6.2 Experimental
6.3.2 Signal stability and convergence criteria
In all the optimizations performed, the signal treatment was identical. Before the beginning of each optimization, the fluorescence signal of either Trp or Tyr was measured. The signal was recorded for 30 seconds (i.e. over 30’000 laser shots), with unshaped UV and IR. The associated depletion δinii was calculated, and the value obtained was used during the whole optimization as a reference, to check for laser drifts.1 Indeed, during the optimization, the fluorescence signals from unshaped UV and IR were measured again at the beginning of each generation, allowing to calculateδiref. Ifδiref had drifted by more thanx%with respect toδiini, the GA software paused the optimization.
1In fact, the depletion signal used as reference was the one at the numerator of the ratio in the first objective.
6.3. RESULTS 117
It would only resume when δiref was again within the threshold imposed. In addition to the control of laser drifts, a shot-to-shot control of the noise was performed. For each individual tested, the fluorescence depletion signals ob-tained were averaged over n laser shots. Among the n shots, all the shots that yielded a signal outside the ±x%interval from the averaged value were rejected. If more than x% of the shots were rejected, the measurement was repeated. All the optimizations presented here were done with x = 10%
threshold, and n = 1000 shots per individual. Note that UV energy and IR energy were also recorded. Even if these signals were not used during the op-timization, they provided useful on-line information about laser stability and allowed to verify if the Dazzlers, in particular the IR Dazzler, had varied the pulses energies during the optimization. Indeed, even if amplitude shaping was in principle not possible, depending on the pulse shape tested, the overall amplitude of the Dazzler acoustic waves could sometimes change, and induce unwanted amplitude modulations of the pulses. As discussed in Chap. 5, the definition of the depletion ratio removes the dependence on fluctuations of the UV pump energy (see Eq. 6.1). Therefore, amplitude modulations of the UV pulse by the UV Dazzler, would not bias the evolution of the op-timization. Concerning the IR pulse, as we have seen before (Sect. 6.3.1), amplitude modulations are not an obstacle for objectives defined as theratio of the depletions (Fig. 6.6). They could, however, influence the evolution of objectives defined as one of the depletion signals (see Eqs. 6.4 and6.5). This issue will be illustrated in Sect. 6.3.3.
Case Objective S/N Outcome
# goal δT rp δT yr J1 |J2
A 1 maxδT yr/δT rp 20 9.6 20 3
B 2 max δT yr/δT rp 33.3 11.5 11.3 |33.3 3 C 2 maxδT yr/δT rp 31.3 9 8.3| 31.3 7 D 1 maxδT rp/δT yr 15 13.2 12.7 7 E 1 maxδT rp/δT yr 18.9 16.7 16.4 7
Table 6.2: Column Objective gives the number of objectives (1 or 2) as well as the goal of the optimization. Column S/N gives the signal-to-noise ratio of δT rp,δT yr and each objective (J1,J2) (more details in the text). Col-umn Outcome indicates if discrimination (3) or no discrimination (7) was attained.
Many optimizations were run, with different objectives definitions and
118 CHAPTER 6. ODD OF AMINO-ACIDS outcomes. In order to assess the criteria for good convergence, studying both unsuccessful and successful optimizations is essential. Tab. 6.2 summarizes the characteristics and outcome of some typical optimizations. From Tab.
6.2we first see that while optimizations aiming at maximizingδT yr/δT rpwere successful, optimizations aiming at maximizing δT rp/δT yr were not. In the latter case, we ran a number of single-objective optimizations, that did not lead to any discriminating solution. We did not perform any two-objective optimizations. Optimizations aiming at maximizingδT yr/δT rp were run, and as some of them provided successful results, we decided to focus our attention on them. These cases will be discussed later (Sect. 6.3.4). Some unsuccessful, and yet interesting, optimizations aiming at maximizing δT yr/δT rp will also be described and discussed in Sect. 6.3.3.
Optimizations aiming at maximizing δT rp/δT yr
In order to understand the causes of failure in the optimizations aiming at maximizingδT rp/δT yr, we calculated for each optimization the signal-to-noise ratio (S/N) of the signals to optimize:
S/N =µ/σ (6.7)
where µ is the mean value and σ the standard deviation. As explained before, the depletion signals from unshaped pulses δiref were recorded all along the optimization process. From these reference signals, the quantities equivalent to the objectives could be calculated, following the definition of each objective, for instance:
δT rpref
δT yrref + +α δrefT rp (6.8) for single-objective optimizations, or:
δT rpref
δT yrref ; δT rpref (6.9) for two-objective optimizations.
This yielded a quantity whose mean value was stable in time, as it orig-inated from the signals measured with unshaped UV and IR, but that pre-sented the same fluctuations as the actual objectives. The S/N of each case are presented in Tab. 6.2. It is obvious from these calculations that the Tyr depletion signal has a lower S/N than the Trp depletion signal. The reason for this difference is that we could attain higher absolute values of depletion
6.3. RESULTS 119 for Trp than for Tyr. Therefore, although σ was similar for both signals, the S/N of Trp was higher than for Tyr because of µ. The high fluctuations of Tyr, in comparison with the lower fluctuations ofδT rp explain why a certain number of optimizations, where the Tyr depletion signal had a prominent role due to the way the objective was defined, did not converge (see Sect.
6.3.3).
Optimizations aiming at maximizing δT yr/δT rp
It is interesting to note that in these optimizations, the level of noise also played an important role. Indeed, from case C of Tab. 6.2, we can see that the noise of the signal associated toJ1 is higher than for case B. This biased the algorithm and led it to converge to a unique solution (only one feasible solution in the first Pareto Front). This case will be further analyzed in Sect.
6.3.3. A general remark that can be drawn from all the optimizations is that two-objective optimizations, were often more sensitive to signal fluctuations than single objective optimizations. Indeed, the first objective was defined as a simple ratio, and asδT yr signal fluctuated, the ratio was also subject to fluctuations. This problem could be overcome with the help of the second objective, often defined as δT rp (see case B), but when the fluctuations on the δT yr signal were too high, this was not sufficient (see case C).
Surprisingly, defining objectives as in case A allowed to overcome effi-ciently fluctuations of the δT yr signal. Indeed, Tab. 6.2 shows that while δT yr had a S/N ∼ 10, δT rp had a S/N ∼ 20, exactly like the objective func-tion J1. This optimization, that lead to a significant discrimination, will be described in detail hereafter (Sect. 6.3.4). It is obvious from these results that in future discrimination experiments, care should be taken to minimize the sources of noise, in order for multiobjective optimizations to converge to reliable solutions. This issue will be further discussed in Sect. 6.4.
We will describe hereafter (Sects. 6.3.3 and 6.3.4) some typical