develop a theoretical description of this multiplewavelength mode-locking, and characterize the mode-locked solutions and their stability for an arbitrary number of frequency channels. The theoretical investigations demonstrate that the stability of the mode-locked pulse solutions of multiple frequency channels depends on the degree of inhomogenity in gain saturation. Specifically, only a small amount of inhomogeneous gain-broadening is needed for multi-frequency operation in the laser. In this presentation, the conditions on the system parameters necessary for generating stable mode-locking is explored for arbitrary number of frequency channels. The model suggests a promising source for multi-frequency photonic applications

Waveguide arrays and spectral filtering for multi-frequency mode-locked pulse sources

Current optical fiber-communication networks increasingly rely on wavelength-division multiplexing (WDM) technologies in conjunction with optical time-division multiplexing (OTDM) of individual WDM channels. The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s, creating a demand for all-optical transmission sources that can generate pico-second modelocked pulses at various wavelengths. Through nonlinear mode-coupling in a wave-guide array and a periodically applied multi-notch frequency filter, robust multi-frequency mode-locking can be achieved in a laser cavity in both the normal and anomalous dispersion regimes. We develop a theoretical description of this multiplewavelength mode-locking, and characterize the mode-locked solutions and their stability for an arbitrary number of frequency channels. The theoretical investigations demonstrate that the stability of the mode-locked pulse solutions of multiple frequency channels depends on the degree of inhomogenity in gain saturation. Specifically, only a small amount of inhomogeneous gain-broadening is needed for multi-frequency operation in the laser. In this presentation, the conditions on the system parameters necessary for generating stable mode-locking is explored for arbitrary number of frequency channels. The model suggests a promising source for multi-frequency photonic applications