Root Mean Square Error of Neural Spike Train Sequence Matching with Optogenetics

Optogenetics is an emerging field of neuroscience where neurons are genetically modified to express light-sensitive receptors that enable external control over when the neurons fire. Given the prominence of neuronal signaling within the brain and throughout the body, optogenetics has significant potential to improve the understanding of the nervous system and to develop treatments for neurological diseases. This paper uses a simple optogenetic model to compare the timing distortion between a randomly-generated target spike sequence and an externally-stimulated neuron spike sequence. The distortion is measured by filtering each sequence and finding the root mean square error between the two filter outputs. The expected distortion is derived in closed form when the target sequence generation rate is sufficiently low. Derivations are verified via simulations.Comment: 6 pages, 5 figures. Will be presented at IEEE Global Communications Conference (IEEE GLOBECOM 2017) in December 201

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included

Varying the Abundance of O Antigen in \u3cem\u3eRhizobium etli\u3c/em\u3e and Its Effect on Symbiosis with \u3cem\u3ePhaseolus vulgaris\u3c/em\u3e

Judged by migration of its lipopolysaccharide (LPS) in gel electrophoresis, the O antigen of Rhizobium etli mutant strain CE166 was apparently of normal size. However, its LPS sugar composition and staining of the LPS bands after electrophoresis indicated that the proportion of its LPS molecules that possessed O antigen was only 40% of the wild-type value. Its LPS also differed from the wild type by lacking quinovosamine (2-amino-2,6-dideoxyglucose). Both of these defects were due to a single genetic locus carrying a Tn5 insertion. The deficiency in O-antigen amount, but not the absence of quinovosamine, was suppressed by transferring into this strain recombinant plasmids that shared a 7.8-kb stretch of the R. etli CE3 lps genetic region α, even though this suppressing DNA did not carry the genetic region mutated in strain CE166. Strain CE166 gave rise to pseudonodules on legume host Phaseolus vulgaris, whereas the mutant suppressed by DNA from lps region α elicited nitrogen-fixing nodules. However, the nodules in the latter case developed slowly and were widely dispersed. Two other R. etli mutants that had one-half or less of the normal amount of O antigen also gave rise to pseudonodules on P. vulgaris. The latter strains were mutated in lps region α and could be restored to normal LPS content and normal symbiosis by complementation with wild-type DNA from this region. Hence, the symbiotic role of LPS requires near-normal abundance of O antigen and may require a structural feature conferred by quinovosamin

Dissection of Nodule Development by Supplementation of \u3cem\u3eRhizobium leguminosarum\u3c/em\u3e biovar \u3cem\u3ephaseoli\u3c/em\u3e Purine Auxotrophs with 4-Aminoimidazole-5-Carboxamide Riboside

Purine auxotrophs of Rhizobium leguminosarum biovar phaseoli CFN42 elicit uninfected pseudonodules on bean (Phaseolus vulgaris L.). Addition of 4-aminoimidazole-5-carboxamide (AICA) riboside to the root medium during incubation of the plant with these mutants leads to enhanced nodule development, although nitrogenase activity is not detected. Nodules elicited in this manner had infection threads and anatomical features characteristic of normal nodules, such as peripheral vasculature rather than the central vasculature of the pseudonodules that were elicited without AICA riboside supplementation. Although 105 to 106 bacteria could be recovered from these nodules after full development, bacteria were not observed in the interior nodule cells. Instead, large cells with extensive internal membranes were present. Approximately 5% of the normal amount of leghemoglobin and 10% of the normal amount of uricase were detected in these nodules. To promote the development of true nodules rather than pseudonodules, AICA riboside was required no later than the second day through no more than the sixth day following inoculation. After this period, removal of AICA riboside from the root medium did not prevent the formation of true nodules. This observation suggests that there is a critical stage of infection, reached before nodule emergence, at which development becomes committed to forming a true nodule rather than a pseudonodule

Modeling Interference-Free Neuron Spikes with Optogenetic Stimulation

This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a cortical neuron's membrane potential and its firing times. The external control is a simple optogenetic model represented by an illumination source that stimulates a saturating or decaying membrane current. This paper considers firing frequencies that are sufficiently low for the membrane potential to return to its resting potential after it fires. The time required for the neuron to charge and for the neuron to recover to the resting potential are numerically fitted to functions of the Izhikevich neuron model parameters and the peak input current. Results show that simple functions of the model parameters and maximum input current can be used to predict the charging and recovery times, even when there are deviations in the actual parameter values. Furthermore, the predictions lead to lower bounds on the firing frequency that can be achieved without significant distortion.Comment: 12 pages, 11 figures, 7 tables. Submitted for publication. Portions of this work appeared previously as arXiv:1710.11569, which is the conference version of this articl

Timing Control of Single Neuron Spikes with Optogenetic Stimulation

This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a cortical neuron's membrane potential and its firing times. The external control is a simple optogenetic model represented by a constant current source that can be turned on or off. This paper considers a firing frequency that is sufficiently low for the membrane potential to return to its resting potential after it fires. The time required for the neuron to charge and for the neuron to recover to the resting potential are fitted to functions of the Izhikevich neuron model parameters. Results show that linear functions of the model parameters can be used to predict the charging times with some accuracy and are sufficient to estimate the highest firing frequency achievable without interspike interference.Comment: 6 pages, 8 figures, 3 tables. To be presented at the 2018 IEEE International Conference on Communications (IEEE ICC 2018) in May 201