Because biological networks exhibit a high-degree of robustness, a systemic understanding of their architecture and function requires an appraisal of the network design principles that confer robustness. In this project, we conduct a computational study of the contribution of three degree-based topological properties  and their combinations on the robustness of transcriptional regulatory networks. We seek to quantify the relative degree of robustness conferred by each property (and combination) and also to determine the extent to which these properties alone can explain the robustness observed in transcriptional networks.E. coli gene regulatory networks. Robustness of these networks were estimated through simulation. Our results indicate that the combination of the three properties we considered explains the majority of the structural robustness observed in the real transcriptional networks. Surprisingly, scale-free degree distribution is, overall, a minor contributor to robustness. Instead, most robustness is gained through topological features that limit the complexity of the overall network and increase the transcription factor subnetwork sparsity.To study individual properties and their combinations, we generated synthetic, random networks that retained one or more of the three properties with values derived from either the yeast or E Coli, which suggests that the design principles examined are present within an array of living systems.Our work demonstrates that (i) different types of robustness are implemented by different topological aspects of the network and (ii) size and sparsity of the transcription factor subnetwork play an important role for robustness induction. Our results are conserved across yeast and  Robustness to evolutionary and environmental perturbations is widely regarded as an important feature of living systems. DespiteWhile unveiling the exact origin of regulatory network robustness is a topic of active research, there is a growing consensus that the structure of the network itself confers a significant degree of robustness, irrespective of the precise biochemical properties of the individual interactions comprising it. This belief is bolstered by the conservation of (1) several large-scale topological properties and 2) certain motifs  within transcriptional regulatory networks across an evolutionarily-diverse array of species e.g.,-11). Fur. Fur11]) certain While this approach has yielded significant insights into design principles of robustness, such individual analyses do not permit evaluating the relative contributions of different topological features to the overall robustness of a network. Without such knowledge, it is difficult to rank the relatively major and minor sources of robustness — an important part of understanding the design principles employed by evolutionary processes. To achieve such a comparative perspective, the robustness of each feature of interest must be evaluated within a single framework and, furthermore, the robustness of the overall network of interest  must also be estimated. These are the foci of the present study.1 to transcriptional network robustness against random perturbation and mutation. In doing so we obtain quantitative insights into the relative robustness conferred by different topological features and, in particular, we demonstrate that the relatively high degree of robustness in scale-free networks is mainly conferred by the relative scarcity of regulatory nodes in such networks. We compare the relative contributions of these features to the structurally-derived topological robustness of two transcriptional networks, E. coli and yeast.In this paper, we evaluate and compare the contributions made by several individual and combinations of first-order degree-based topological featureshow much robustness is derived from the different degree-based properties, irrespective of how they come to be in the network. Said differently, it is certainly important to know how structures come to be present in a network, but here we are simply interested in characterizing the extent to which structures that are present contribute to the robustness of the network. Adding an evolutionary context to the present study is an exciting and important direction for future work.It is important to note that we are intentionally conducting this analysis without considering the evolutionary processes that may have produced the features being considered. We have done this in order to approach, as precisely as possible, the question of E. coli and yeast transcriptional networks can be explained through limiting the complexity of the overall network and maintaining sparsity of the inter-regulator-links, rather than by imposing a scale-free degree distribution on the network. Finally, we determine that combining the individual topological features considered generally produces significant, but incremental improvements in robustness.In comparing the robustness of different topological features, we make a number of novel findings. First, we obtain strong evidence that robustness against three different types of perturbations often considered in literature  are implemented by different combinations of topological features. Second, we show that a transcriptional regulatory system with a small number of regulators acting semi-independently  is capable of robustly retaining its mRNA expression vector. Furthermore, a substantial portion of the robustness observed in the The comparison of the robustness conferred by certain topological features required 1) identifying the topological network features to consider, (2) formalizing the types of robustness to consider, (3) developing methods to generate synthetic random networks preserving the topological features of real networks, and (4) establishing a way to compute the robustness of arbitrary directed networks under a model of transcriptional network dynamics. We discuss each design consideration briefly before presenting results. Complete details are available in the Methods section and the Additional file identifyWe considered three salient first-order degree-based topological properties of transcriptional regulatory networks: (1) transcription factor to target (TF-target) ratio, (2) scale free-exponential (SFE) degree distribution , (3) suppressed cross-talk among the TFs (TFs have fewer inter-connections than would be expected by chance),18. ThesOut of these three properties, the SFE property is widely regarded as a robustness inducer as scale free networks have greater resilience to random node removal than unconstrained random networks,12,16. Hcross-talk suppression. This can be considered a feature that participates in decreasing the error propagation: having too many inter-connections among transcription factors hurts modular organization and can eventually increase the error propagation between different parts of the network[In addition to relative scarcity, we observe that transcription factors exhibit less inter-connectivity than would be expected by chance, a feature we call  network. Availab network,23-26. TE. coli and yeast transcriptional regulatory networks [As the reference networks for this study, we used published interaction maps of etworks),25. Tabletworks), the pubetworks). Neitheretworks). But as Closely following prior work, we considered three kinds of robustness: (1) knockout robustness (against the deletion of random nodes in the network), 2) parametric robustness (against changes in the strength of interactions), and (3) initial condition robustness  parametr,29. Broatarget property/properties of the generative method and its networks). Each generative method was used to produce a set of 1000 networks . The specific values for the target properties of an ensemble were drawn from their respective reference network: e.g., the TF cross-talk ensemble for the yeast reference contained networks that had the same amount of TF cross-talk as in the yeast reference, but had random topology in all other respects. Random weights were assigned to interaction edges, respecting only the activation-repression ratio (the ratio between activating and repressing interactions) of the appropriate reference network. Note that the activation-repression ratio is unknown for the Yeast network. We determined, however, that the choice of activation-repression ratio does not effect the relative ordering of the ensembles based on their robustness and therefore, does not affect the conclusion of our work . Finally, in all cases the size of the network (number of nodes and edges) was set to the size of the reference network.In order to assess the robustness conferred by a specific single or combination of topological properties, we developed methods for generating networks with those individual or combinations of properties , meso-features such as community structures and higher-order degree-based features (such as degree assortativity). In order to achieve this, we created a shuffled network ensemble where the edges of the reference network were switched to remove any local clustering, keeping all the degree based features invariant. Then we randomly assigned edge weights and initial expression level of the genes keeping to construct a shuffled network ensemble. Networks in the ensemble retain all the first-order degree based features: the three features described as well as the indegree-outdegree-combination (the 2-tuple defining the in and out-degree of a gene) of each gene in the network. The shuffled network ensemble is the directed equivalent to the configuration model random graphs and has The dynamics of each network in these ensembles were simulated using a standard discrete-time, boolean network dynamics model based on. The staRobustness of a single transcriptional regulatory network against a specific type of perturbation can be defined as the the probability that a perturbation of that type does not alter the final output state reached by the network (assuming a fixed starting state),15. ThusAs the networks in an ensemble can originally reach either steady state or oscillatory state, we introduced separate measures of robustness to distinguish these two cases: steady state retention ratio (SRR) and oscillatory-state retention ratio (ORR), respectively. SRR (ORR) of a network originally reaching a steady (oscillatory) state refers to the fraction of perturbations for which the steady (oscillatory) state vector remains invariant even after the perturbation. For a network ensemble and each perturbation type , we compute the SRR or ORR values for each network contained in it using 100 different random perturbations of the same perturbation type applied to each network within the ensemble. If the network originally reaches a steady state, the SRR of the network is the fraction of these 100 perturbations that produce the same unperturbed steady state vector after perturbation. ORR for a network against a perturbation type can be computed in a similar manner for the networks reaching oscillatory states. It is noteworthy that both SRR and ORR measures of robustness yielded the same results and conclusions presented in this paper.robustness profile for a given perturbation-reference pair. Each individual bar represents the average SRR (or ORR) value for all networks in the ensemble reaching a steady (or oscillatory) state. The error bars report the standard deviation of the SRR (or ORR) measure for the corresponding ensemble. For knockout perturbations, one node knockout has been considered; for parametric perturbation, the weights have been perturbed by 0.05 (1% of the average edge weight); for initial condition perturbation, 1% of the values in the initial state have been flipped. Note that we have confirmed that the trends we report hold for different perturbation amplitudes, different ways of implementing the underlying perturbations and different definition of robustness.The robustness (in terms of SRR and ORR) of different ensembles for different perturbations are reported in FigureE. coli, Figures% of all binary relative robustness score relationships are conserved between yeast and E. coli in their SRR profiles for knockout robustness (92.85%for ORR profiles). Conservation of relationships are similarly high for parametric robustness (96.42% for SRR and 89.28% for ORR) and initial condition robustness (92.85%for both SRR and ORR).Comparing the profiles for each perturbation type across species, we observe that the overall shape of the profiles are strongly conserved  compared to the ER networks, but it is significantly lower than the corresponding values observed in the networks retaining the TTR property, which indicates the SFE property is not sufficient to explain the robustness observed in the networks. For initial condition robustness, however, SFE does not increase or decrease robustness significantly. When the SFE degree distribution characteristics is added to a network that preserves other properties, we see a insignificant increase in the knockout robustness. For parametric robustness, the increase is also insignificant for the E. coli ensemble that already preserves both the TTR and CTR properties. Overall, the SFE degree distribution property does positively influence robustness to some extent, but its impact is minor compared to that of cross-talk ratio and the TF-target ratio. This finding is consistent with previous work[The scale-free topology has been widely acknowledged as a major robustness inducing factor in regulatory networks,16,17. Ious work,20.It is worth pointing out that the robustness induction effect of transcription factor to target ratio (TTR) is hardly surprising. A system with a relatively small number of transcription factors will be more robust against random knockout of genes simply because such a random knockout will rarely hit a transcription factor. Similarly, a random change of initial condition affecting only the target genes does not have any impact on the final state reached by the system. However, the novelty of our finding lies in our demonstration that this property can account for a substantial portion of knockout and initial condition robustness that was previously attributed solely to scale-free-exponential distribution.p < 0.001) improve robustness compared to the ER networks. Furthermore, the networks that retain both these properties induce even greater knockout robustness. For parametric perturbations, CTR is a stronger individual contributor to robustness than TTR or SFE. The introduction of suppressed CTR to a network that preserves the TTR or TTR+SFE properties significantly (p < 0.001) boosts the robustness (SRR/ ORR) values for both yeast and E. coli networks. Note that the magnitude of impact of cross-talk ratio property differs between the yeast and E.coli references. However, the residual effect of the CTR on networks preserving TTR and TTR+SFE properties remain similar. For initial condition robustness, TTR boosts the robustness for both E. coli and yeast networks. CTR, on the other hand, significantly decreases robustness when applied to a network that preserves other properties.As described above, the TTR and CTR properties are major drivers of robustness in the regulatory networks we studied. For knockout perturbation, both TTR and CTR significantly , while abundance of transcription factors (TTR) does not directly render the network more or less susceptible; this explains why CTR is a sole major influencer over this type of robustness.Under initial condition perturbation, the values of a subset of nodes are being changed in the initial state. A small value of CTR means transcription factors tend to drive genes independently: thus genes are affected by one or a few TFs, which makes these networks more robust against small random perturbations to the initial state. On the other hand, if the transcription factors are highly connected, the effect of changing a gene’s initial state can be neutralized by the impact of other transcription factors, which may explain the dual impact of CTR on initial condition robustness.It is important to realize, however, that absolute robustness against initial condition perturbation is not desirable because it produces a system that is unable to implement complex input/output relationships . This limits both expressiveness of the transcriptional system as well as adaptability and evolvability. TherefoThe shuffled network ensemble (rightmost blue bars) preserves all the independently considered first-order degree-based properties as well as the exact combination of in-degree and out-degree of the nodes, a property of the real network which is not preserved in other ensembles  different types of robustness are implemented by different topological aspects of the network, (ii) size and sparsity of the transcription factor subnetwork play an important role for robustness induction, and (iii) some degree-based features present in real transcriptional networks actually decrease their overall robustness. These conclusions are validated for a discrete time network dynamics model that was previously used to model the dynamics of the budding yeast cell cycle network and closAll three different types of robustness considered are biologically important. A transcriptional regulatory network should be resilient, at least moderately, against removal of random genes, change in interaction strength due to environmental or mutational effect and initial concentration variation due to environmental shifts. We show that these three types of robustness are engendered by different combination of topological properties and the impacts of a given topological property on three different types of robustness are different. This observation suggests that obtaining one kind of robustness may require a trade-off in terms of another form of robustness. For example, absolute robustness against initial condition perturbation is generally undesirable, for if a network’s output becomes invariant with the change of input, the system loses its functional flexibility. On the other hand, every system should be capable of adapting to small changes due to knockout perturbation. Therefore, the topological features can be evolutionarily tuned to have higher robustness against knockout maintaining an optimal level of initial condition robustness. Future investigations may explore how this trade-off is achieved by evolutionary constraints that shape the system.E. coli and yeast transcriptional networks can be explained through maintaining sparsity of the transcription factor subnetwork and limiting the complexity of the overall network.Prior work has shown that selection favors sparser biological networks to achieve robustness. Our woridentify and quantify the relative contributions of different degree-based features to transcriptional network robustness, we leave a thorough investigation into the cause of this correlation for future work. That said, we offer the following hypothesis that explains a mechanism by which IOC could plausibly decrease the robustness of a network.Quite surprisingly, our results show that for the parametric perturbation, the exact in-out degree correlations present in real transcriptional networks decrease the robustness of those networks to parametric perturbation. Notably, this is not the case for knockout and initial condition robustness: in both cases preserving IOC increases the initial condition robustness compared to all other ensembles. As our goal in this study was to As the Additional fileRobustness of biological systems against random mutations and environmental perturbations is a widely observed phenomenon. In this study, we assess the relative contribution of first-order degree-based network properties to the robustness of transcriptional regulatory networks. Through extensive simulations, we show that the scale-free-exponential degree distribution, in itself, is a minor contributor to transcriptional network robustness. Much of the effect it exerts can be explained by the relative abundance of target genes compared to transcription factor genes in such systems. Moreover, suppression of cross regulatory edges connecting two transcription factors has a profound impact on the robustness of the networks against certain perturbations. These three properties are sufficient to explain the amount of knockout robustness a transcriptional network derives from first-order degree-based properties; interestingly, the in-degree/out-degree correlations present in real networks account for a non-trivial portion of the parametric and initial condition robustness present.More broadly, our comparative approach to assessing the robustness conferred by individual topological features and present in reference, real-world networks enables us to ascertain, for the first time, the extent to which different topological properties (and their combinations) induce the robustness observed in these real-world systems. We consider this to be an important and essential step in better understanding the means by which robustness is implemented in transcriptional networks. Our approach may also be applied to the study of robustness in other networks, however they may arise. Thus, while we have applied our approach to transcriptional networks, other domains both within and beyond cellular biology may benefit from the use of such methods on their own complex systems.E. coli regulatory networks. The E.coli regulatory network, consisting of 1680 genes and 4144 interactions, was downloaded from the RegulonDB database (Release: 7.4 Date: March 2012)[As reference, real-world transcriptional networks, we used yeast and ch 2012). The yeach 2012).TF); all others we call targets. In addition, each interaction in the network is designated as being either activating (positive) or repressing (negative). It is important to note that the precise biochemical parameters for interactions are not known for large biochemical networks. As a result, the dynamics of the real and synthetic networks were estimated by generating an ensemble of networks with identical topologies, but parameter values drawn from a distribution.In these networks, all nodes correspond to genes. Those that regulate (have edges to) other genes are transcription factors . The TF-target ratio is the ratio of the number of TF-coding genes and the number of non-TF genes.The degree distribution is the allocation of interactions to nodes over the entire network. We consider the in-degree and out-degree distributions separately. For the reference networks, the in-degree distribution follows an exponential distribution but the out-degree is a power-law distribution. We refer to this degree distribution as Scale-Free-Exponential (SFE) degree distribution in the text.N and E denote the number of nodes and edges in a network and NTF and ETF denote the number of TFs and the number of edges connecting two TFs respectively, then the Cross-talk ratio (CTR) will be equal tokin〉 represents the average in-degree for TFs and for all the nodes respectively.This property refers to the ratio between the observed count of TF-TF interactions to their expected count in an equal sized random network having an equal number of TF-coding genes where edges can be formed independently between a TF as starting point and any gene (either TF or non-TF) as ending point. If E. coli activation-repression ratio value is used for the yeast ensembles as well. This property, along with the number of nodes and edges of the reference network, was retained in all the network ensembles.In a TRN, every interaction (edge) is either activating or repressing. The activation-repression ratio is the ratio of the number of activating edges and number of repressing edges. As the activation-repression information was not reported in the yeast dataset we used, or any other recent datasets,37,38, tn, the in-out degree combination (IOC) of the node is the two-tuplen respectively. The shuffled network ensemble contained networks which retained the IOC for each node in the reference networks.This property refers to the exact combination of in-degree and out-degree for each of the nodes in a network. Formally, for a node In order to determine how a specific topological property or a combination of properties influences robustness, we constructed different network ensembles (1000 networks per ensemble) that preserve a different set of properties of the original networks. For each combination of properties, we developed an algorithm that explicitly constrained only the value of those properties in the networks produced. Details for each property and combination considered are given in the Additional filet + 1 is dependent on the output of its TFs at time t and the weight of the TF interactions on the node. This leads to the use of nonlinear difference equations for modeling the dynamics of regulatory systems[We employed a network dynamics model that was used to model the dynamics of the budding yeast cell cycle network. Providi systems.a at time t + 1,t. We express this asTF(a) is the set of TFs for a, i.e. the set of nodes that have an edge to a. We chose the function f  such that f(x) = 1 if x > 0, f(x) = 0 if x < 0, andx = 0.In a regulatory network, the expression level of gene Thus, a gene is expressed  to 100 random perturbations (of the same type).For knockout perturbations, we randomly delete one or two nodes from the network; for parametric perturbation, we randomly add ±E.coli transcriptional network. Then we applied 1000 random initial state configurations on each of these networks and recorded the output states the networks converge to. The set of states where a network can reach through dynamical simulation defines the attractors of the system and the number of different initial conditions associated with a particular attractor state is an estimation of the size of its basin of attraction of the system. To determine the impact of network complexity on robustness, we also computed the knockout and initial condition robustness (in terms of SRR) for each network in the network ensemble.The purpose of the basin of attraction analysis is to ascertain how the number of transcription factors impacts the dynamical complexity of the network. We constructed an ensemble of networks consisting of 1000 networks preserving the average degree of the The computational work was implemented in Python. NetworkX was used to load, manipulate, and manage individual networks and Numpy was integral to the implementation of the simulator,41.1 By first-order degree-based, we refer to features that depend primarily on the degree and linking patterns of the node itself rather than on features that involve analysis of the linking patterns of two or more nodes, such as degree assortativity.TF: Transcription factor; TTR: Transcription factor to target ratio; CTR: Cross Talk Ratio; SFE: Scale-Free-Exponential; IOC: In-out degree combination.The authors declare no competing interests.Both FAZ and DR participated in the study design, analysis of results and writing the manuscript. The network generation and dynamical simulation frameworks were developed by FAZ. Both authors read and approved the final manuscript.Supplementary Information. In the supplementary information document, we discuss algorithms for generating the synthetic networks conforming to different random network models that have been used in our study and include some additional results to support the claims of our study.Click here for file


Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution. Adaptation is ubiquitous in the nervous system, from synaptic depression Since adaptation requires some form of memory and inference of the stimulus statistics to which the system should adapt, the mechanism and nature of adaptation have been studied extensively. For example, the dynamic structure of the retinal ganglion cell receptive fields Despite its ubiquitous presence, it is still not clear what are the limits to adaptation, and in particular, which stimulus changes should lead to adaptive responses and which should not. This is because adaptation, by its very nature, comes with an inherent caveat or cost: stimuli can no longer be read out from instantaneous responses of an adapting system, but can also involve responses potentially stretching far into the past (i) are there any signatures of adaptation to higher-order statistics, especially if spatially uniform stimuli that match the naturalistic range of skew/kurtosis are used instead of the spatial textures (as used by Ref (ii) do changes in higher-order stimulus statistics affect the cells' rate of information coding; and finally, (iii) what would be theoretically expected changes for LN-type neurons in response to changes in higher-order stimulus statistics if the neurons were maximizing the amount of transmitted information.Spatial textures were used previously to study the responses of cat LGN neurons to stimuli containing higher-order statistical structure To characterize adaptation to stimulus statistics beyond luminance and contrast, we studied retinal responses to spatially uniform stimuli where light intensities were drawn independently from distributions with tunable amounts of skewness and kurtosis. We organized our analysis as follows. First, we report in detail on our choice of stimuli; next, we use 2D linear-nonlinear (LN) models to characterize the cells' responses, and analyze in detail the changes in the linear (L) stage when higher-order statistics change, followed by the analysis of nonlinear (N) stage changes. To assess the functional significance of these changes, we compare them to changes induced during contrast adaptation. We conclude by examining theoretically optimal LN coding of higher-order statistics stimuli, and compare these predictions to data.To sample the range of naturally occurring values for contrast, skewness and kurtosis, we took a sample of 501 calibrated grayscale images from the Penn Natural Image Database (PNIDb) In our analyses, contrast is defined as Ambystoma tigrinum) 2, 5% CO2) Ringer medium which contained 110 mM NaCl, 22 mM NaHCO3, 2.5 mM KCl, 1 mM CaCl2, 1.6 mM MgCl2, and 18 mM glucose, at room temperature. The electrode diameter was 10 µm and electrode spacing varied between 40 and 80 µm. Recordings of 24–30 hours were achieved consistently. Extracellularly recorded signals were amplified , digitized at 10 kHz on four personal computers and stored for off-line spike sorting and analysis. Spike sorting was done by extracting from each potential waveform the amplitude and width, followed by manual clustering using an in-house program written in MATLAB  at a frame rate of 60 Hz such that each stimulus frame was presented twice in a row (for a stimulus sampling rate of 30 Hz) using standard optics. This rate was chosen because it has been shown previously that it is roughly the slowest rate that is still sufficiently high for linear filter estimation using full field flicker stimulus  We performed two experiments. In the first (23 cells), all 9 stimuli were displayed in long, non-repeated sequences  Here The filters extended over For performance reasons we estimated To quantitatively compare the shapes of the filters across stimuli in experiment 1, we needed to ensure that each stimulus condition had enough spikes for good filter inference. We required each cell to have an average firing rate of at least To estimate an error on our determination of linear filters, and specifically on the balance index After having reconstructed the linear filters In the framework of LN encoding models, one assumes that only a small number The information was estimated from Eq (2) with rates computed in separately to each stimulus condition separately to each stimulus condition globally to all stimulus stimuli For all neurons recorded in experiment 2 (with non-repeated and repeated stimuli), we computed several information-theoretic quantities: (i+ii) The biphasic filter was parametrized by two parameters To computationally simulate the effect that the (lack of) adaptation would have on the information rate when the stimulus statistics changes, we used the LN models inferred at high contrast C++ to predict the firing rate To characterize how the retina encodes higher-order statistics (HOS) of the luminance distribution, we presented it with a set of 9 synthetic spatially homogenous stimuli ean  see ; Table 1To quantify how retinal neurons change their code when contrast, skewness, or kurtosis of the stimulus change, we constructed accurate encoding models for the recorded neurons, and compared their properties under the different stimuli. We thus followed Ref We recorded from 23 retinal ganglion cells that were presented with 9 types of non-repeated stimuli global model for each cell, where a single set of filters was fit across all stimulus conditions  captured must be higher or equal to the information captured by the joint model, by construction; we next asked about the significance and magnitude of this difference. In all skewed conditions , the median differences were small  of the stimulus into the cell's firing rate. We estimated these 2D nonlinear functions from the data by binning  in  see . This fiDoes the nonlinearity change with the stimulus condition? The number of spikes is in general insufficient to reliably sample and then systematically compare the 2D nonlinear functions across cells and stimuli. We thus decided to base our comparisons directly on the firing rate prediction performance. The 2D models for cells in experiment 2 are fit on the non-repeated segments, and are subsequently tested by predicting PSTH in response to repeated stimulus presentations for which we could measure the true PSTH; here, too, the prediction was done either with models fit separately at each condition, or with the global model, where 2 linear filters and the nonlinearity were fit simultaneously across all stimuli, as shown in Finally, we can ask how successfully the global models recapitulate the overall firing rate changes with the stimulus statistics. We observed that the encoding properties of salamander ganglion cells depend on higher-order statistics of the luminance levels in a way that is statistically significant for some of the conditions, but the observed changes in model parameters and the related model performance measures were fractionally small, usually ranging from no significant change to measured nonlinearity for C++ (high contrast) stimulus lined up well with the rescaled nonlinearity from the C+ (low contrast) stimulus, indicating the ability of the neuron to adapt to contrast. This observation was generally true for most (19 out of 23) neurons in our dataset, as shown in We analyzed the recordings from experiment 1 where neurons were also exposed to high (C++) and low (C+) contrast Gaussian stimuli. Since our analysis kept the filters normalized to unit length, contrast adaptation would be reflected in the change of the shape of the nonlinearity. Indeed, this can be seen in When the stimulus contrast changes, retinal ganglion cells adjust their gain, matching the variation of the signal about the mean to the dynamic range of the firing rate at the output, thereby keeping the information rate high. Without adaptation, the information rate would drop because the neurons have a limited output range and they are noisy. “Noise” in the context of LN encoding models is the stochasticity related to the spike generation: from the stimulus This effect is easy to understand if we compare the extent to which the 9 stimulus distributions differ a priori, after filtering by the neuron's linear filters, and after passing through the nonlinear function. For this analysis we used real linear filters and nonlinear functions reconstructed for all neurons in experiment 1  the linear filter was biphasic, with a “fast” lobe of amplitude (ii) we maximized the information rate (iii) the effective noise of the neuron, or fraction of output entropy that is lost to noise, For stimulus types (i) we have theoretically shown that biphasic filters outperform monophasic (single lobe) filters for all skewed and Gaussian stimulus ensembles examined; (ii) the neurons should adjust the biphasic linear filter away from the balanced configuration  by systematically adjusting the weight under the fast and slow lobes so that, e.g. in case of the OFF cell, negative skew favors larger weight in the slow lobe; but also that (iii) these adaptive changes would only lead to small relative information gains.Focusing on the case of an OFF cell, we found that an optimally adapting cell would increase the area under the fast (negative) lobe and would decrease the area under the slow (positive) lobe with increasing skewness. We used the balance ratio The optimal changes in the filter shape predicted here for a change in skewness are qualitatively consistent with changes in real filters observed in We explored adaptation to higher-order statistics in the light signal, by analyzing the responses of salamander retinal ganglion cells to temporally uncorrelated and spatially uniform stimuli with Gaussian, skewed and kurtotic luminance distributions. While the retina is highly adaptive to changes in first and second order statistics, we found much smaller changes in neural encoding in response to variations in stimulus skewness and kurtosis. A specific instance of this has been reported in relation to switches between a Gaussian and a binary stimulus of the same variance; there appeared to be no adaptation to kurtosis, but higher-order statistics could, interestingly, affect the dynamics of adaptation to contrast To establish our result, we compared the shape of linear filters across the stimulus conditions directly ? First, there might be cells that respond selectively to HOS which are rare and haven't been observed in our experiment. Another explanation is that in salamanders, and unlike in humans, there simply is no sensitivity to higher order moments of the luminance distribution. The third option is that the removal of HOS statistics by linear filtering is not complete, only approximate, and the remaining deviations get encoded into the spike trains. Lastly, there exists another interesting explanation. Central limit theorem guarantees that the distribution of filter outputs will converge to a Gaussian. However, linear filtering  induces temporal correlations in the filter output, and consequently could induce temporal correlations in the spike train. Those correlations could differ between two stimulus distributions matched in mean and variance, and differing in HOS. In contrast, for natural stimuli with long temporal correlations, the linear filtering in the receptive field might not (fully) remove the signatures of HOS, as we explain below, thus allowing downstream processing to detect and respond to HOS changes.Even if an adaptive code were to confer  coding benefit, it would also incur additional costs due to its ambiguity. The same response from an adapting neuron can, for example, signal two different light intensities, depending on the stimulus history. Downstream neurons must therefore rely either on keeping track of the adaptive state of the encoding neuron, or on using diversity in the neural population in a proper way to estimate the stimulus. Moreover, nontrivial processing is required also on the encoding side: the adaptive neuron needs to infer from the stimulus itself whether some underlying property of the stimulus, such as the mean luminance or contrast, has changed and thus an adaptive response needs to be triggered. Such detection might not be easy, and in particular, might require a substantial number of independent stimulus examples (and thus time). In short, adaptive codes most likely incur computational costs that invariant codes do not. One explanation for the lack of dynamic adaptation to higher-order statistics is therefore that it does not yield much gain in information, while potentially increasing the coding cost and complexity. Instead of implementing a costly adaptation mechanism able to dynamically change the filter shape on an individual cell basis in response to stimulus skew, the neural population could, for example, be structurally adapted to the overall luminance distribution of natural scenes, by (e.g.) properly partitioning the population between ON- and OFF-like cells Taken together, while some of the  changes in the encoding properties of retinal ganglion cells that we report may be statistically significant, the issue of whether these changes constitute “adaptation” is likely to remain a matter of interpretation. The changes are consistent with adaptation, and are also qualitatively consistent with the theoretically expected changes in optimal filter shape for different values of skewness. On the other hand, their functional effect on information encoding is small compared to the changes during, and benefits of, the adaptation to contrast. This is expected based on a simple theoretical argument, and confirmed in a toy model of an adapting LN neuron. Sparse, highly kurtotic stimuli (like K+) merit further attention, and point to the possibility that an alternative experimental design could be more successful in pursuing adaptation to HOS. To be concrete, we discuss below three limitations of our current analysis and conclude by making suggestions for follow-up experiments.exclude adaptation if LN model parameters don't change, or if they change very slightly. If information were encoded in, for example, spike-train temporal correlations, and the neuron modulated that correlation structure with the stimulus condition, our analysis would have missed such changes. One could attempt to capture the effects of spike interactions by, e.g., generalized linear models First, we have used LN models fitted to data to probe for adaptation, by looking for stimulus-statistics-induced changes in the model parameters. While this is a standard procedure in sensory neuroscience, we note that one cannot Second, we were restricted to the low range of contrasts by the limitations of our display device. If HOS adaptation mechanisms were conditioned on the light signals having a high contrast, our current experimental design would preclude us from detecting such adaptation. More fundamentally, it is not clear what are the actual statistics that the neurons are adapting to Third, our reasoning about the limited benefits of HOS adaptation in LN-type neurons rests on the application of the central limit theorem. We used full field stimuli  to address an absence of the observed adaptation in Ref


The most widely spread measure of performance, accuracy, suffers from a paradox: predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. Despite optimizing classification error rate, high accuracy models may fail to capture crucial information transfer in the classification task. We present evidence of this behavior by means of a combinatorial analysis where every possible contingency matrix of 2, 3 and 4 classes classifiers are depicted on the entropy triangle, a more reliable information-theoretic tool for classification assessment.Motivated by this, we develop from first principles a measure of classification performance that takes into consideration the information learned by classifiers. We are then able to obtain the entropy-modulated accuracy (EMA), a pessimistic estimate of the expected accuracy with the influence of the input distribution factored out, and the normalized information transfer factor (NIT), a measure of how efficient is the transmission of information from the input to the output set of classes.The EMA is a more natural measure of classification performance than accuracy when the heuristic to maximize is the transfer of information through the classifier instead of classification error count. The NIT factor measures the effectiveness of the learning process in classifiers and also makes it harder for them to “cheat” using techniques like specialization, while also promoting the interpretability of results. Their use is demonstrated in a mind reading task competition that aims at decoding the identity of a video stimulus based on magnetoencephalography recordings. We show how the EMA and the NIT factor reject rankings based in accuracy, choosing more meaningful and interpretable classifiers. Classification is an ubiquitous task in Science, Technology and the Humanities prior, instance or true classesprior class distributioninstances or patterns, each belonging to only one of those classes, but we do not know precisely which. A classification is a process whereby each of those instances is assigned to one among a set of decision or predicted classesposterior class distribution, To set the theoretical backdrop for our discussion, consider a set of confusion matrix, a special contingency table brain decoding or mind reading task consisting in automatically identifying the class of video stimulus shown to the subjects based on magnetoencephalography (MEG) data. Five different types of stimuli were presented: the first three ones (short clips (6–26 s. long) and the last two (long clips (approximately 10 min. long).To measure the performance of the classification process we use its de facto standard for performance visualization for binary—that is, two-class—classification is the Receiver-Operating-Characteristic (ROC) sec:mms: sec:entropy-triangle. In any case, neither device provides a single figure-of-merit or performance measure to compare systems, a practice cherished by researchers.Performance evaluation takes the form of the exploratory analysis of this confusion matrix or joint distribution. For instance, the accuracy, defined as the fraction of correctly classified instances, not to do so out of the influence of prior class distributions on similar measures.As a single figure-of-merit, by far the most widespread performance criterion used is high accuracy is not necessarily an indicator of high classifier performance and therein lies the accuracy paradoxsec:crit-accur-using. In particular, if a single class contains most of the data, a majority classifier that assigns all input cases to this majority class , defined in (3), is a better measure of classifier performance than accuracy for several reasons: it is well-grounded in information-theoretical terms, it provides an intuitive interpretation of the statistical learning process as the transfer of the information from the phenomena that are being modeled over a virtual channel, it factors out the influence of the input and output class distributions, it is invariant to permutations in the columns of the confusion matrix enabling the identification of cross-labeling errors common in unsupervised learning methods, and it is a pessimistic estimate of accuracy. For the same reasons, the normalized information transfer factor ( NIT factor ), defined as in (5), adds to some of the previous advantages the fact that it is capable of assessing the effectiveness of the learning process in the classifier, it is co-variant with expected mutual information (MI) In Section sec:example-use, we suggest how to apply these metrics to a classification task, instantiating the process for a mind-reading challenge using multi-classification on magnetoencephalography signals, that shows one clear instance where ranking by EMA and NIT factor provides a more interpretable classifier than accuracy-based ranking. We provide further evidence, examples and a comparison with other metrics in File S1. The paper is closed with a sec:discussion where we also compare EMA and the NIT factor with two previously proposed measures for classification assessment and show the superiority of our proposal.In sec:datasets for the details). Then, their entropy decomposition was calculated and plotted in the ET . To assess the theoretical adequacy of accuracy, we generated some samples of the space of joint count distributions for A number of observations can be gleaned from this figure:Matrices of a particular accuracy level are interspersed with those of many other accuracy levels. This phenomenon is the more prevalent the lower the accuracy level, although the behavior differs for different For every prescribed accuracy level, the normalized mutual information ranges in Conversely, matrices with different accuracy may exhibit the same normalized mutual information, for instance, check at There is an accumulation of distributions with high entropy , equally likely  classes: the higher this number, the worse the classifier will be.Since To illustrate this, notice that when the training process of the classifier has been able to capitalize on all mutual information to leave no remaining perplexity, artificial lower bound for (2), normalized information transfer factor can be rewritten as,Notice that when the entropy of not depend directly on the input or output distribution. Conveniently, since the normalized information transfer factor is a monotonic function of normalized mutual information the relative height in the ET offers a visual tool to quickly inspect such effectiveness. Finally, when evaluating a set of systems in the same task, For the reasons above, we posit the EMA in (3) to measure the performance of classification tasks, and the NIT factor in (4) or (5) to measure the effectiveness of the classifier learning process.In this Section we present an example of how to use the EMA and the NIT factor in automatic classifier evaluation tasks. We consider the case of the MEG mind reading challenge organized by the PASCAL  network Use  to assess the effective number of classes of the data. At Use EMA to rank classifiers.Use the ET to individually assess each classifier. From the ET diagram it is evident that those classifiers with highest mutual information and accuracy—the first seven classifiers—are not specialized while classifier Use the NIT factor to assess whether the population of classifiers has solved the task. Overall, for the top ranked classifier we have File S1.The result of this process is an assessment of a (population of) classifiers, whereby one may discuss the advantages of EMA and NIT factor vis–vis other performance measures, for instance, accuracy. Further examples of using this procedure to evaluate classification tasks can be found in the The authors of the report on the MEG Mind Reading challenge attempted an analysis of the ranking results and specifically compare classifier Our rejection of this judgement comes from believing that the goal of recovering class structure is as worthy as minimizing classification errors. The interpretability of the results of domain adaptation problem—the mismatch in training and testing conditions—with advanced machine learning techniques, many of the other teams, including test samples provided along with the train samples, when validating the learned classifier, thus explicitly boosting test set accuracy.The EMA and the NIT factor prove apt at considering the value of representing the underlying structure with their tight relation to perplexity. In fact, according to Perplexity has already been used as a performance measurement for language modeling where it refers to the expected average of alternatives a model has at every word history It cannot be stressed enough that since the EMA and the NIT factor concentrate in the prior class distribution and mutual information, it is harder for classifiers to boost their performance by manipulating the posterior class distribution through specialization: only the increase in information transfer through reporting the classification error is not the ultimate goal. Furthermore, in cases where Considering robustness, the EMA, being a harsher, worst-case criterion, might be more deserving of trust than easygoing and unreliable accuracy to, for instance, guide decision making. It certainly has a more interpretable and less easily bendable criterion—specially if As seen in the MEG mind reading example, the EMA and the NIT factor are capable of determining whether a task has been effectively solved or not. But it cannot distinguish whether this is caused by technical limitations in the classifier selection process or because the task is inherently “hard”. Only the kind of iterated classification effort of community research that attempts many different classifier-building techniques on the same task can be effective for this purpose.Nevertheless, the effective input perplexity on the learning method or model. In contrast, EMA would provide a different point in the ET for each classifier whence the best of these classifiers could be chosen. Complementarily, on the population of classifiers, a statistical description of the NIT factor could be used to assess the learning capabilities of the method.Several other measures have sprouted to deal with the inadequacies of accuracy such as the Area-Under-the-(ROC)-Curve File S1 a comparison of the classical Matthew Correlation Coefficient (MCC) In classification proper, to illustrate the disparity of the conclusions that can be reached with alternative performance measures, we have included in File S1) as customary. We also provide the tables detailing perplexities, EMA, NIT factor, File S1 ). The entries in the tables are ordered by accuracy. For the TASS and M&N data we also supply the ET's with the color bar according to EMA, File S1 Section, reveals that MCC' is highly correlated with accuracy in ranking results and shows similar shortcomings. Even though CEN performs a little better, it is highly biased towards majority classifiers providing over optimistic assessment for them. Notably, once the ET, EMA and the NIT factor have shed light on the problem, reassessment of prior evidences for either CEN or MCC prove them not to be so advantageous in evaluating classifiers.For each task we provide the heat maps of the confusion matrices  classifiers and our intuition is that they are the kind of classifiers that generate the accuracy paradox The position of the coordinates of a classifier on the Entropy Triangle characterizes its performance, and we use this characterization to visually assess it indicated in Notice that in The formulae above and the occurrence of twice the expected mutual information in The space of short clips (6–26 s. long) with artificial stimuli (screen savers showing animated shapes or text), natural stimuli (sceneries like mountains or oceans) and football stimuli  and a second category of long clips (approximately 10 min. long) with The MEG mind reading task aims at decoding the identity of a video stimulus based on magnetoencephalography (MEG) recordings done during naturalistic stimulation http://www.mathworks.com/matlabcentral/fileexchange/30914The MATLAB code to draw the entropy triangles in Figure S1Heat maps of the classifiers of the MEG mind reading competition . Rows correspond to stimulus (TIFF)Click here for additional data file.Figure S2Heat maps of the classifiers of the TASS competition . Rows correspond to stimulus A Color bar represents EMA B Color bar represents C Color bar represents (TIFF)Click here for additional data file.Figure S3Entropy decomposition for the classifiers of the TASS competition (A) with the color bar representing EMA, (B) , and (C) (Color online) (TIFF)Click here for additional data file.Figure S4Heatmaps of the classifiers of the TASS competition . Rows correspond to stimulus A Color bar represents EMA B Color bar represents C Color bar represents (TIFF)Click here for additional data file.Figure S5Entropy decomposition for MN phonetic confusion matrices (A) with the color bar representing EMA, (B) , and (C) .(Color online) (TIFF)Click here for additional data file.File S1Supporting Information. A comparison of the classical Matthew Correlation Coefficient (MCC) (PDF)Click here for additional data file.


Automated cell imaging systems facilitate fast and reliable analysis of biological events at the cellular level. In these systems, the first step is usually cell segmentation that greatly affects the success of the subsequent system steps. On the other hand, similar to other image segmentation problems, cell segmentation is an ill-posed problem that typically necessitates the use of domain-specific knowledge to obtain successful segmentations even by human subjects. The approaches that can incorporate this knowledge into their segmentation algorithms have potential to greatly improve segmentation results. In this work, we propose a new approach for the effective segmentation of live cells from phase contrast microscopy. This approach introduces a new set of “smart markers” for a marker-controlled watershed algorithm, for which the identification of its markers is critical. The proposed approach relies on using domain-specific knowledge, in the form of visual characteristics of the cells, to define the markers. We evaluate our approach on a total of 1,954 cells. The experimental results demonstrate that this approach, which uses the proposed definition of smart markers, is quite effective in identifying better markers compared to its counterparts. This will, in turn, be effective in improving the segmentation performance of a marker-controlled watershed algorithm. Automated imaging systems are becoming popular to analyze cellular events of fixed or live cells. These cellular imaging systems have potential not only for decreasing processing time but also for reducing human errors in the analysis. In almost all of the systems, cell segmentation constitutes the first step, which greatly affects the performance of the other system steps. Although there are several algorithms for the segmentation of fixed cell images from a light or a fluorescence microscope, there exist only few for the segmentation of live cells from phase contrast microscopy. In this paper, we focus on the implementation of a robust segmentation algorithm for live cells in culture media.In general, previous studies have approached the cell segmentation problem in two different contexts: segmenting monolayer isolated cells and segmenting cells that grow in clumps on layers. For monolayer isolated cell segmentation, the studies first differentiate cell pixels from the background using global thresholding For the segmentation of clumped cells, the previous studies mainly use active contour models and marker-controlled watershed algorithms. The active contour models define an energy function usually on the edge map of an image, associated with the cell contours, and achieve segmentation by finding the contours that minimize the energy function Image segmentation in general is an ill-posed problem. The success highly depends on the intent of segmentation as well as the knowledge about the image content. This is especially the case for the problems, in which domain specific knowledge is necessary even for human subjects to achieve successful segmentations. Live cell segmentation is one of such problems. In live cell images, cells of the same cell line or the same tissue may show different morphologies and intensity/texture characteristics. Moreover, these characteristics could be different from a cell line or a tissue to another. For example, KATO-3 gastric cancer cells can be grouped into four morphological classes based on their visual characteristics . The firIn this paper, we propose a new algorithm for the effective and robust segmentation of live cells. In the proposed algorithm, our main contribution is the incorporation of domain specific knowledge into the definition of a new set of “smart markers” for a watershed algorithm. In order to determine the smart markers, the proposed algorithm identifies different pixel groups with different visual properties, based on the biological background knowledge, and processes these groups with respect to each other, again using the background knowledge of different cell characteristics. Working with live cell images taken from the KATO-3 cell line, our experiments demonstrate that the proposed algorithm, which uses this new smart marker definition, is effective in finding better markers compared to its counterparts, which will in turn improve the segmentation performance of a marker-controlled watershed algorithm. The proposed algorithm differs from the previous ones in two main aspects. First, it defines the smart markers based on the background knowledge specific to the image whereas the previous algorithms define them using intensity, gradient, and distance measures without considering the image specific properties. Second, the previous algorithms typically find more markers than the actual cells, resulting in oversegmentation, and hence, they usually necessitate using a merge process after their watershed algorithms. In contrary, the proposed algorithm can find more markers that are one-to-one mapped to the actual cells and can give less oversegmented results without using an external merge process.Five different cell lines are used in the experiments. The human gastric cancer cell line (KATO-3) was inoculated in growth medium containing High glucose (4500 mg/L D-Glucose) DMEM with 10% FBS, 1% NEAA, 1% Penicilin/Streptomycin, and 1% L-glutamine. The human liver cancer cell line (Huh7) and the human breast cancer cell line (MCF7) were inoculated in complete growth medium composed of DMEM, with 10% FBS, 1% NEAA and 1% Penicilin/Streptomycin. The human endometrial carcinoma cell line (MFE-296) was cultivated in growth medium containing 40% RPMI 1640, 40% MEM , 10% FBS, 2 mM L-glutamine and 1The proposed algorithm relies on defining three basic types on image pixels—according to the intensity and gradient of these pixels and their surroundings, associating these basic types with the cells of different characteristics, and extracting the markers on each of these basic types by considering the morphological characteristics of their associated cells. The details of this algorithm are explained in the following subsections. A schematic overview of the algorithm is provided in In this work, we develop our algorithm focusing on the KATO-3 human gastric cancer cell line. Therefore, we consider the characteristics of its cells in the definition of the basic pixel types and the markers. Nevertheless, this idea can also be applied to other cell lines or tissues, provided that the basic types reflecting the characteristics of their cells are defined. In our experiments, we also obtain preliminary results on four different cell lines to explore the applicability of this algorithm to others.bright, dark-center, and dark pixels, respectively. These three pixel types are used for characterizing the four morphological classes of the KATO-3 gastric cancer cells; these classes are explained in the introduction and illustrated in This part consists of transforming an image into three basic types of pixel groups, each of which corresponds to a cell region of different characteristics. These types correspond to (i) bright pixels, (ii) dark pixels fully surrounded by bright pixels, and (iii) dark pixels only partially surrounded by bright pixels. They are herein referred to as Bright pixels correspond to high intensity regions in the image. Hence, we obtain them by thresholding the gray-level image with the Otsu method Dark pixels correspond to relatively darker regions with high gradient values. Here one should note that dark cell regions have an intensity distribution similar to the background. Thus, using only intensities, without considering gradient values, would yield errors in pixel quantization. In this work, we use the Sobel operators on gray-level intensities to define gradient values. Computing a new Otsu threshold Cell pixel quantization starts with identifying bright and dark cell pixels. dark-center pixel group as follows: We consider all pixels except the bright ones and find the connected components on these pixels. Let th connected component and After this quantization, dark pixels are further grouped into two based on whether they are fully surrounded by bright pixels; that is, some of the dark pixels are identified as dark-center pixels. However, there usually exists noise in the quantized pixels, which leads to errors in the definition of dark-center pixels. Thus, we postprocess the quantized pixels to alleviate the noise. For that, we first eliminate narrow dark pixel regions around the boundaries of bright regions and then apply a majority filter on the quantized pixels. For the example live cell images shown in The final step is to eliminate holes and artifacts from the pixel groups. First, we fill holes in between cell pixels provided that the holes are smaller than an area threshold The proposed algorithm defines the markers for each of the three pixel types separately, according to the characteristics of the regions that each type corresponds to. Since the markers are defined considering the background knowledge of the corresponding region characteristics, it is expected to find more markers that are one-to-one mapped to the actual cells, and thus, to obtain less under and oversegmented results.In order to define the markers on dark and dark-center pixels, we employ an iterative erosion algorithm. This algorithm erodes the given pixel groups iteratively until the size of a group falls below a threshold. In our work, we select this threshold separately for dark and dark-center pixels, considering their region characteristics. Since dark-center pixels usually correspond to relatively smaller regions compared to dark pixels, we use a size threshold To define the markers on bright pixels, we take the following observation into consideration. Bright pixels can be found both inside a particular class of cells and the boundaries of the others. To alleviate the negative effects of the boundaries, we first dilate the previously found markers and then locate circles on the remaining bright pixels using the modified version of the circle-fit algorithm We conduct our experiments on 44 live cell images of the KATO-3 human gastric cancer cell line. The dataset contains a total of 1954 cells most of which grow in clumps on layers. Each image has a resolution of In our experiments, the images are randomly divided into training and test sets. The training set includes 474 cells of 10 different images whereas the test set includes 1480 cells of the remaining 34 images. The cells in the training set are used to estimate the parameters of our algorithm as well as those that we use in our comparisons. The cells in the test set are not used in the parameter estimation at all.Marker-controlled watershed algorithms first identify markers on an image and then start the flooding process from these markers. The success of the segmentation is closely related with how well the markers are identified on the image. One can obtain more accurate segmentation results if there is one-to-one correspondence between the markers and the actual cells. Since the correct identification of the markers greatly affects the segmentation results as well as the main contribution of this paper is on the marker definition, in this section, we report the experimental results in terms of the markers, but not the segmentation boundaries. However, it is also possible to apply a watershed algorithm on the markers to obtain the boundaries. This possibility will be explored in the next section.precision, recall, and F-score measures in our evaluation.In our experiments, we evaluate the results both visually and quantitatively. For that, we consider the centroids of the annotated cells as the gold standards and the centroids of the identified markers as the computed cells and use a distance-based evaluation algorithm to obtain the quantitative results. In this marker-based evaluation algorithm, each marker (computed cell) is matched to every gold standard cell provided that the distance between the marker and the gold standard cell is less than a predefined distance threshold. By making use of these matchings, we compute the number of one-to-one matches, oversegmentations, undersegmentations, false detections, and misses, whose definitions are given below. Additionally, we use the one-to-one match if the marker is matched to a single gold standard cell that is not matched with any other markers.A marker (or a gold standard cell) corresponds to oversegmentation, if more than one marker is matched to this gold standard cell. The number of such markers is considered in reporting the quantitative results.A gold standard cell corresponds to undersegmentation if it is matched more than one gold standard cell. The number of such gold standard cells is considered in reporting the quantitative results.A marker corresponds to false detection, if it is not matched to any gold standard cells.A marker corresponds to miss, if none of the markers are matched to this gold standard cell.A gold standard cell corresponds to The proposed algorithm has five external model parameters. The first three of these parameters are used for cell pixel quantization whereas the other two are used for smart marker extraction. These parameters are the Sobel threshold constant From all possible combinations of the parameter sets, we select the one that gives the maximum F-score on the training cells. This selection automatically evaluates the combinations based on their F-scores and does not involve any manual or visual examination. After this procedure, the parameters are selected as intensity-based algorithm. It defines the markers computing regional minima on gray-level intensities We compare our results against those of the three marker identification algorithms. The first is the distance-based algorithm which is similar to the intensity-based algorithm except that it uses the inverse of the distance transform instead of intensities. It obtains the distance transform map on the initial segmentation of the image such that the minimum distance from each foreground pixel to a background pixel is computed. Similarly, it uses the The second one is the conditional-erosion algorithm, which defines the markers on the initial segmentation map of the image by making use of iterative erosions The last is the These algorithms also have their own parameters. Besides, the method used to obtain the initial segmentation maps introduces additional ones. In our experiments, we use a similar method to select these parameters: we first list different values for each parameter, consider different combinations of the parameter values, and select the combination that yields the maximum F-score on the training cells.We present the quantitative results obtained on the training and test sets in The results show that the definition of smart markers leads to higher precision and recall values. Compared to the other algorithms, it gives more one-to-one matches with relatively less false detections and misses. In Moreover, the results show that the distance-based and conditional-erosion algorithms give less one-to-one matches due to a high number of misses. The visual results of these algorithms . Here we use the geodesic distance from a pixel to a marker boundary as the growing criterion. Let Our experiments showed that the smart marker definition increases the success in terms of marker localization. This, in turn, is expected to also increase the success of a watershed algorithm. To examine this, we implement a watershed algorithm that takes the smart markers as starting locations and grows them by using the marker types and the pixel groups (We present area-based evaluation of these watershed algorithms for the training and test sets in Our implementation uses C for cell pixel quantization and MATLAB® for smart marker extraction. The average computational time for a single image is 2.63 seconds using a computer with an Intel Core 2 Duo 2.4 GHz processor and 4 GB of RAM. However, it is possible to obtain speedups by implementing the smart marker extraction step also with C. This would be considered as future work.


This paper presents a solution to estimate the driver activity regardless of the type, model, and year of fabrication of the vehicle. The solution is based on an alternative sensor system  that reflects the activity of the pedals in an indirect way, to estimate that activity by means of a multilayer perceptron neural network with a single hidden layer.It is accepted that the activity of the vehicle pedals ( Nowadays there are strong research efforts invested in the modeling of the driver behavior using driving signals by means of hidden Markov models (HMMs) ,2 and dypostures . In thispostures –7.Observable and measurable driving signals can be divided into three categories : (1) driThe instantaneous and simultaneous measurement of the three car pedals is a difficult task in the great majority of vehicles. In fact, there are 3 methods to directly measure the status of the car pedals: using position sensors , using petc.). Because of the previously mentioned problems, this paper describes an approach to pedal activity estimation. The basic idea is to use the measurements of some sensors, either on-board the vehicle or added ones which are easier to deploy and adjust, to implement a feedforward artificial neural network to indirectly estimate the driver action on the control pedals.The authors of this paper have the design experience of a universal and non-disturbing solution (Miveco Resesarch Project ) to regiArtificial neural networks (ANNs) are one of the most powerful tools that have been widely employed in recent years in various fields such as sensors –18, measPÃ) of any driver on the pedals of any unit of the same vehicle model using real experimental tests with particular vehicle model and several drivers. Thus, instead of directly using sensors associated with driving pedals to provide the (PA) information, the authors introduce in this paper a sensor system that includes alternative devices easier to implement and provide (MV) information of driving dynamics. The main idea of this work is to develop a mathematical model to estimate the pedals activity (etc.) that don’t support the innovative electronic system to register the vehicle pedals signals.There are other learning machine methods that are beyond the scope of this paper to deal with function approximation problems such as support vector regression (SVR) which uses support vector machines (SVM) . So thisThe paper is arranged as follows. Section 2 shows the methodology followed to collect the PA and MV variables and visualizes the relation between them. Section 3 illustrates the inverse modelling strategy used to develop the neural models using MLP neural networks. Section 4 shows the structure of the proposed models and the results of testing them. Conclusions are included in Section 5.2.This section describes the methodology followed to obtain the PA and MV signals. As result of previous research authors’ work ; an in-vFrom these experimental tests, the authors have selected four easily measured variables of the driving dynamics that reflect the activity on the vehicle control pedals: regime engine (RE), instantaneous velocity of the vehicle (VS), frontal inclination (FI), and linear acceleration (LA).i.e., MTi, RPM8000, and GPS) are easy to install, don’t need special placement (except for the RPM sensor which is connected to the cigarette lighter) and their outputs are applied directly to the serial port of the PC that acts as a monitoring and storage element during the test.The first subsystem in The second subsystem  is in chIn i.e., on/off, and that of the throttle and brake pedals, i.e., the continuous variation between two limited values of these two pedals.As a result of the previous section, the authors propose an inverse model with four input easily measurable variables (MV) and three output variables (PA). The input variables are the regime engine (RE), frontal inclination (FI), linear acceleration (LA) and vehicle speed (VS). In addition, the output variables are the estimation of the three vehicle pedals activity: throttle, brake, and clutch.3.The inverse modelling process followed to develop the neural network estimators in this work is illustrated in Concerning the data preparation task, the early stopping technique is used to improve the generalization performance. In this technique the entire normalized data set has been divided randomly into training (80%), validation (10%), and testing (10%) subsets. The validation subset is employed during the training phase by monitoring the validation set error. It normally decreases during the initial phase of the training, as does the training set error. However when the network begins to over fit the data, the validation set error begins to rise . When itNumerous neural networks are available for function approximation problems. A Multilayer Perceptron MLP neural network trained with backpropagation is chosen as it has many useful properties for the pedals estimation problem. It can efficiently learn large data sets as compared to Radial Basis Function RBF networks and Generalized Regression neural networks GRNN, it has been already shown to be effective for function approximation problems, it can efficiently establish a nonlinear relationship between a group of variables, it has been already used in inverse modeling processes , it has Since the backpropagation learning algorithm was first popularized, there have been extensive research efforts to accelerate its convergence because the basic algorithm is too slow for most practical applications. These researches fall into two categories, heuristic techniques and numerical techniques. In this work, the feedforward neural network is trained with the Levenberg-Marquardt numerical optimization method because it is the fastest for function approximation problems of networks containing up to a few hundred weights . MoreoveThe Levenberg-Marquardt algorithm updates the network weights and biases (x vector) using the formula described in When a particular training algorithm fails on an MLP, it could be due to one of two reasons. The learning rule fails to converge to the proper values of the network parameters, perhaps due to unsuitable network initialization. Or the inability of the given network to implement the desired function, perhaps due to a insufficient number of hidden neurons. To avoid the first possibility, the neural network models were trained and tested 10 times and the network architecture with the lowest root mean square error (RMSE) on the testing data set is chosen.Concerning the second possibility, there is no theory yet to explain how many hidden neurons are needed to approximate any given function. If there are too few hidden neurons, a high training error and high generalization error would result due to underfitting and high statistical bias. On the other hand, if there are too many hidden neurons, there would be a low training error, but there would still be a high generalization error, due to overfitting and high variance. In most situations, there is no way to determine the best number of hidden neurons without training several networks and estimating the generalization error of each ,30,32,34i.e., throttle, brake, and clutch) from the easily measured variables . These models have been tested with the testing subset in order to evaluate their ability for generalization. The next section shows the testing results of these models.Once the optimum number of hidden neurons is obtained, a neural network with that optimum number of hidden neurons is trained several times in order to determine the best learning parameters. Finally, a neural network with the optimal number of hidden neurons and learning parameters is trained several times in order to determine the best number of training epochs. At this point, three neural network models were developed to estimate the pedals activity  behaviour, not a continuous behaviour like the throttle and brake, which requires different processing to obtain a good model.An alternative approach is to use the regime engine (rpm) and vehicle speed (km/h) signals to deduce the gear position signal , as described in . Startin5.The main contribution of this work is the presentation of a solution to estimate the driving activity avoiding the use of onboard sensors directly applied to the control pedals. The solution is based on an alternative sensorial system (easily measured variables), and on a neural network estimator .In this way, after a training period using the registered variables, the proposed system of models provides information about the driver’s activity in a simple and accurate way.ad hoc pedal sensors requiring mechanical adaptation for each vehicle, the related variables are registered by sensors that are easily and systematically installed independently of the vehicle type and model. On the other hand, they can minimally affect the driving of the vehicle contrary to the use of the conventional sensors used to capture the direct action on the vehicle pedals.From the alternative variables point of view, observable and measurable driving signals such as the regime engine (RPM meter), vehicle speed (GPS), frontal inclination of the chassis and linear acceleration of the vehicle  have been chosen. Instead of using etc.) and requires training using direct measurements of the pedals in order to determine the model parameters. The car must be tested with different drivers to determine the specific estimator for each car model.From the ANN modelling point of view, three inverse neural models based on multilayer perceptron with one hidden layer are designed. To validate the obtained models, well known criteria are utilized such as RMSE and regression analysis parameters. The model structure is valid for any vehicle (car, van, bus, lorry, industrial, The system has been tested with experiments using commercial vehicles, in a chassis dynamometer as well as on urban circuits; consequently this ensures the validity of the proposed models.


Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity. The formation of synaptic connections between neurons requires physical contact between axonal segments of one neuron and dendritic segments of another neuron. These physical contact sites are potential locations where synapses could be formed; they are called morpho-density fields (MDFs), describe the statistical distributions of axonal and dendritic mass in the space around the soma. Axonal and dendritic MDFs are also referred to in the literature as fiber densities In this paper, we use the density field approach in combination with model-generated neurons in order to estimate neural connectivity. Density fields of axonal and dendritic morphologies, which we call We build upon the work of Liley and Wright In both Biological neurons of any specified type show large variations in their morphology, and the estimation of stable density fields therefore requires large data sets. Sparse experimental data sets will inevitably result in large uncertainties in the density fields and hence in the connectivity estimates. With large data sets of model-generated neurons, however, density fields and connectivity measures can be estimated with much lower variability. Evidently, the model-generated neurons must reflect truly their biological variability. As the parameters of the generating model are optimized on a limited experimental data set, our method remains dependent on the sampling variation in the experimental data, as well as on the quality of the model and the assumptions used in creating density fields and calculating synaptic connectivity.The paper is organized as follows. In the We generated 100,000 L2/3 pyramidal neurons from the rat cortex using the NETMORPH software tool Pyramidal neurons in rat cortical layers 2 and 3 typically show cylindrical symmetry in the branching patterns. This is due to the orientation of their axonal and dendritic arbors: the axon root segment grows downward from the soma, while the apical dendrite extends upward and the root segments of the basal dendrites have a lateral/downward orientation. Furthermore, as a result of the behavior of the growth cones, the axon and dendrites branch extensively during development to produce large arbors. This cylindrical symmetry is exploited in the sequel.x denote an arbitrary point in the space around the soma. Consider all possible axonal morphologies x. Then the axonal morpho-density at x is defined asx is defined likewise. The collections morpho-density fields (MDFs), respectively, for that neuron type.Suppose we center the neuron soma at the origin. Let x would equal the average dendritic segment length per x. However, in a third step we exploited the cylindrical symmetry of the MDFs, as was done in We constructed estimators for expectation) can be computed using MDFs, since the MDFs contain the average segment length density of the neuronal mass. Hence, for any neuron pair we computed expected number of potential synapses. Connectivity between a pre-synaptic and a post-synaptic neuron is measured by the expected number of potential synapses between the two neurons. A potential synapse is a site where an axonal segment of the pre-synaptic neuron and a dendritic segment of the post-synaptic neuron meet within a certain distance tion see .In templatesThe assumption of uniformly-distributed segment orientations is arguable. Dropping this assumption implies that in the computation of formula (2) the actual orientations of the segments have to be taken into account. This naturally leads to the axonal and dendritic ) is see (5)where For sparse templates To investigate the influence of sparsity of data, we compared our MDF approach to two sparse data approaches. First we computed (5) for simulated data, consisting of 10 to 1000 neurons. For each sample size 20 different data sets were simulated and Second, we applied one of the existing sparse data approaches, the smoothing method presented by Stepanyants and Chklovskii Given the estimated number of potential synapses for various displacements, it is possible to generate a random directed weighted neural network to represent L2/3 pyramidal neurons in the rat cortex. The vertices represent the neurons, and each directed edge from one vertex to another represents a potential synaptic connection from the pre-synaptic neuron to the post-synaptic neuron. The weight of the connection between any neuron pair represents the strength of the connection and is based on the estimated number of potential synapses. We randomly generated locations (the vertices) for the somata of simulated pyramidal neurons within a cylinder with no two vertices closer than 20 small-world coefficient is typically used for assessing the efficiency of the network efficiency of a weighted graph global efficiency of a graph islocal efficiency iscost of a weighted network expresses the weighted number of realized connections and is defined aseconomic small-world network has high global and local efficiency, while the cost of such a network is low Once a neural network has been generated, the efficiency of its connectivity pattern can be investigated. In biological neural networks, strong inter-connectivity among neighboring neurons may enhance local computational efficiency, and short paths between local clusters may enhance the transmission of information throughout the network In order to apply these efficiency measures to our generated neural networks, we needed to define both an adjacency matrix and a weight matrix for each generated network. The adjacency value Similarly, The heatmaps in rons see .In cant see .From In the first sparse data approach we investigated the influence of sparsity on the variability  of the estimated number of potential synapses To investigate the dependence of the standard deviation on the displacement, In the second sparse data approach we applied the smoothing method (6). We generated 10 NETMORPH L2/3 pyramidal neurons and stored the positions, lengths and orientations for all neurite segments comprising each arbor. As in 3  of axonal and dendritic morphologies describe the statistical distributions of axonal and dendritic mass in the space around the soma. The MDFs are extremely useful for visualization of the density of neurite segments for any specified neuron type. The vivid detail in the MDFs, as demonstrated in In In contrast to these approaches described above, our MDF approach is not based on a limited data set of neuron morphologies, and does not rely on several restricting assumptions characteristic of other approaches: spherical symmetry of dendritic fields Our obtained estimates Nevertheless, it should be acknowledged that the sparsity of experimental data affects the MDF approach as well. That is because the estimates of the NETMORPH parameters are derived from the morphological characteristics of a single set of experimental neurons. Because of the lack of large datasets of reconstructed neurons, we could not investigate how the connectivity estimates would change if another sample of neurons was used. Another sample, or an extension of the current sample, could result in different experimental distributions, different NETMORPH parameters and consequently also different connectivity estimates. Whether these differences would be non-negligible requires further investigation. The availability of experimental data on neuronal morphologies will increase over time, and methods for deriving estimates for these parameters will keep improving, so that the generated neurons which form the basis of our estimators of the MDFs will become even more realistic representations of biological neurons. Meanwhile we have demonstrated convincingly that, given a fixed set of experimental neurons, we obtain connectivity estimates with a much smaller standard deviation using the MDF approach , Table 1The MDFs do not carry spatial correlation information. It is certainly the case that, in a single instance of a neuron, the presence of a neurite segment at one location increases the likelihood of segments being found concurrently at neighboring locations. In order to take this spatial correlation into account, one would need to store the full arbor geometry densities We have further shown that the assumption of uniformly-distributed segment orientations is not violated significantly in the ensemble of generated neurons. The histograms in  see . Hence, The generated networks based on the estimated connectivity values appear to be economic small-world networks in terms of global efficiency, local efficiency and cost values. However, it is still an open question whether these measures are optimal for quantifying efficiency of weighted networks. Different approaches to answering this question are currently being investigated (see the review in The present study has shown how the uncertainty in the expected number of potential synapses between two neurons depends on the size of the data set, as visualized in In summary, our morpho-density approach to estimating neuronal connectivity incorporates the characteristics of neuronal growth and network formation without being directly dependent on small data sets. We have shown that the so-obtained estimated connectivity values have a much lower standard deviation than connectivity values based on sparse data. Moreover, this approach is not restricted to L2/3 pyramidal neurons, but can be applied to any type of neuron, and combinations of different types. Therefore, we anticipate that our approach may serve as an important tool for analyzing the shapes of neuronal morphologies as well as the generation and study of synaptic connectivity of neural networks.