Download The Spike Mod Apk Ios //TOP\\

Update: The coinage by Kent Beck looks like the 'original' one to me, although his usage of the word doesn't make much sense in my opinion. Coding up a quick test is 'putting a spike through the project'?

Sometimes I call this a "spike," because we are driving a spike through the entire design. [...] Because people variously associate "spike" with volleyball, railroads, or dogs, I have begun using "architectural prototype" to describe this implementation.

Download The Spike Mod Apk Ios

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"Spike" is an Extreme Programming term meaning "experiment". We use the word because we think of a spike has a quick, almost brute-force experiment aimed at learning just one thing. think of driving a big nail through a board.

-- Extreme Programming Adventures in C# - Ron Jeffries

I believe it is an engineering expression. A spike is a temporary solution, something you try out to see if it works, before you make the permanent solution. Railroad engineers talk about spiking a track switch: inserting a rail spike into the switch, so it cannot be moved.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the virus behind the worldwide outbreak of COVID-19 disease. One of the key biological characteristics of SARS-CoV-2, as well as several other viruses, is the presence of spike proteins that allow these viruses to penetrate host cells and cause infection.

We track hospital and ambulance data to look for unexpected increases, or spikes, in drug-involved overdoses. If we see a spike, we send out an alert. Our alerts give as much detail as we can to prevent overdose deaths.

The SPIKE-distance is an estimator of the dissimilarity between two (or more) spike trains. In contrast to most other spike train distances (such as the Victor-Purpura distance) it is time-resolved and is able to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among two or more spike trains. Additional features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. The SPIKE-distance can also be formulated as a causal measure which is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real-time.

The final definition presented here is the one introduced in Kreuz et al., 2013, which improves considerably on the original proposal (Kreuz et al., 2011). Mathematical properties and expectation values for Poisson spike train can be found in Mulansky et al., 2015.

The bivariate SPIKE-distance \(D_S\) (Kreuz et al., 2013) relies on instantaneous values in the sense that in a first step the two sequences of discrete spike times are transformed into a (quasi-) continuous measure profile \(S (t)\), that is, a temporal sequence of instantaneous dissimilarity values. The distance is then defined as the temporal average of the measure profile.

The instantaneous dissimilarity values \(S (t)\) are derived from differences between the spike times of the two spike trains. First, for each neuron \(n = 1,2\) one assigns to each time instant (Figure 1) three piecewise constant quantities. These are the time of the previous spike

The ambiguity regarding the definition of the very first and the very last interspike interval is resolved by adding to each spike train an auxiliary leading spike at time \(t = 0\) (the beginning of the recording) and an auxiliary trailing spike at time \(t = T\) (the end of the recording).

The instantaneous dissimilarity values are calculated in two steps: First for each spike the distance to the nearest spike in the other spike train is calculated, then for each time instant the local spike time differences are selected, weighted, and normalized. Each time instant is uniquely surrounded by four corner spikes: the preceding spike of the first spike train \(t_{\mathrm {P}}^{(1)}\), the following spike of the first spike train \(t_{\mathrm {F}}^{(1)}\), the preceding spike of the second spike train \(t_{\mathrm {P}}^{(2)}\), and, finally, the following spike of the second spike train \(t_{\mathrm {F}}^{(2)}\). Each of these corner spikes can be identified with a spike time difference to the nearest spike in the other spike train, for example, for the previous spike of the first spike train

the intervals from the time instant under consideration to the previous and the following spikes for each neuron \(n = 1, 2\). The local weighting for the spike time differences of the first spike train reads

This quantity weights the spike time differences for each spike train according to the relative distance of the corner spike from the time instant under investigation. This way relative distances within each spike train are taken care of, while relative distances between spike trains are not yet. In order to get these ratios straight, in a last step the two contributions from the two spike trains are locally weighted by their instantaneous interspike intervals. This yields the dissimilarity profile

An example plot of a dissimilarity profile obtained for two spike trains is shown in Figure 2A. The observed monotonous increase of the instantaneous values followed by a monotonous decrease mirrors exactly the actual change in the match between the spike times of the two spike trains.

In the case of multivariate datasets consisting of a larger number of spike trains (\(N > 2\)) it is convenient to average the bivariate SPIKE-distance over all pairs of spike trains to obtain the averaged bivariate SPIKE-distance. The same kind of time-resolved visualization as in the bivariate case is possible, because the two averages over time and over pairs of spike trains commute. One thus can first calculate the instantaneous average \(S^a (t)\) over all pairwise instantaneous spike differences \(S^{mn} (t)\)

The real-time SPIKE-distance (Kreuz et al., 2012) is a modification of the SPIKE-distance with the key difference that the corresponding time profile \(S_r (t)\) can be calculated online because it relies on past information only. From the perspective of an online measure, the information provided by the following spikes, both their position and the length of the interspike interval, is not yet available. Like the regular SPIKE-distance \(D_S\), this causal variant is also based on local spike time differences but now only two corner spikes are available, and the spikes of comparison are restricted to past spikes, e.g., for the preceding spike of the first spike train

Since there are no following spikes available, there is no local weighting, and since there is no interspike interval, the normalization is achieved by dividing the average corner spike difference by twice the average time interval to the preceding spikes. This yields a causal indicator of local spike train dissimilarity:

Example plots of the dissimilarity profiles obtained for the bivariate and the multivariate example already used in Figure 2 are shown in Figure 3. As can be seen for the bivariate example (Figure 3A), any spike time difference is considered most relevant right at the later of two spikes when \(S_r(t)\) goes back to a local maximum value. In the case where the two preceding spikes are closest to each other, it goes back to its maximum value of one, since at these points the mean time interval to the two preceding spikes is exactly half their difference. Any successive period of common non-spiking leads to a decrease of the instantaneous distance values. This is a desired property since common non-spiking is as much a sign of synchrony as common spiking. The decrease is hyperbolic and its slope depends on the preceding spike time difference.

The local uncertainty can only be resolved when more and more information becomes available. This is illustrated in Figure 4 with two spiking events which are identical (one spike per spike train) except for the omitted second half of the second event. While for both events the instantaneous values in the first part necessarily have to be identical (and very high since only some of the neurons have recently spiked), the differences in the second part are clearly reflected by different continuations of the dissimilarity profile.

From this matrix it is possible to extract any information desired. By selecting a pair of spike trains one obtains the bivariate dissimilarity profile for this pair of spike trains (as shown in Figure 2A and Figure 3A). Selecting a time instant yields an instantaneous matrix of pairwise spike train dissimilarities. This matrix can be used to divide the spike trains into instantaneous clusters, i.e., groups of spike trains with low intra-group and high intergroup dissimilarity.

Examples for four different time instants are shown in Figure 5 in which artificially generated spike trains exhibit a different clustering behavior every 500 ms (Figure 5A). This varying clustering structure is correctly reflected in the pairwise dissimilarity matrices (Figure 5B) of both the regular and the real-time SPIKE-distance. The main difference between the two measures is clearly visible in the first column where the regular SPIKE-distance averages over past and future behavior and thus superimposes the checkered pattern of the first interval with the more disordered clustering of the second interval. The real-time variant is not yet aware of the latter interval and reflects the checkered pattern of the past interval only. Another difference can be seen in the second column where the real-time SPIKE-distance exhibits the large instantaneous values obtained during uncompleted firing events.

Another way to reduce the information of the dissimilarity matrix is averaging. There are two possibilities which commute: the spatial average over spike train pairs and the temporal average. As could be seen in Figure 2B and Figure 3B, the local average over spike train pairs yields a dissimilarity profile for the whole population. Temporal averaging on the other hand leads to a bivariate distance matrix; examples are shown in Figure 6. Finally, in both cases application of the respective remaining average results in one distance value which describes the overall level of synchrony for a group of spike trains over a given time interval. 006ab0faaa