P Robin Hiesinger
email: robin.hiesinger@fu-berlin.de

Bassem A Hassan
email: bassem.hassan@icm-institute.org

The Evolution of Variability and Robustness in Neural Development

As in all biological systems, neurons and their networks must balance precision with variability. Phenotypic precision and phenotypic variability can both occur with remarkable robustness, where robustness is defined as the ability to tolerate perturbation. Variability in genotype-phenotype mapping produces phenotypic variability despite identical genetic information. The resulting variability among genetically identical neurons can contribute to the robustness of brain development. Similarly, variability of genetically identical individuals can contribute to evolutionary robustness. We discuss here shared principles of developmental robustness and evolutionary robustness, and highlight scenarios where such principles result in neural networks that achieve robustness of precision or variability.

From Variability to Robustness in Brain Development and Evolution

. These observations showcase variability despite identical genes, suggesting that nonheritable factors play important roles in generating variability during neuronal development.

The outcome of neural development is selected not only for optimized function but also for robustness. The robustness of a system is defined as its ability to tolerate perturbation (Table 1). Imagine, for instance, an enzyme that functions optimally but loses all activity if any of its amino acids are changed by mutation. By contrast, imagine another enzyme that is somewhat less efficient but can tolerate the majority of single amino acid exchanges without significant reduction in its activity. In any species with a mutation rate higher than zero, the latter enzyme has a selective advantage because it is more robust. Robustness to excessive variation may contribute to the evolvability of biological systems. This is because robustness allows the accumulation of mutations (cryptic genetic variation [START_REF] Gibson | Uncovering cryptic genetic variation[END_REF]), and thus eventually 'evolutionary innovation', with minimal effects on fitness in the intervening time (reviewed in [START_REF] Felix | Pervasive robustness in biological systems[END_REF][START_REF] Wagner | Robustness and evolvability: a paradox resolved[END_REF][START_REF] Masel | Robustness and evolvability[END_REF]), although the generality of this idea has been questioned [START_REF] Mayer | Evolvability and robustness: a paradox restored[END_REF]. Importantly, the robustness of the phenotype of an organism to perturbation is due in large part to developmental processes that can tolerate random genetic mutations and unpredictable environmental perturbations. This has historically been described as 'canalization of development' [START_REF] Waddington | Canalization of development and the inheritance of acquired characters[END_REF]. The relationship between Highlights Identical genes do not ensure identical processes during neural development, partly owing to the intrinsic noise in molecular processes.

Noisy neural development may result in either invariable or variable adult structure and function.

Developmental noise and variability contribute to robustness to perturbation.

Evolutionary robustness and developmental robustness share some of the same principles. developmental processes and phenotypic robustness is often difficult to describe because of nonlinearities inherent in the molecular and cellular processes underlying development [START_REF] Beck | LINE-1 retrotransposition activity in human genomes[END_REF].

Evolutionary robustness requires variability among individuals. Individuals are the outcome of development, and this outcome can be variable or precise, and both can be robustly so (i.e., both variability and precision among individuals in the population can be robust to perturbation). Similarly, developmental processes can be deterministic or noisy, and both robustly so (Table 1). However, invariant outcomes do not necessarily require deterministic developmental mechanisms. As we will discuss in the first section, some neural network features may need to be precise, but the developmental processes generating them may need to be noisy to achieve that precision. In this case, variability among neurons may be crucial to achieve developmental robustness, similarly to how variability among individuals is crucial for evolutionary robustness. We define as 'noisy' a process in which at any point in time the precise state or value is unpredictable. However, in contrast to a truly random process, there might be a dependency on previous states of the system or an inherent bias. We use noisy synonymously with imprecise, non-deterministic, and probabilistic.

Growth cone filopodia extension/retraction dynamics are unpredictable, but are typically biased towards the 'leading edge'. Dscam splice variants are non-predictable, but may not have equal probability for all variants.

Deterministic process

A process in which any future state or value of the system is precisely predictable. Hence, a deterministic process always produces the same outcome.

Transcription of the same DNA sequence will deterministically yield the same RNA sequence, given identical conditions and no error rate. To the extent that the error rate increases, the process can become noisy. Note that a deterministic outcome depends on the exact state or value under consideration: given a large number of dice throws, the average outcome will deterministically converge to 3.5. Two sister cells may stochastically attain either fate A or B, but the process can deterministically ensure that exactly one cell becomes A and one cell becomes B.

Variable outcome

We define the outcome of process as variable if that outcome is unpredictable and different when repeated.

Variability can originate from stochastic or noisy processes. Rolling a dice leads to variable outcomes that are stochastically distributed [START_REF] Goodman | Isogenic grasshoppers: genetic variability in the morphology of identified neurons[END_REF][START_REF] Ward | Electron microscopical reconstruction of the anterior sensory anatomy of the nematode Caenorhabditis elegans[END_REF][START_REF] Mohr | The similarity of brain morphology in healthy monozygotic twins[END_REF][START_REF] Belle | Tridimensional visualization and analysis of early human development[END_REF][START_REF] Gibson | Uncovering cryptic genetic variation[END_REF][START_REF] Felix | Pervasive robustness in biological systems[END_REF]. Noisy growth cone filopodia dynamics lead to variability in the direction of growth.

Robust (or canalized) outcome

Robustness is the property of tolerating perturbation. Both precision or variability can be robust. We use robustness of precision synonymously with Waddington's canalization.

The precise expression or function of a protein can be robust to mutation, in other words many (possibly most) mutations only quantitatively change expression or function levels. These changes may be subthreshold with respect to its consequences or gradually affect a higher-order process. Dscam splicing in neurons and V(D)J recombination in immune cells create variability. The variability as such can be robust to genetic or environmental perturbation. Waddington's classic concept of canalization is restricted to robustness of precision, in other words constancy of outcome in the wild type, which is often reduced in Drosophila mutants.

Therefore, in both developmental and evolutionary contexts, noise in a preceding step can lead either to a precise or to a variable outcome in the subsequent step.

The differences between monozygotic twins, and between left and right peripheral innervation patterns, suggest that noisy development underlies variable outcomes even in the absence of germline mutations. Hence, developmental processes can be noisy as a result of genetic or non-genetic causes. Phenotypic variability of circuit function owing to heritable genetic differences is subject to evolutionary selection. However, can phenotypic variability result from identical genes and noisy development, including somatic, non-heritable genetic differences?

In the second section of this Opinion we discuss how variability itself might be evolutionarily selectable during neural development.

In the following two sections we therefore ask two questions. First, how does phenotypic variability in neural development arise even when genes are identical? Second, what are the possible evolutionary consequences of this type of phenotypic variability?

Developmental Sources of Variability Despite Identical Genes

Intrinsically noisy developmental processes can lead to either variability or precision in the outcome. We have previously discussed the contribution of genetically encoded noisy developmental processes in brain wiring [START_REF] Hassan | Beyond molecular codes: simple rules to wire complex brains[END_REF]. Our core argument was that synapse-specific brain wiring is achievable through molecular functions that not only tolerate noise but actively utilize it. Prominent examples include dendritic self-avoidance based on stochastic filopodial growth and noisy splicing of a cell adhesion molecule [START_REF] Kise | Role of self-avoidance in neuronal wiring[END_REF][START_REF] Zipursky | The molecular basis of self-avoidance[END_REF]. Mechanisms based on noise may be part of a multistep developmental process that also includes molecular functions, such as synaptic matchmaking, that do not utilize noise but must tolerate it. Roger Sperry's influential chemoaffinity theory [START_REF] Sperry | Chemoaffinity in the orderly growth of nerve fiber patterns and connections[END_REF] is the foundational framework for the latter type of molecular functions. Chemoaffinity has since then been extended by many elegant studies that revealed functions of 'connectivity molecules' that function as 'Sperry molecules' to various degrees [START_REF] Petrovic | Axonal wiring in neural development: target-independent mechanisms help to establish precision and complexity[END_REF][START_REF] Zipursky | Chemoaffinity revisited: dscams, protocadherins, and neural circuit assembly[END_REF][START_REF] De Wit | Specification of synaptic connectivity by cell surface interactions[END_REF]. By contrast, a framework of rules focuses on the principle that is executed through molecular actions [START_REF] Hassan | Beyond molecular codes: simple rules to wire complex brains[END_REF]. Importantly, developmental rules (such as self-avoidance or lateral inhibition) govern both noisy (as opposed to only 'noise-tolerating') and deterministic molecular mechanisms, exactly as physical laws govern both noisy and deterministic behaviors of matter. To understand the evolution of variability and robustness, we need to understand developmental rules that operate on noisy molecular mechanisms and cellular dynamics.

Phenotypic outcomes can be highly precise not only as a result of deterministic processes but can also be due to intrinsically stochastic processes. A good example of the latter is the precisely controlled number of neurons in C. elegans, where exactly 302 neurons result from developmental cell competition that does not allow the prediction of which cells will die in the process [START_REF] White | The structure of the nervous system of the nematode Caenorhabditis elegans[END_REF]. Similarly, photoreceptor neurons in the fly eye differentiate following a nondeterministic cell-sorting process that does not allow one to predict which cells will become neurons and which cells will die; nonetheless, the number of cells of a single eye facet (called an ommatidium) is invariable, and the precision of optical axes within and across ommatidia is astounding [START_REF] Kumar | Building an ommatidium one cell at a time[END_REF]. Thus, when does developmental noise lead to invariable phenotypes, and when does it lead to phenotypic variability?

First, we need to consider that neural circuits, like any biological structure, grow based on algorithmic information. An algorithm is defined as a series of steps where the output of preceding steps becomes the input of the following step. Algorithmic information, as opposed to total endpoint information (i.e., blueprints), is defined by the rules applied at each step, and not by the precise input/output values. This is the basis for developmental flexibility. During fly eye development, for instance, half the cells can be continuously experimentally killed through continued expression of an apoptosis inducer in progenitor cells. Remarkably, a morphologically normal eye and precise eye-brain wiring develop, and this technique is routinely used in fly laboratories to generate homozygous mutant eyes [START_REF] Newsome | Analysis of Drosophila photoreceptor axon guidance in eye-specific mosaics[END_REF][START_REF] Stowers | A genetic method for generating Drosophila eyes composed exclusively of mitotic clones of a single genotype[END_REF]. This is because, during eye development, stochastic recruitment and cell killing are an integral part of the rules. We note that the noisy, flexible nature of eye development also manifests itself in apparent genetic redundancy: two mutations that independently increase cell death or reduce the accuracy of patterned cell sorting through different mechanisms may result in a disrupted outcome, while each mutation alone may lie within the margins of what noisy, flexible development can still compensate for.

Algorithmic growth not only accommodates stochastic processes but can even make such processes an integral part of the algorithmic rules [START_REF] Hassan | Beyond molecular codes: simple rules to wire complex brains[END_REF]. The extent to which variability in phenotypic outcome is under evolutionary selection can determine the extent to which noisy development is 'preserved'. In the case of the fly, the optical axes between the individual single eye facets (ommatidia) of the compound eye and the precision of the underlying wiring of photoreceptor axons in the brain must be precise for spatial vision to function. By contrast, the precise number of ommatidia per complex eye is variable and is likely under much less selective pressure. Hence, the same underlying noisy growth leads not only to astonishing precision in the geometry of the fly eye and the underlying brain wiring pattern, but also to a significantly variable number of component eye facets between individual flies. Perhaps even more remarkably, the sizes of the left and right eyes of the same fly, while highly correlated, are nonetheless not identical [START_REF] Vollmer | A quantitative analysis of growth control in the Drosophila eye disc[END_REF].

Another aspect to consider is that, in many respects, individual neurons operate as autonomous agents during neural development. Neurons grow axonal growth cones and dendritic branches through local decision-making processes in an unknown environment. Each branch of the dendritic tree grows without knowledge of a branch at the other end of the tree, let alone the branches of other trees. Similarly, the axonal growth cone individually responds to what it encounters in the environment. This allows local decisions in the face of an obstacle, loss of branches, and imprecision in the molecular environment. Each of the autonomously acting agents can be considered to be a player in a game with set rules. Each player makes individual, noisy, and local decisions, even in genetically identical left and right brain hemispheres, but following the same rules.

To illustrate this point, consider molecule families such as the highly variable Drosophila Dscams and vertebrate protocadherins. For both types of molecules specific isoforms are expressed noisily in a cell-autonomous fashion, such that only a few of potentially thousands of possible variants are expressed in each neuron. This variable identity allows a neuron to distinguish self from non-self. Self-avoidance based on noisy filopodial extension dynamics and neuronal dendrite recognition of self leads to spread-out growth of its dendritic tree [START_REF] Kise | Role of self-avoidance in neuronal wiring[END_REF][START_REF] Zipursky | The molecular basis of self-avoidance[END_REF]. We would argue that the functionally significant dendrite spreading is under evolutionary selection, while the precise location of individual branching points is not. Dendrite spreading is based on a developmental rule-set consisting of iterated noisy filopodial growth, self-avoidance, and branching. The process leads to robustness of stereotypically spread-out dendritic trees (which are functionally important), but variability in the precise branching pattern (which is not). In fact, Dscam and protocadherins are not only examples of molecules that execute developmental rules based on noisy processes in an algorithmic fashion, but are also prime examples of evolutionary selection for variability per se, as discussed in the second section of this article.

In contrast to Dscam and protocadherins, several cell adhesion molecules have been shown to function with remarkable specificity in the matchmaking of specific synaptic partners, including sidekick-2 [START_REF] Krishnaswamy | Sidekick 2 directs formation of a retinal circuit that detects differential motion[END_REF] in the mouse retina, teneurins in the fly olfactory system [START_REF] Hong | Teneurins instruct synaptic partner matching in an olfactory map[END_REF], and Syg-1/Syg-2 in a C. elegans motor neuron [START_REF] Shen | Synaptic specificity is generated by the synaptic guidepost protein SYG-2 and its receptor, SYG-1[END_REF]. Interestingly, none of these mutants affect the ability of a neuron to make synapses per se, and in the absence of each of these molecules synapses are formed in varying numbers with other, often incorrect, partners. We would argue that these are examples of molecular adhesion that bias the probabilistic nature of synapse formationa developmental rule based on a noisy process. In terms of algorithmic growth, this biasing typically occurs towards the end of the synaptic specification process. Interestingly, sets of molecules have been identified in gene expression profiles that are sufficient to predict synaptic partners in C. elegans [START_REF] Baruch | Using expression profiles of Caenorhabditis elegans neurons to identify genes that mediate synaptic connectivity[END_REF][START_REF] Kaufman | Gene expression of Caenorhabditis elegans neurons carries information on their synaptic connectivity[END_REF] and Drosophila [START_REF] Li | Classifying Drosophila olfactory projection neuron subtypes by single-cell RNA sequencing[END_REF]. While it is tempting to interpret these molecules in terms of 'lock and key' for a synaptic code, genes that computationally predict partnerships may not function as part of the developmental algorithm at all, in the same way as the expression of a neurotransmitter in a presynaptic cell and its receptor in postsynaptic cell does not dictate their connectivity.

Is noisy development really essential to create robustness in the outcome? As discussed above, dendritic growth based on self-avoidance is robust because of (i) noisy filopodial exploration, and (ii) local decisions of dendrites when to 'self-avoid'. However, at least in theory, robustness could still be achieved with deterministic filopodial exploration, but not without local decision-making, as discussed below. We must therefore consider how a deterministic model could work, and when noisy development may be advantageous or even be required for robustness (Figure 1A-C).

Biological examples show that stochastic filopodial dynamics provide a substrate for synaptotropic growth towards a brain region with more synaptic partners; similarly, stochastic filopodial dynamics provide the substrate for self-avoidance to generate dendrite spreading [START_REF] Vaughn | Fine structure of synaptogenesis in the vertebrate central nervous system[END_REF][START_REF] Niell | Theoretical analysis of a synaptotropic dendrite growth mechanism[END_REF][START_REF] Niell | In vivo imaging of synapse formation on a growing dendritic arbor[END_REF]. In theory, however, a deterministic filopodial 'probing program' could work, provided that it probed all possible directions evenly, by searching every N degrees rotationally in a 360 circle (Figure 1C). Provided that the growing dendritic tree can operate as an autonomous agent, such a theoretical deterministic behavior would allow similar flexibility when hitting obstacles or during growth towards regions with increased synaptic partner availability. However, we are not aware of neuronal examples where deterministic axonal or dendritic filopodial probing of an unknown environment occurs. On the other hand, examples abound of axonal and dendritic growth based on non-deterministic, flexible, and robust development [START_REF] Zschatzsch | Regulation of branching dynamics by axon-intrinsic asymmetries in tyrosine kinase receptor signaling. Elife 3, e01699 34[END_REF][34][START_REF] Ozel | Filopodial dynamics and growth cone stabilization in Drosophila visual circuit development[END_REF]. An interesting question concerns what is 'easier' to encodein terms of information costand what is more robust in the face of perturbation through mutation: a deterministic algorithm or an algorithm that employs intrinsically stochastic processes?

Arguably, random exploration is the ideal way for an axon or dendrite to evenly explore an unknown environment. Any deterministic algorithm designed to both comprehensively and evenly explore the environment may come close to, but never fully achieve, the random ideal. If intrinsically noisy molecular processes create random exploration, this may be less costly to genetically encode than a deterministic program that ensures both even and complete exploration (Figure 1). A random process creates a precise Gaussian distribution around the mean, 'majority' behavior (Figure 1A,B). The importance of the width of this distribution (i.e., noisiness) becomes clear when a selection pressure or perturbation is applied. Consider the case of an exploring axonal or dendritic arbor whose target may be closer or further away. If filopodial exploration is precise (the distribution narrow), the likelihood of missing the target increases (Figure 1A). By contrast, a noisier (wider) random distribution will increase the probability of finding the target (Figure 1B). Increasing this probability through a deterministic process may come at a much higher cost (Figure 1C). Hence, there are good theoretical reasons why, and empirical examples of how, (neuro-)developmental processes utilize noise to minimize cost and create robustness in the face of uncertainty or perturbation.

Lastly, an important question to consider in this context is: what is the source and nature of noise during neural development? An obvious source of noise is apparent at the molecular level. Molecular noise can be defined as 'stochastic fluctuations inherent to biochemical processes due to the discreteness of molecules and their random collision' [START_REF] Hafner | Stochastic simulations in systems biology[END_REF]. For example, molecular noise is an essential feature of the bacterial chemotaxis network, and explains individually variable behavior in bacteria [START_REF] Korobkova | From molecular noise to behavioural variability in a single bacterium[END_REF]. In addition, somatic genetic mutations during development can create clones of cells that are genetically different from each other. For instance, human monozygotic twins show somatic genetic alterations such as copy-number variation [START_REF] Bruder | Phenotypically concordant and discordant monozygotic twins display different DNA copy-number-variation profiles[END_REF][START_REF] Maiti | Ontogenetic de novo copy number variations (CNVs) as a source of genetic individuality: studies on two families with MZD twins for schizophrenia[END_REF] as well as epigenetic changes such as DNA methylation and histone acetylation [START_REF] Fraga | Epigenetic differences arise during the lifetime of monozygotic twins[END_REF]. These somatic genetic differences are stochastic, non-heritable by nature, and can create phenotypic differences such as disease susceptibility or distinct behavioral personality traits. Mechanisms that create somatic genetic diversity, such as transposable element mobilization, are highly active in the human brain, as well as in the brains of other species including insects and rodents [START_REF] Waddell | Neural transposition in the Drosophila brain: is it all bad news?[END_REF][START_REF] Lapp | The dynamic genome: transposons and environmental adaptation in the nervous system[END_REF]. The retrotransposon LINE-1 alone may have the potential to render every neuron in a mammalian brain genomically unique [START_REF] Faulkner | L1 mosaicism in mammals: extent, effects, and evolution[END_REF]. filopodial exploration deviating from the mean. The filopodial distribution is narrow, the cost is low (yellow area), and the probability of identifying a target deviating from the mean is reduced (black connection bars on the right). (B) Directed growth with a wide random distribution of filopodial exploration. The cost is higher (yellow area) and the probability of identifying a target deviating from the mean is high. (C) Directed growth with deterministic 'circular exploration'. The cost is highest (yellow area) and the probability of identifying a target deviating from the mean is not much higher than in (B).

In summary, identical genes do not encode identical processes or outcomes during neural development. Noisy developmental processes can change both the genome of each individual cell as well as the behavior of two genetically identical neurons. Noise thereby contributes to both variability and robustness in the developmental outcome. In the next section we discuss how phenotypic variability in neural development can be an evolutionarily selectable property.

Evolution of Robustness, Robustness of Evolution

We have thus far argued that intrinsically noisy developmental processes can contribute to both robustly variable and invariable phenotypic outcomes. Noisy processes actively facilitate robustness in the contexts of algorithmic development and neurons that operate as 'autonomous agents' during development. The evolutionary selection of a noisy process is therefore plausible if robustness is advantageous. Robustness of invariable outcomes is relatively easy to understand: if a developmental process can achieve, for instance, a precise fly eye anatomy and visual map wiring even though half of the cells may die during development, then this is an advantageous, and selectable, type of robustness.

Phenotypic variability is similarly easy to understand if selection of individual phenotypic variants means selection of genotypic variants. However, as we have seen, variable phenotypic outcomes can also result from identical genes, based on intrinsically noisy developmental processes. From an evolutionary perspective, only genetically encoded variants are selectable. Individual phenotypic variants resulting from intrinsically noisy development of identical genomes are invisible to the all-seeing eye of natural selection because they are not heritable. Or are they? Phenotypic variability has been investigated in genetically identical individuals of species that reproduce through parthenogenesis, for example the grasshopper [START_REF] Goodman | Isogenic grasshoppers: genetic variability in the morphology of identified neurons[END_REF] and the clonal marbled crayfish [START_REF] Vogt | Production of different phenotypes from the same genotype in the same environment by developmental variation[END_REF]. Isogenic batch-mates of this clonal crayfish reared under identical conditions exhibit a large degree of variation in coloration, growth, lifespan, reproduction, behavior, and number of sense organs. The fact that variation was also found with respect to fluctuating asymmetry strongly indicates the intrinsically stochastic developmental component of the phenotype of an individual. Strikingly, the marbled crayfish is a highly robust, highly fecund, and fast-spreading species that appears to adapt well to a variety of ecological niches.

In clonal species, the selective advantage of phenotypic variability is obvious: if selection pressure for (or against) some specific phenotypic variant increases, other variants with the same genome survive. However, the observation that the same genotype can produce different phenotypes (even under identical environmental conditions) implies that different genotypes can produce overlapping phenotypes. As shown in Figure 2, if genotype-phenotype mapping is precise (the distribution is narrow), a single mutation (from genotype A to genotype B in Figure 2) will result in failure for all individuals (be it neurons or animals). By contrast, a noisier (wider) stochastic distribution will allow a certain (sometimes precise!) number of individuals to succeed. A simple hypothetical illustration of this would be two mice where one has a promoter mutation that lowers the isoform variability of a protocadherin, leading to faulty dendritic selfavoidance. Because the rules that govern these developmental events utilize noisy processes, and are robust by their very nature, these manifestly different genomes can nonetheless each generate a distribution of phenotypes, some of which are indistinguishable (Figure 2). Thus, even under strong selection pressure, more than one of these genotypes can give rise to a phenotype that enhances fitness and will thus pass a selection bottleneck (Figure 2). Therefore, at least a degree of genetic diversity will be maintained, and the population can in principle recover faster than would be expected if a given genotype only gives rise to one phenotype. The advent of CRISPR-mediated genome-editing technology should allow formal testing of this idea in genetically identical animals. If this hypothesis is correct, then CRISPR-mediated genome editing of a given naturally occurring allele to another should shift the mean population value of a phenotype under the control of the edited gene, but there will still be individuals who have the same phenotype while carrying different alleles.

A study of individual left versus right walking preference in Drosophila demonstrates that preference variabilityrather than the actual walking preferenceis the heritable trait [START_REF] Ayroles | Behavioral idiosyncrasy reveals genetic control of phenotypic variability[END_REF]. Specifically, the authors found that individual flies repeatedly preferred to walk to the right or to the leftor showed no preferencewhen given a free choice in a Y-maze. The population thus displayed variation across a handedness-preference mean. When 'left-handed' (or 'righthanded') flies were crossed with each other, the offspring regenerated the entire range of handedness behavior, with no change in the mean handedness of the population. Remarkably, QTL mapping identified a developmental synaptic connectivity gene whose function affects the variability of walking handedness across the population, but not the mean population performance. What is perhaps more remarkable is that the gene identified as a locus of handedness variabilityencoding a protein of the teneurin familyis often cited as a prime example of a molecule that mediates invariable and deterministic synaptic matching in the fly olfactory system [START_REF] Hong | Teneurins instruct synaptic partner matching in an olfactory map[END_REF]. Interestingly, a recent study provided a quantitative characterization of wiring variability in the fly olfactory system [START_REF] Tobin | Wiring variations that enable and constrain neural computation in a sensory microcircuit[END_REF]. The authors identified imprecisions due to inherently (Bottom graph) The same two genotypes with noisy genotype-phenotype mapping. Greater variation (wider distributions) around the same mean may allow more individuals (grey area under red curve) to survive selection pressure (yellow area).

noisy development (which they call 'noise') or due to plastic changes (e.g., homeostatic compensation, which they call 'signal'). However, as discussed here, we note that such variability in the outcome may in some cases also be advantageous for the fly or the population.

Similarly, another recent study provides an exquisite example of an intrinsically noisy neurodevelopmental process in Drosophila in which both variable and invariant outcomes co-occur [START_REF] Enriquez | Differing strategies despite shared lineages of motor neurons and glia to achieve robust development of an adult neuropil in Drosophila[END_REF]. In this case, the same progenitor can produce motor neurons predictably with high precision and glial cells with high variability. The authors make a strong case that this coordinated 'hard wired motor neuron generation and flexible glia production' contributes to the robust development and evolution of neural circuitry. In sum, while it is obviously true that the individual variants resulting from non-genetic variation are not selectable, variability itself is. This idea has also been formulated as a bet-hedging strategy: the same genotype 'bets' on possible selection pressure with a distribution of phenotypes [START_REF] Honegger | Stochasticity, individuality and behavior[END_REF]. From the perspective of neural development, intrinsically stochastic processes can produce a wide range of phenotypically selectable variability in circuit connectivity and behavior from a narrower range of pre-existing genetic variants. Hence, individuals from more genotypes can be successful if non-genetic variation is larger during development.

Concluding Remarks

We have discussed how noise, variability, and robustness are intimately linked in neural development, exactly as they are in evolution (see Outstanding Questions). Specifically, reproducible precision can be the outcome of noisy development in particular when robustness is a selective advantage (first question). Conversely, the genotype-phenotype map will allow for variability if that variability itself represents a selective advantage (second question). Hence, both noisy development and variability in the outcome can contribute in different ways to evolutionary diversity (third question).

Our discussion draws an analogy between developmental and evolutionary robustness. In the example summarized in Figure 1, larger variation in filopodial exploration leads to increased 'wiring success'. In this example, the noisy entities are the filopodia and the robust outcome is dendritic growth [START_REF] Niell | Theoretical analysis of a synaptotropic dendrite growth mechanism[END_REF]. At a level higher, the variable entity can be neurons and the robust outcome is network behavior, as shown for rhythms in small neural circuits, for example [START_REF] Marder | Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms[END_REF]. In the case of phenotypic variability of neural circuits and animal behavior, the robust outcome is population behavior (Figure 2). As such, neural development may be no different from other developmental processes, but it is the variability and robustness of neural development that most profoundly influence personality! Thus, as Jean-Jacques Kupiec argues [START_REF] Kupiec | L'Origine des Individus[END_REF] much as random genetic mutation constrained by natural selection underlies the origin of speciesmolecular noise, including random somatic mutations, constrained by simple developmental rules, may underlie the origin of individuals.

Outstanding Questions

To what extent is reproducible precision in neural circuits the result of noisy development?

How precise is genotype-phenotype mapping for brain wiring; in other words, how variable can neural circuit wiring be given identical genes?

To what extent does variability based on identical genes contribute to evolutionary diversity?

Figure 1 .

 1 Figure 1. Developmental Robustness. (A) Directed growth of axonal or dendritic arbors may occur with little random

Figure 2 .

 2 Figure 2. Evolutionary Robustness. (Top graph) Two genotypes A and B with precise genotype-phenotype mapping.

Table 1 .

 1 Operational Definitions and Examples for Key Terms

	Term	Definition	Examples
	Stochastic (or 'truly random') process	A process in which at any point in time the precise	Dice roll. For each roll of a 'fair' dice, the probability of each of
		state or value is (i) unpredictable and neither depends	the six outcomes is exactly 1/6 and does not depend on
		on (ii) previous values or states of the system, nor on	previous throws of the dice.
		(iii) an inherent bias of the system. We use the term	The meiotic segregation of chromosomes. The distribution of X
		stochastic synonymously with random.	and Y chromosomes is 1/2 and does not depend on previous
			'drawings'. Notably, there are factors that bias this outcome
			and there remains doubt as to what extent biological
			processes in general are truly stochastic. See noisy process.
	Noisy (imprecise, non-deterministic
	or probabilistic) process

Acknowledgments

We thank Drs Sophie Armitage, Jens Rolff, Ursula Habenicht, and Ariane Ramaekers for comments on the manuscript and all members of the laboratories of P.R.H. and B.A.H for discussion. This work was supported by an Einstein BIH (Berlin Institute of Health) Fellowship to B.A.H. Work in the Laboratory of P.R.H. is supported by grants from the Deutsche Forschungsgemeinschaft (DFG; grants SFB958 and SFB/TRR186) and the National Institutes of Health (NIH; RO1EY018884). Work in the laboratory of B.A.H. is supported by the program 'Investissements d'Avenir' (ANR-10-IAIHU-06), the ICM, and an Allen Distinguished Investigator award from the Paul G. Allen Frontiers Group.


J M Dienot
email: jm.dienot@iut-tarbes.fr

Effects of Thermal Aggressions on Susceptibility Responses and Immunity Figures of PWM patterns

Keywords: Susceptibility, Immunity, Thermal, PWM, Nearfield, aggression, Temperature, Default criteria, TEM, VTOP1% DUTY1% VBASE1% Temp: 85°C

In embedded and on-board electronics context, environmental temperature has an influence on the real electromagnetic compliance and EMC figures. We present studies and results of temperature impacts on susceptibility and immunity figures. Specific dual thermal-electromagnetic set-up have been developed for this. A campaign of EMC-Thermal-parametric measurements has been realized on PWM patterns of digital PCBs dedicated for electronic drive and command. Temperature dependent susceptibility behaviors are presented, in the range of 3GHz for harmonic aggressions, that leads to discuss of new cases of EM sensitivity, couplings and immunity approach on electronic devices.

I. INTRODUCTION

For many years, previous experimental and simulation works try to estimate the realistic impact of external temperature on emissions and susceptibility cases of electronic devices [START_REF] Dienot | Experimental study of thermal influence on EMC emission of digital circuit on PCB[END_REF]- [START_REF] Dienot | Real-Cases of Electromagnetic Immunity and Reliability in Embedded Electronics Architectures[END_REF]. EMC effects and High temperature can be inherently generated around electronic devices, in technology as Smart Power ICs, High Power modules and Driver Chips [START_REF] Hoene | Simulating electromagnetic interactions in high power density converters[END_REF] [START_REF] Weber | EMI Couplings from Automotive Traction Systems[END_REF]. An aggressive, external, quasi-static temperature, with high values as 150°-200°C, can be inherently generated inside and around an electronic chip, either by motion thermal systems(Car), or by high-power chip's consumption and radiators associated (Processors, Power Converters).

Actual state-of-the art of radiated EMC characterizations, both emission and immunity, can be performed over Printed Circuit Board(PCB) and Integrated Circuits(IC) with Near-Field scan table [START_REF] Baudry | Applications of the Near-Field Techniques in EMC Investigations[END_REF] [START_REF] Slattery | Near-field measurements of VLSI devices[END_REF] and/or Transverse Electro-Magnetic (TEM) Cells [START_REF] Muccioli | Investigations of the theoretical basis for using a 1 GHz TEM cell to evaluate the radiated emissions from integrated circuits[END_REF]. In these two cases, often dedicated PCB's are especially designed, inherently for TEM cell, to comply with Standardized Cell Aperture (10cm*10cm), and to separate inside/outer electromagnetic sources and victims [START_REF] Muccioli | Investigations of the theoretical basis for using a 1 GHz TEM cell to evaluate the radiated emissions from integrated circuits[END_REF].

To accede to parametric thermal characterization, we propose improvements of these radiated test set-ups, with a combination of warming device solution, up to 250°C, inserted in the Near-Field or TEM benches, and spatial or on-board temperature acquisition systems. Near-field and TEM mode aggression cases are described, and specific test PCBs, including the devices and both electromagnetic and temperature sensors, are carefully designed for this. To perform the dual thermal-immunity test, we start on reference immunity behavior of gate devices and integrated circuits, with failure's criteria that are representative of the component feature. Pulse Width Modulation (PWM) pattern characteristics, in both time/frequency domains, are well representative of significant and critical immunity cases. For example, in driving DC/AC currents in converters, transformers and motors, a slight shift in nominal duty cycle rate (α) less than 1%, can induce a severe fail in the command tasks and current injection.

We present susceptibility responses of PWM circuits to both harmonic and temperature aggressions, and try to identify the impacts on main PWM signals characteristics. With this experimental approach, impacts of temperature on the coupling's mechanisms over the PCB's wires and inside the devices can be identified and analyzed to improve immunity solutions closed to real conditions.

II. NEW THERMAL-IMMUNITY METHODS

A. Near-Field aggression test bench

Separate E-Field and H-field measurement or injection, considered as Near-Field approach, are realized over different areas of PCB with dedicated probe's set like H-spires and Edipoles, and associated to a motorized table system. Electromagnetic probes have been fabricated with highfrequency semi-rigid coaxial cable to inject RF power from MHz until 3GHz [START_REF] Dienot | Dual experimental approach for thermal impacts on electromagnetic behavior of electronic circuit board configurations[END_REF]. A warming plate, using inductive heating, is used to generate temperature until 300-350°C over a fixed glass area. It is placed under the PCB, with a specific conductive test support. A thermal contact probe, with a touch end of 0.1mm diameter, and a thin body support of 8cm long, has been coupled on the same scan table moving fixture, with a different Z-axis reference, as seen in Erreur ! Source du renvoi introuvable.. When moving, and positioning the measurement point, thermal probe stays in with the body of the electric element, as near-field probes are just over. With this configuration, we can inject localized RF power at specific or sensitive area and wires of a PCB test, and relate it with the local real temperature of the injection zone. Some rigorous calibrations procedures must be completed before, because of the mutual influence of the EM probe and Thermal Probe. The warming plate can also modify the real level of injection of the probe. During the development of this set-up, we use a Microstrip receptor as a reference calibration. We observe that the shift in RF level injected can be about a maximum of 1.2 to 1.5 dB at high temperature. These discrepancies, between level injected from the generator and the victim, is used as a correction factor for a good validity of the experiment.

To complete the set-up, a IR-camera has been inserted, with a specific fixture, to have a 2D measurement of real temperature repartition on the PCB the EM and Thermal probes, and other elements in the flux of the heating [START_REF] Nguenche | Mise en oeuvre d'un système d'acquisition thermographique 3D pour la caractérisation CEM Multi-physiques de modules électroniques[END_REF].

B. TEM Cell aggression test bench

Transverse Electrical-Magnetic Cell (Crawford TEM cell) or GTEM (GHz TEM) are commonly used for EMC characterization, from MHz up to 10GHz, at PCB and Integrated Circuits levels [START_REF] Muccioli | Investigations of the theoretical basis for using a 1 GHz TEM cell to evaluate the radiated emissions from integrated circuits[END_REF][13] [START_REF] Gao | Integrated EM immunity design and diagnosis system for electronic devices[END_REF]. As a well-suited alternative to large size experimental equipment for conventional radiated far field characterization, it allows very pertinent solutions for selective electromagnetic characterization of single electronic devices enclosed in the shielded cell environment. For this, special prototype of Printed Circuit Boards must be designed for the use in TEM cells, with the respect of three constraints: the dimension of the aperture of the cell, the completion of shielding quality of the system with a one-face metallic plane, and the choice of inside-components to be coupled with TEM Cell Septum in TEM modes.

Starting from this configuration, a special fixture arm has been realized, so to maintain both the PCB -TEM Cell device over the warming plate, at a height of 4cm, so to keep efficient heating action (Fig. 2). The new constraint is to place electrical and thermal connections very close to the PCB, and with 90° angle, so to avoid direct contact with the hot warming plate. Acquisition of real external temperature close on board is realized by thin thermal resistor in SMD or Thin Film technology. A special attention has been made, for pertinent immunity measurements, with the thermal routing network [START_REF] Dienot | Dual experimental approach for thermal impacts on electromagnetic behavior of electronic circuit board configurations[END_REF]. A specific roadmap procedure and computational algorithm has been developed to drive the experiment and all the postprocessing data's. As for the previous experiment, to refine the measurement of real temperature distribution all over the test board, the IR-camera system has been developed and inserted on this set-up. This improvement is especially helpful for TEM Cell characterization, both for calibration and to rely the different internal and external temperature on the PCB surface and on the TEM cell.

III. APPLICATION ON PWM CIRCUIT BOARDS

A. Susceptibility tests on PWM patterns

Main applications of control boards concern the fine drive of power converter designed for well-suited motion or energy supply function [START_REF] Hoene | Simulating electromagnetic interactions in high power density converters[END_REF], where high variation of temperature is clearly present. We want to focus on the more realistic EMC behavior of these circuits with non-ambient temperature environment. Some PCB prototypes have been designed for these studies, using either SMD chips reported on PCB, either Programmable Integrated Circuits type with Pulse Width Modulation pattern inside. PWM generators are controlled by cyclic rate input command.

Main susceptibility aspects are generally, for digital mode device, the drifts of thresholds levels and switching times, due to the couplings of external parasitic signals on supply and I/O ports [START_REF] Pues | A Black-Box Measurement-Based Modeling Method for the RF Emission and Immunity Behavior of ICs[END_REF]. Result of EM aggression show significant shifts in nominal characteristics of the output signal, in time domain. In consequence, the relative amplitude of waveform of current switching device, IVDD, has significant shifts with both harmonic frequency and temperature aggression. The main significant effect is related to the potential shift of average signal during a PWM sequence, normally designed by the cyclic rate, so to drive current injection in power switches. So, IR Cam.

Temp. Control.

for our main immunity criteria, we choose to observe both discrepancies, in the frequency domain, with the survey of the spectrum waveform of the output switching current for example, and in time domain for main parameters as Duty cycle rate of the Output signal, as illustrate in Fig. 3 . The EM aggression presented here have been realized in harmonic mode, using an Amplifier-RF source system. Power injection is realized from 1MHz to 3GHZ, with a maximum level of 40dBm. Susceptibility effect and Immunity test validation of the device are determined by the variations of the output signal: cyclic rate characteristics (time-domain, digital oscilloscope) and switching current frequency characteristics (frequency domain, spectrum analyzer), outside the range of default.

B. First demonstrator: Integrated PWM Circuit

The first study concerns a PCB with a PWM Integrated Circuit and electrical network up on one layer, which has been placed on dual thermal-EM near-field bench (Fig. 4). The level of supply is VDD=5V, provided by a high-speed current switching voltage source, in respect with internal IC consumption time rate. Programmable circuit operates in synchronous mode, with a clock reference of 5MHz. Two inputs are used to modulate the output square signal, with an absolute cyclic rate from 5% to 46% (Input 2) and inversion mode (Input 3). Signal output is delivered on internal capacitance load (500fF) in parallel to external capacitance load(1pf). For our study, coupling the wave aggression impact with temperature, we look especially on the shift in frequency and amplitude of main peak of the current consumption spectrum: relative amplitude of waveform of current switching device, IVDD, is reported with significant harmonic frequency impact couplings, at ambient temperature, in the 100 MHz-800MHz zone (Fig. 5). This variation is enforced when increasing, step by step, the external temperature and so the device package measured temperature. This indicates and confirms the modifications of switching current performances, and more significantly, an impact of high external temperature on electrical behavior of the programmable chip under electromagnetic pressure. of supply is VDD=5V. The nominal frequency of the two PWM is f0=10kHz. Four main default's criteria are defined for these test: the shift on duty cycle rate α, on frequency f0, on switching margins VTOP-VBASE, and on the mean value VMEAN. This board has been tested with the TEM cell/thermal configuration, represented in Fig. 6. The two output signals, PWM00 and PWM01, have nominal characteristics at 20°: f0=10kHz, Vpp = 4.65V, a1= 71.3%, a2= 27.43%. A digital wide-band and high sampling rate oscilloscope realizes the acquisition and the control of these parameters. Each default's criteria are tested independently, in the range of 10% to 1% of their nominal value (TABLE I. . Then, EM aggression is realized, by sweeping the frequency between 1MHz and 3GHz, and the levels of RF power from -40dBm to 40dBm. The first step is to acquire a susceptibility figure at ambient temperature, when the warming plate is OFF. This first figure shows the susceptibility responses of our PCB, for the four criteria's chosen. A main common sensitive zone is depicted in the range of 300MHz-500MHz. At 600MHz, we have a specific susceptibility effect, with some criteria's as VMEAN that is less sensitive to EM aggressions. This is due to coupling modes and resonances that are enforced in this range of frequency. This first test, realized at ambient temperature(20-22°C), is the reference susceptibility test presented in Fig. 7. Immunity table reference(20°C) for the four criterias: à duty cycle α £ frequency jitter Δ Switching margins • VMEAN Then, in a second way, we repeat the experiment with steps of temperature of 20°. At About 90°, the shifts of PWM characteristics over 1% are continuously due to this temperature, because of the high impact of temperature on semi-conductor on the board. Among a wide number of parametric results, depending both of frequency, injection levels, temperature steps, and the kind of defaults, we present a synthetizes of the main significant results, with parametric Immunity figures as following

As the apparition of a default on the duty cycle with a maximum shift of 1% is critical for our applications, Fig. 8. is dedicated to this parameter. Compared to the reference measure at 20°C, it's significant that the levels of EM aggression for the "cyclic rate criteria" are lower of about 10 to 20 dB, in some narrow range of frequency, as 200 MHz, 700 MHz, and a minimum for all the temperature at 900MHz (GSM Band!) Fig. 8. Immunity table at temperature steps of 20°C for criteria "1%" on duty cycle α

The second main result of these immunity investigation is presented in Fig. 9. This is a comparison of susceptibility effects at the worst case of thermal aggression, about 85°C, with IC still in normal activity. The effects of dual EM-Thermal aggressions for both five criteria's of PWM susceptibility have been represented, in 3D-view, so to be compared: Duty@10%, Duty@1%, VTOP@1%, VBASE@1% and VMEAN@1%. Table I resumes the criteria considered and the range of the nominal values controlled during dual electromagnetic-thermal aggressions.

This figure shows a real global shift of the sensitivity of the PCB and the PWM signals, at the maximum allowed temperature of test (85-90°) of the experiment. The previous sensitive zones are all enforced (280 MHz / 500 MHz/ 720 MHz/850Mhz), for all the criteria's. Also, the most sensitive signal parameter at this temperature is the Mean Value (VMEAN) of the PWM, which is unfortunately the worst case of integrity or robustness of the nominal specification of the PWM pattern for driving. Some narrow range of frequency becomes very sensitive and very weak (@250MHz), that indicates that the couplings of external RF Wave is maximum on the PCB, due to the action of temperature on both electrical resonances and shift of the Chip's impedances and switching margins. IV. CONCLUSIONS With these works, new modified EMC characterization approach is in progress, for real-case EMC investigations. Specific test benches have been developed based on conventional Near-Field and TEM cell immunity test setups. External aggression of light range of temperature (20°-100°) has been correctly added, so to combine both EM-Thermal effects on susceptibility of electronic chips on PCB. The first test bench (Near-Field) is dedicated to conventional PCB, with the need of localized EM injection and temperature measurements, often on the component-face of the PCB. The second one, using a TEM cell, is dedicated for demonstrator PCB, where specific design and routing of chips and thermal sensors must be initially performed for the test. A focus has been made on immunity cases on PWM signals, which need to be well driven for main applications. After a measurement campaign that has produced a wide range of different susceptibility responses of the demonstrators, main significant results are synthesized in this work. These parametric immunity cases for PCB boards confirm a main influence of temperature on susceptibility levels of programmable or discrete chips: some critical defaults, as the shift of more than 1% of the duty cycle rate or Mean value VMEAN, are very sensitive with a nonambient temperature, and critical for immunity of these applications.

With this review of thermal-immunity experimental study on PCB, some refinements and calibration progress of the two set-ups must be completed: the mutual influence on measurements and aggression of both TEM Cell, Near-Field probes and Thermal probes must be considered. In parallel, modeling investigations are also actually performed to try to understand and reproduce these effects of external temperature on EMC characteristics (emission, susceptibility) on electronic PCB, as already initiated for Emissions in [START_REF] Dienot | Characterization and simulation of digital device electromagnetic noise under non-ambient temperature conditions[END_REF]. With this modeling completion study, a first complete review of new EMC behavior cases dealing with new embedded and hybrid technology constraints will be validated, so to promote the merging of new concerns of EMC approach on electrical transport and embedded applications [START_REF] Dienot | Real-Cases of Electromagnetic Immunity and Reliability in Embedded Electronics Architectures[END_REF]

Fig. 1 .

 1 Fig. 1. Schematic of the experimental dual thermal-near field set-up configuration for immunity testing on conventional PCB.

Fig. 2 .

 2 Fig. 2. 2D schematic of Heated TEM-Cell configuration for immunity testing on 10cmx10cm PCB.

Fig. 3 .

 3 Fig. 3. Views of signal shifts on nominal PWM waveforms during harmonic aggression.

Fig. 4 .

 4 Fig. 4. Upper view of the layer of the first PCB configuration

Fig. 5 .

 5 Fig. 5. Relative variation of switching amplitude of Integrated PWM circuit with dual thermal-harmonic wave aggressions

Fig. 6 .

 6 Fig. 6. View of the heated TEM-Cell configuration for immunity testing.

Fig. 7 .

 7 Fig. 7.Immunity table reference(20°C) for the four criterias: à duty cycle α £ frequency jitter Δ Switching margins • VMEAN

Fig. 9 .

 9 Fig. 9. 3D table representation of worst-case's immunity with PCB temperature of 85°C, for 5 criterions of the PWM: Duty10%, Duty1%, Vtop1%, Vbase1%, Vmean1%

TABLE I .

 I PWM CRITERIA'S VALUES.

	PWM parameter	Nominal Value	Range
	Duty Cycle a min	27.42 %	24.67 % / 30.16 (10%)
			27.14%/27.69%(1%)
	Duty Cycle a max	71,3 %	64.17 % / 78.43 (10%)
			70.58%/72.01%(1%)
	VTOP	4.65 V	4.6V/4.69V
	VBASE	0.01 V	-0.05V/+0.05V
	VMEAN (a min)	1,265V	1.25V/1.277V
	VMEAN (a max)	3.348V	3.31/3.38
	Frequency	9.67 kHz	9.57kHz / 9.76kHz