Sentence examples for spike problem from inspiring English sources

Overall, the optimal control is simply given by the BANG control U until (v_{2}) reaches the guard, after which the boundary control is used exactly as in the single spike problem.

We consider the minimum-time selective spiking problem P1.

Note that by successively reducing the guard voltage, the selective spiking problem may become infeasible as discussed in Sect.

We noted earlier that the initial conditions for the selective spiking problem nominally lie on either the (v_{1}) or (v_{2}) axis, under the assumption that one of the neurons has just produced a spike.

The time optimal feedback control (u^ inmathcal{U}) for the selective spiking problem P1 for Neuron 1 is given by u^{ast} = textstylebegin{cases} U& textit{for }v_{2}< V_{G}, u_{mathrm{arc}}& textit{for } v_{2}=V_{G}, end{cases} (17) where (u_{mathrm{arc}}=frac{a_{2}}{b_{2}} V_{G}) is the unique control that keeps (v_{2}(t)=V_{G}) invariant.

The time optimal control (u^ inmathcal{U}) for the selective spiking problem P1 for Neuron 1, if such a solution exists, is u^{ast} = textstylebegin{cases} 0 & textit{for }mathbf{v} invarGamma_, U & textit{for }mathbf{v} invarGamma_, end{cases} (40) with (varGamma_{pm}) defined as before.

This is similar to the selective spiking problem of Neuron 1, and indeed the best control is a combination of BANG and boundary control as in (17), u^{ast} = textstylebegin{cases} U &text{for } t leq t_{c} text{ where } v_{2}(t_{c}) = V_{T}, u_{mathrm{arc}}&text{for } t_{c} < t leq{tau_{1}} text{ where } v_{1}({tau_{1}}) = v_{mathrm{nd}}.

Knowing this rise can allow us to insulate neurons from each other in the spike control problem, formulated in the next section.

Poulter's young friend Rory McIlroy of Northern Ireland quickly responded, also via Twitter: "I wear spikes.... Problem!?!?" "Yes, problem," answered Poulter, who has more than 1.1 million Twitter followers.

"It's not like we've seen a spike in problems leading to this," said James Rilee, the mayor of Roxbury Township, which counts 25,000 people in its 21 square miles.

We illustrate the method in application to a spike-processing problem.