ABC efflux transporters are polyspecific members of the ABC superfamily that, acting as drug and metabolite carriers, provide a biochemical barrier against drug penetration and contribute to detoxification. Their overexpression is linked to multidrug resistance issues in a diversity of diseases. Breast cancer resistance protein (BCRP) is the most expressed ABC efflux transporter throughout the intestine and the blood-brain barrier, limiting oral absorption and brain bioavailability of its substrates. Early recognition of BCRP substrates is thus essential to optimize oral drug absorption, design of novel therapeutics for central nervous system conditions, and overcome BCRP-mediated cross-resistance issues. We present the development of an ensemble of ligand-based machine learning algorithms for the early recognition of BCRP substrates, from a database of 262 substrates and nonsubstrates compiled from the literature. Such dataset was rationally partitioned into training and test sets by application of a 2-step clustering procedure. The models were developed through application of linear discriminant analysis to random subsamples of Dragon molecular descriptors. Simple data fusion and statistical comparison of partial areas under the curve of ROC curves were applied to obtain the best 2-model combination, which presented 82% and 74.5% of overall accuracy in the training and test set, respectively.  ATP-binding cassette (ABC) efflux transporters comprise a diversity of active carriers which provide an efficient mechanism of defense against foreign chemicals , among them drugs. To elicit the therapeutic response, drugs must often cross a number of cellular barriers, such as the gut wall and the capillaries endothelial cells. ABC efflux transporters limit drug absorption and distribution by translocating drugs from the cytoplasm to the cell exterior. These transporters are preferentially expressed at tissues that present barrier and/or excretory functions, for example, the intestinal wall, the canalicular membrane of hepatocytes in the liver, or the luminal membrane of the tubular cells in the kidney , 2, reduEven though P-glycoprotein  was the first identified and is the most extensively studied member of the ABC superfamily, recent studies suggest that the effect of another member, breast cancer resistance protein  might have been underestimated in the past. A number of reports indicate that BCRP is the most abundantly expressed ABC efflux transporter in different segments of human intestine, both at mRNA , 9 and pThe most advanced research regarding ABC transporters modulation relates to add-on therapies of specific inhibitors of ABC transporters, a strategy that was originally conceived for cancer treatment. Although preclinical and initial clinical results with first- and second-generation inhibitors have been encouraging, some trials stopped at phase III due to serious adverse effects , 14–16; in silico models for the early identification of BCRP substrates, in order to assist virtual screening and computer-aided design of novel BCRP nonsubstrates therapeutics. Recently, Hazai et al. obtained a support vector machine model based on 5 Dragon descriptors , where D is the number of descriptors in a given descriptor pool and d is the number of descriptors included in a given model. This is very computationally demanding or even unfeasible when D is large, as in the present work. Therefore, we resort to a stepwise approach which, although faster, leads to suboptimal solutions. A binary, dummy variable codifying the category of each compound was used as dependent variable (class = 1 for substrates and class = −1 for nonsubstrates). Stepwise forward multiple linear regression was used to select the descriptors from each random pool that best discriminated the category of the compounds. Obtaining all possible descriptors subsets would demand a0 is constant and ai is the coefficient associated with molecular descriptor di. Due to the values arbitrarily assigned to substrates and nonsubstrates, substrates will tend to have positive df values, and nonsubstrates will tend to assume negative values.Linear discriminant analysis (LDA) was used to characterize the correspondent linear discriminant functions (dfs). Dfs assume the following general form:The binary classification scheme reduces the error associated with combining data obtained in different labs and conditions . MultiplTwo important indicators of the performance of a given QSAR model are sensitivity (Se) and specificity (Sp). They are defined by the following expressions:By modifying the selection threshold from the lowest to the highest score provided by the individual models or the model ensemble, Se and Sp will evolve in opposite ways. Consequently, it is not possible to optimize both parameters simultaneously, and a tradeoff has to be found. ROC curves are a wide-used tool to assess and compare the performance of different models . They arIt has been pointed out that there is no general rule for balancing errors . BalanciIt has been suggested that AUC of the ROC curves may not be the best parameter to compare different models, especially if the modeler is interested in comparing a particular region of the ROC curve instead of the entire curve . A key requirement for the success of virtual screening is the ability of the combination of a scoring function to rank actives early in a large set of compounds; this has been referred as the early recognition problem . Thereforoc.jar  values joined by straight lines  values, and its value is related to the U statistic for the two-sample Mann-Whitney/Wilcoxon rank-sum test [A and B in the formula) were tested with a two-sample z-test:In the nonparametric approach, the AUC is estimated by the trapezoid defined by the empirical set of Se. In stratified bootstrap, each replicate contains the same number of cases and controls than the original sample. Stratification is especially useful if one group has only little observations, or if groups are not balanced [For a pAUC estimation between two given Sp values, pROC package  was usedbalanced .enrichvs package for R [For the evaluation of the model performance, several enrichment descriptors were calculated for each model: area under the accumulation curve (AUCc) , enrichmge for R .An issue that emerges from using a reduced dataset (such as our 98-compound test set) is that the enrichment metrics derived exhibit a higher variance compared to significantly large datasets. Experiments conducted by Truchon and Bayly  show thaThe other problem is related to the high ratio of actives which mainly hinders the early recognition ability in what is known as the “saturation effect.” That is, for datasets with a high ratio of hits , once hit compounds saturate the early part of the ordered list, the enrichment metric cannot get any higher. To estimate in a more realistic way the utility of our model in a real virtual screening approach, we have dispersed our test set among 479 putative substrates acting as decoys. Such putative substrates are substrates of BCRP from other species rather than human or highly similar compounds to human BCRP substrates which have been retrieved from either ZINC database or Pubchem. This simulated database thus contains 27 known nonsubstrates among 550 known or putative substrates among 550 known or putative substrates; that is, the nonsubstrates ratio is less than 0.05, representing a more challenging set to assess the enrichment ability of our models. Note that some of these putative substrates (decoys) might actually be nonsubstrates; thus, the true performance of our models may be even higher than the one obtained through this simulated experiment. Based on the considerations exposed in the previous section, varying tolerance values between 0.1 and 0.5 and the maximum number of steps in the stepwise forward procedure between 10 and 15, we obtained 196-individual models from the 102-descriptor pools. Exhaustive 2-model combinations of these 196 models were performed by applying the MAX and AVE data fusion strategies. The AVE data fusion scheme outperformed the use of the MAX operator. This is in line with previous reports empirically showing that consensus prediction by simple averaging of outputs of individual models is an efficient way to enhance predictive performances –69.The statistical comparison of the ROC curves  proved tWe have developed a 2-model ensemble based on conformation independent Dragon descriptors for the identification of BCRP substrates and nonsubstrates. Since the descriptors incorporated into the models do not require preprocessing of the predicted chemical structure, the ensemble is particularly suitable to be applied in virtual screening campaigns of large chemical libraries in a highly efficient manner. Statistical comparison of ROC curves indicates that the best 2-ensemble model outperforms the best individual models generated. One should keep in mind that the broad substrate specificity of BCRP  makes it difficult to find a single linear relationship capable of accurately classifying substrates and nonsubstrates, a fact that justifies the application of more complex strategies such as ensemble learning or locally weighted regression methods. Unlike previously developed modeling efforts towards recognition of BCRP substrates and nonsubstrates, our models have been derived from a relatively large dataset which was split into representative training and test set through clustering analysis; the obtained training set presents a fair balance between the number of substrates and nonsubstrates. The studied ensemble is a potentially valuable tool to assist virtual screening and computer-aided drug design campaigns, as suggested by the outcome of the simulated virtual screening campaign. With the help of the constructed ROC curves, Sp and Se may be balanced to attend specific user requirements. The structures of chemical compounds which compose the training and test sets are presented as Supplementary Material.Click here for additional data file.


Trait-mediated indirect interactions (TMII) can be as important as density-mediated indirect interactions. Here, we provide evidence for a novel trait-mediated cascade (where one TMII affects another TMII) and demonstrate that the mechanism consists of a predator eavesdropping on chemical signaling. Ants protect scale insects from predation by adult coccinellid beetles – the first TMII. However, parasitic phorid flies reduce ant foraging activity by 50% – the second TMII, providing a window of opportunity for female beetles to oviposit in high-quality microsites. Beetle larvae are protected from ant predation and benefit from living in patches with high scale densities. We demonstrate that female beetles can detect pheromones released by the ant when attacked by phorids, and that only females, and especially gravid females, are attracted to the ant pheromone. As ants reduce their movement when under attack by phorids, we conclude that phorids facilitate beetle oviposition, thus producing the TMII cascade. Long appreciated by traditional naturalists, the idea of a trophic cascade gained popularity in the ecological literature through debates that emerged from Hairston, Smith, and Slobodkin's publication of the famous “green world hypothesis”  an ant–hemipteran mutualism unit, where the ants interfere with the ability of predators to attack scale insects, and (2) a phorid-ant-hemipteran unit where the phorids reduce the foraging activity of the ants, thus reducing their ability to interfere with the predator of the hemipteran mutualist. We also demonstrate that the linkage between the TMII units is mediated by semiochemicals, more specifically ant pheromones that are used for alerting nest mates about the presence of parasitoids, thus disrupting the ant's ability to interfere with the behavior of the predator, especially with the ability of the predator to engage in oviposition behavior.Azteca instabilis, protects a significant pest of coffee, the green scale, Coccus viridis, against most natural enemies  by being able to detect the phorid-alert pheromone?A. orbigera, is able to detect volatile pheromones from the ants and, more importantly, that the coccinellid beetles have the ability to detect the unique alarm pheromone (or pheromones) released by ants specifically when under attack by phorids, therefore taking advantage of a window of opportunity to search out safe sites for oviposition.Here, we test the hypothesis that the coccinellid beetle, To test the hypothesis that beetles are able to detect volatile pheromones released by ants, we employed a standard olfactometer  or reared in the laboratory after field collections from the same site. Five colonies of A. orbigera, was able to detect and be attracted to pheromones from A. instabilis, we conducted behavioral assays in a two-arm olfactometer, modified from the four-armed Perplex olfactometer . We connected the cages to the two-arm olfactometer and waited for at least 10 min until the ants calmed down. We then released three to five freshly collected phorid flies into one of the tents and placed one adult beetle in the neutral zone of the olfactometer. When at least one phorid fly started attacking the ants, we started recording the location of the beetle. We conducted these trials with both male and female beetles.To test beetles' response to the general odor of ants, 20 ants were placed in one of the source chambers and the other left empty. We waited for at least 10 min to let the ants calm down before placing the beetle in the arena and running the assay. To determine beetle attraction to ant pheromones, 20 ants were crushed and placed in one of the source chambers and the other left empty. Crushing the ants liberates all the pheromones produced by ants and is a method frequently used in these types of bioassays  no ants/no phorids, (2) ants/no phorids, and (3) ants + phorids. The chambers where the experiment was conducted consisted of containers of 1 L containing a coffee branch with four to six coffee leaves infected with scale insects. The ant/no phorid treatment contained 40 workers of A. instabilis and the ants + phorids treatment contained 40 workers of A. instabilis plus two to three phorid flies. After 24 h, the coffee branch was removed from the experimental chamber and placed under a dissecting microscope, where it was carefully examined for eggs of A. orbigera. The three individual gravid beetles were returned to the beetle pool with other individuals. For the next trial all three beetles were again randomly selected and assigned to treatments. The experiment was replicated nine times.To determine if gravid females P = 1−BINOMDIST ). For each trial, we added all recordings for the control, the treatment, and the neutral (no-response) zones, and categorized the trial based on the zone that had the higher number of recordings (control or treatment). Trials categorized as “no-response” were eliminated from the analyses. To investigate the relationship between days after copulation and level of attraction to ant pheromones, a simple linear regression analysis was used. In this particular case, instead of using the categories (control or treatment), we calculated a strength index by averaging the number of the position of the beetle at each recording period . To test whether ants deter female beetles from ovipositing and whether phorid parasitoids facilitate oviposition, a Wilcoxon rank-sum test was conducted.Beetle preferences were determined by directly calculating the probability of finding something other than a 50% response with a binomial distribution using Excel binomial distribution function , we were able to determine that the phorid-alert pheromone is produced in the ventral part of the abdomen, most likely in the Pavan or Dufour's gland , distincTesting mated and unmated females demonstrated that the attraction to ant pheromones is manifested only after mating, and that before mating, female beetles have an aversion to ant pheromones A. FemaleA. orbigera on the no ant/no phorid treatment is not significantly different from the average number of eggs oviposited on the ants + phorids treatment  and be protected from parasitoids . These interactions are illustrated in C. viridis, is reported to be an important pest of coffee causing considerable damage in some cases , suggesting that they control scale insects outside Azteca patches, which in the study area represent only about 3–5% of the coffee area  are quite common in natural ecosystems and that these sorts of TMII cascades could be more common than previously thought.These chemically mediated indirect complex interactions can have practical implications for the management of coffee, as C. To our knowledge, ours is one of the few studies that document these cascading effects (the others being from the same study system; Liere and Larsen Ecological research long ago transcended the limits of classical density-dependent interactions, and the literature is now replete with examples of chemical, behavioral, and morphological changes of organisms in response to challenges from other organisms, such as the threat of predation. Indeed, such trait-mediated indirect interactions significantly affect species coexistence, trophic length, and energy and material flows within ecosystems (Werner and Peacor


Real-time brain-machine interfaces (BMI) have focused on either estimating the continuous movement trajectory or target intent. However, natural movement often incorporates both. Additionally, BMIs can be modeled as a feedback control system in which the subject modulates the neural activity to move the prosthetic device towards a desired target while receiving real-time sensory feedback of the state of the movement. We develop a novel real-time BMI using an optimal feedback control design that jointly estimates the movement target and trajectory of monkeys in two stages. First, the target is decoded from neural spiking activity before movement initiation. Second, the trajectory is decoded by combining the decoded target with the peri-movement spiking activity using an optimal feedback control design. This design exploits a recursive Bayesian decoder that uses an optimal feedback control model of the sensorimotor system to take into account the intended target location and the sensory feedback in its trajectory estimation from spiking activity. The real-time BMI processes the spiking activity directly using point process modeling. We implement the BMI in experiments consisting of an instructed-delay center-out task in which monkeys are presented with a target location on the screen during a delay period and then have to move a cursor to it without touching the incorrect targets. We show that the two-stage BMI performs more accurately than either stage alone. Correct target prediction can compensate for inaccurate trajectory estimation and vice versa. The optimal feedback control design also results in trajectories that are smoother and have lower estimation error. The two-stage decoder also performs better than linear regression approaches in offline cross-validation analyses. Our results demonstrate the advantage of a BMI design that jointly estimates the target and trajectory of movement and more closely mimics the sensorimotor control system. There has been a large body of work in the past decade on real-time brain-machine interfaces (BMI) demonstrating that neural signals from the motor cortical areas can be used to control computer cursors or robotic arms in human and non-human primates The successful real-time attempts at individual decoding of the continuous trajectory or the target of movement motivate the development of a new type of real-time BMIs that aim to estimate jointly both the trajectory of the movement and the intended target. This approach is justified by two main reasons. First, the activity in the motor cortical areas has been shown to be related to both target and kinematics of movement In addition to modeling both the target and trajectory information, similar to the natural sensorimotor system, a BMI system can be modeled as a feedback control system. When using a BMI, the subject (controller) decides on the control commands and consequently modulates the neural activity to move the prosthetic device to a desired target  while receiving real-time visual feedback of the state of the movement. Based on these considerations, a more principled BMI design that aims to mirror the sensorimotor control system and jointly decode the movement target and the corresponding trajectory would allow for a potentially more accurate movement execution.Here we develop a real-time BMI that uses a novel optimal feedback control design and combines information about target and trajectory intent, and demonstrate its implementation in sensorimotor tasks performed by two rhesus monkeys. This BMI employs a novel two-stage approach. In the first stage, it uses the neural spiking activity prior to movement initiation to predict the intended target of the movement. In the second stage, it combines this prediction with the peri-movement spiking activity to estimate the movement trajectory. To decode the trajectory, inspired by the optimal feedback control theory of the sensorimotor system without touching any of the incorrect targets under a limited time constraint. Hence only trajectories that reached the correct target and at no point touched an incorrect target placed at the other three sides of the screen were rewarded . Unlike many BMI motor tasks in which the subject can freely move until reaching a target, this task required the monkey to reach the correct target rewarded . A perforewarded  and the The BMI processing consisted of two stages and decoded two aspects of movement. During the first stage, it used a maximum-likelihood (ML) decoder based on a point process model of the neural spiking activity to predict the monkey's intended target of movement during the delay period after target presentation but before movement initiation . In the second stage, the BMI combined this decoded target with the peri-movement activity to estimate the trajectory. In this stage, the spiking activity of each neuron was modeled as a point process fitted to position and velocity. The BMI estimated the trajectory using an optimal feedback control design that combined the decoded target with the peri-movement activity. This design is inspired by the optimal feedback control theory of the sensorimotor control system used to explain its function Models for the BMI were trained on the neural spiking activity during the training session at the beginning of each day. Neural recordings were made during target presentation prior to the presentation of the “go” cue, which signaled that the monkey could move the joystick, as well as during movement itself after the “go” cue .Each training session consisted of an average of 89±2 trials. Point process models relating the spiking activity of each recorded neuron to target location and movement kinematics were constructed based on the known target location and cursor position for each trial and the recorded multiple-neuronal activity using the generalized linear models (GLM) framework During the delay period, the ensemble spiking activity (20±2 neurons) predicted the correct target with high accuracy in the training sessions . The prediction accuracy of the trained point process target models across sessions , measured as the percentage of trials on which the models correctly predicted the target using the delay neural activity, was 81±3% (mean ± s.d.). To examine further the contribution of the individual neurons to the target prediction accuracy, we performed a neuron dropping analysis in which the spiking activity of a single neuron during the delay period was used to decode the target . We founensemble .During movement, the premotor neurons were tuned to position and velocity. Fitting the point process models for the kinematics using the GLM framework We tested the performance of the two-stage decoder in an offline analysis of the training sessions data using leave-one-out cross-validation. We also compared to the performance of the second stage of the decoder alone by replacing the feedback-controlled state-space model in the FC-P-PPF  with a random-walk (RW) model, which uses no prior target information and only enforces smoothness in the trajectory. The resulting filter is the RW-PPF . We also compared the performance of the two-stage decoder to that of the linear ridge regression decoder t-test, t-test, We found that the acquisition accuracy of the two-stage decoder across sessions was 83±3%, higher compared to 61±7% for the RW-PPF that used only the peri-movement activity  to decode the trajectory. Note that the cursor was held at the center during the delay period. We found that using the two-stage BMI, the monkeys could perform the task with an average accuracy of 77±9% . To asseWe found that the two stages of the BMI performed in a complementary manner to achieve its overall accuracy; the correct target predictions could compensate for the inaccurate performance of the kinematics decoder and the ongoing trajectory estimation could correct the incorrect target predictions. To illustrate this complementary property of the BMI and how its two stages contributed to its overall performance, we compared with the performance of each of its stages alone using either the target-related delay or the kinematic-related peri-movement activities. To compare the accuracy of the BMI with that of using only the peri-movement activity, i.e., using the second stage of the BMI alone without target information, we decoded the trajectory offline using RW-PPF on the same real-time data set . The ave31% . This sue errors . More spst stage . More spThe acquisition time in the BMI sessions, i.e., time until the trial ended by rewarding the monkey, was close to the natural acquisition time in the training sessions. In our experiments we used a short 3 s time-out condition to make the task more challenging and the required acquisition time closer to that of monkey's own movement. The median acquisition time for the natural movement was 0.6To determine differences in BMI performance across monkeys and therefore the robustness of the two-stage BMI to individual variability, we examined differences in performances between the two monkeys, A and B. For monkey A, the real-time BMI accuracy  was 67Together these findings suggest that although the performance of one stage in the two-stage BMI may not be equal across monkeys or recording areas, by combining both target and trajectory related information the two-stage approach provides a robust computational system that maintains good accuracy under variable experimental conditions . All surgery was performed under inhalational anesthesia in combination with Ketamine and opiate analgesia, and every effort was made to minimize suffering, in accordance with the recommendations of the Weatherall report, “The use of non-human primates in research”. Animals were housed in their cages in the primate animal facility. Animals were fed regularly with regulated fluid administration and were given environmental enrichment. Animals were completely unrestrained within their home cages. At the conclusion of experiments one animal was euthanized to allow for histological verification of recording sites with Ketamine and Pentobarbital, in conformance with recommendations of the American Veterinary Medical Association (AVMA) Guidelines on Euthanasia.macaca mulatta) in the study. During the tasks, the animals were seated in a primate chair . The primates' head were restrained using a head post, and a spout was placed in front of their mouth to deliver juice using an automated solenoid. A spring-loaded, two-degrees of freedom manipulandum was mounted anterior to chair on the side contralateral to recording. A computer monitor was placed in front of the animals at eye level which displayed the task. A NI DAQ card  was used for the I/O behavioral interface, and the behavioral program was run in Matlab  using custom made software (www.monkeylogic.net).We used two adult male rhesus monkeys , at which time the monkeys could use the joystick to move the cursor from the center of the screen to the instructed target. Once the cursor reached the target, the animal received a drop of juice following a 320 ms delay if the correct target was reached and no incorrect targets were touched by the cursor. If during a trial, the animals moved prematurely, failed to reach any target during the allowed time or touched an incorrect target before reaching the correct target, the trial aborted. Note that all targets had the same size as illustrated in A titanium head post and recording electrodes were surgically implanted in each monkey contralateral to the side of joystick use. All procedures were performed in an IACUC-approved aseptic primate surgical facility. Prior to electrode implantation, craniotomies were performed over the sites of interest using standard stereotactic coordinates. Once the cortex was exposed and the sulcal anatomy identified, several silicone microelectrode arrays were placed in the cortex  into the PMd and supplementary motor areas. The electrodes were secured into place using fibrin glue, silicone sealant, and methylmethacrolate. The distal leads were then attached to a female connector and secured to the skull with titanium miniplates and dental acrylic. Anatomic post-mortem confirmation of electrode positioning was performed in one monkey. The second monkey is still performing behavioral tasks.Recordings began at two weeks following surgical recovery. A Plexon multichannel acquisition processor was used to amplify and band-pass filter the neuronal signals (150 Hz decoder . The curfirst touching any of the other (incorrect) targets results in an error, at best any chance-based decoder would first reach the correct target with equal probability among the four possible. Hence the performance of such a chance-based decoder is at most 25%. We also examined the performance of a linear regression decoder on shuffled neural activity and confirmed that it approximately resulted in Since the task requires reaching the correct target and since The BMI decodes the monkeys' intended target of movement by recording the ensemble spiking activity during the 800 ms delay interval prior to the “go” cue. Note that the delay between the start of target presentation and “go” cue is 1000 ms. We do not use the activity in the first 200 ms in the BMI in order to allow sufficient time for the visual target information to reach the PMd and SMA In the second stage, the BMI combines the decoded target with the peri-movement ensemble spiking activity using a recursive Bayesian decoder with an optimal feedback control design. A recursive Bayesian decoder in general consists of two probabilistic models: the prior model on the time sequence of kinematic states, and the observation model relating the neural signal to these states. The prior model should in general incorporate any prior information available about the kinematic states, which for a goal-directed movement includes the intended target. We build the prior movement model of the decoder using an optimal feedback control design, which takes into account the decoded target location and the sensory feedback. To develop the observation model, we use a point process model of the spiking activity whose instantaneous rate is a log-linear function of kinematics. The resulting decoder hence processes the spikes directly in real time and operates at the millisecond time scale of the spiking activity. In the next few sections we present the prior movement model and the neural observation model used in the decoder for estimation of goal-directed movements, and the decoder recursions.known arrival time Previous offline work have built goal-directed prior models for reaching movements by conditioning a linear Gaussian state-space model, also known as a random-walk model, on being at the target at a Since the goal of the decoder is to estimate the intended movement of the subject, a prior movement model that aims to emulate the sensorimotor processing underlying motor control could result in more accurate estimation of movement. Hence we build the prior goal-directed state-space model for the movement kinematics based on the optimal feedback control theory of the sensorimotor system The difference in applying this framework to natural arm movement Motivated by this view, we develop a prior feedback-controlled state-space model for the kinematics that exploits the information about the target location and takes into account the sensory feedback. We introduced this model in W, and A and B are parameters of the forward model. Here we assume that the sensory feedback T is the movement duration, R is positive definite, then the optimal control signal at any time, feedback of the state at that time Denoting the sequence of kinematic states by R should be appropriately designed for an application of interest and T. Note also that the sensory feedback is incorporated in the control term since the control term is simply a linear function of the current kinematic state (see (5)), assumed to be known through the feedback. This is in turn reflected in the prior model in (6).Substituting (5) in (3) reduces this state-space model to the optimal feedback-controlled state-space modeld* and taking the state to be We can now specialize these to the reaching movements used in our experiments. For a reaching movement the cost function should enforce end-point positional accuracy, stopping condition, and energetic efficiency Having specified the forward dynamics model and the cost function for the reaching movement, the feedback matrices We build the observation model for each neuron as a point process whose instantaneous firing rate is a function of kinematics t and We used a modified version of the cosine tuning model P-values can also be obtained for all the model parameters We assumed that the spiking activity of the neurons are conditionally independent given the kinematic states and hence the observation model for the ensemble is given byHaving the prior and the observation models we can now develop the recursions for the Bayesian decoder. However, the prior model built in (6) is dependent on the movement duration, For now we assume that the movement duration is known. The minimum mean-square error (MMSE) estimator is given by the mean of the posterior density that is To provide some insight into these recursions, note that in the prediction step given in (15) the feedback-controlled prior model is used to move the estimate forward. In the update step given in (18) the estimate is found by making a correction or update to this prediction. Here, T, not known a priori to the real-time BMI The feedback-controlled state-space model in (6)  is a function of movement duration, Our framework works by discretizing the duration, finding the kinematic estimate for each discretized duration using an FC-PPF, running these FC-PPF filters in parallel, and finding the likelihood of each of the discretized duration points jointly with the corresponding trajectory estimate, all purely based on the neural spiking activity and in real time. The decoder then optimally combines the trajectory estimates corresponding to the discretized durations to get the overall trajectory estimate. The result is the feedback-controlled parallel point process filter (FC-P-PPF) that we have derived in detail in B = 0 reduces the state-space model in (3) to the random-walk model and consequently the recursions of FC-PPF with this choice recover the RW-PPF.Setting R, the mean subtracted position variable by We also find the performance of the linear ridge regression decoder on the neural data. The commonly used regression decoder in the BMI literature is the ordinary linear least squares regression decoder that is fit by minimizing the residual squared error. The linear least squares regression, however, can result in high mean-square estimation error due to a high error variance, for example in cases with correlated regressors In our implementation of the BMI, the first stage of the decoder makes a decision about the intended target. However, instead, the BMI can easily include all targets in the FC-P-PPF but weight them properly by their corresponding likelihood calculated from the first stage similar to a previous offline study d* accordingly in the cost function in (7). Given the present results, it is conceivable that a similar complementary performance could be observed for the two-stage BMI in the case where more targets are present, especially given that in this case it will be harder for either stage alone to result in accurate performance (for example the first stage needs to decode one out of more targets). Investigating the behavior of the decoder in experimental setups with more target locations will be a valuable future research direction.Even though in the present experiments we used four targets, the decoder can generalize to the case with more targets. This is because the prior model in (6) can be generalized to arbitrary target locations by just replacing Finally, in our work we use the target onset and “go” cues to indicate the boundaries between baseline, plan, and movement epochs as is typically done in BMI experiments To find the number of neurons that were sufficient to obtain an accurate target prediction during the delay period, we performed a single neuron analysis in which the spiking activity of a single neuron was used to decode the target . We thenThe roughness coefficient for a sequence is an indicator of how smooth it is For a trajectory of duration Figure S1Neuron dropping analysis. (A–D) Activity of a single neuron under the four targets in one training session. In the top figure, each row corresponds to a different trial and the black dots indicate the spike times. The bottom figure shows the corresponding firing rate. Activity is aligned to the target presentation time and vertical dashed lines indicate the target presentation and “go” cue times. The target prediction accuracy  of this neuron is 65%. (E) Target prediction accuracy as a function of the number of top neurons. The solid lines show the target prediction accuracy of six training sessions as a function of the number of neurons included in the prediction (The curve for each session is shown in a different color for clarity). Neurons were sorted based on their single neuron accuracy. Chance level accuracy for target classification is 25%.(TIF)Click here for additional data file.Figure S2Offline SNR comparisons. The bars show mean quantities and the error bars show the standard deviation (s.d.) around the mean across sessions. SNR is obtained from the training sessions using leave-one-out cross-validation.(TIF)Click here for additional data file.Figure S3Offline accuracy of the two-stage decoder on the training sessions data. Accuracies of the two-stage decoder, the first stage target prediction, and the RW-PPF  on the training sessions joystick movements are shown. The bars show mean quantities and the error bars show the standard deviation around the mean across sessions. Comparisons of the RMS error and the smoothness of the decoded trajectories for the two-stage decoder and RW-PPF are given in (TIF)Click here for additional data file.Figure S4Comparison of the trajectory estimates. For completeness, we also found the accuracy of the ridge regression decoder on the same real-time BMI data set. It is important to note, however, that since the performance of the ridge regression here is found offline, it is likely lower from its performance if used in real time and practiced by the monkey. The black line shows the trajectory estimate of the real-time BMI. The blue line shows that of RW-PPF using only the peri-movement activity, and the red line shows that of a linear ridge regression decoder, both run offline but using the same real-time data set as the BMI. (A) Sample trials in which the ridge regression decoder is correct. (B) Sample trials in which the ridge regression decoder is incorrect. The average accuracy of the linear ridge regression decoder on the BMI data sets was 50±11% Click here for additional data file.


Wireless sensor networks (WSNs) are an important tool for monitoring distributed remote environments. As one of the key technologies involved in WSNs, node fault detection is indispensable in most WSN applications. It is well known that the distributed fault detection (DFD) scheme checks out the failed nodes by exchanging data and mutually testing among neighbor nodes in this network., but the fault detection accuracy of a DFD scheme would decrease rapidly when the number of neighbor nodes to be diagnosed is small and the node's failure ratio is high. In this paper, an improved DFD scheme is proposed by defining new detection criteria. Simulation results demonstrate that the improved DFD scheme performs well in the above situation and can increase the fault detection accuracy greatly. The target is to cooperatively sense, collect and process the information about objects in the coverage area, and then send it to the observer for processing and analyzing. It is a system with multi-functional and low energy consumption see -4)..4]).Massive low-cost sensor nodes are often deployed in uncontrollable and hostile environments. Therefore, failure in sensor nodes can occur more easily than in other systems;The applications of WSNs are being widened. WSNs are also deployed in some occasions such as monitoring of nuclear reactor where high security is required. Fault detection for sensor nodes in this specified application is of great importance;It is troublesome and not practical to manually examine whether the nodes are functioning normally;Correct information cannot be obtained by the control center because failed nodes would produce erroneous data. Moreover, it may result in collapse of the whole network in serious cases;Nodes are usually battery-powered and the energy is limited, so it is common for faults to occur due to battery depletion.Failed nodes may decrease the quality of service (Qos) of the entire WSN. It is important and necessary to study the fault detection methods for nodes in WSNs for the following reasons -6:MassiWSN node faults are usually due to the following causes: the failure of modules (such as communication and sensing module) due to fabrication process problems, environmental factors, enemy attacks and so on; battery power depletion; being out of the communication range of the entire network.The node status in WSNs can be divided into two types -8: normaThe remainder of the paper is organized as follows: In Section 2, related works in the area of fault detection in WSNs is reviewed. In Section 3, the DFD node fault detection scheme is introduced and the theory and realization of improved DFD node fault detection scheme is described in detail. The advantages and disadvantages of the two schemes are also analyzed. Simulation examples compare the fault detection accuracy of the two schemes with different network sizes, average number of neighbor nodes and failure ratios in Section 4. The paper is concluded in Section 5.2.In this section, we briefly review the related works in the area of fault detection in WSNs. The existence of faulty sensor measurements in WSNS will cause not only a degradation of the network quality of service, but also a huge burden on the limited energy. Article  investigIn  the desiRef.  proposesIn , a taxonArticle  proposeset al. in [An energy efficient fault-tolerant detection scheme is proposed in  to introt al. in  did not Article  presentsIn wireless sensor networks, multi-hop routing is commonly performed through a routing tree. Eventually, the routing tree needs to be rebuilt to accommodate failures, balance the energy consumption, or improve data aggregation. Most of the current solutions do not detect when the routing topology that needs to be rebuilt. Article  shows itThe authors in  proposed3.3.1.Several terms used in this paper are explained as follows:Fault detection accuracy: when determining the status of a node with a certain node fault detection scheme, the result can be divided into four cases which are: diagnosing the normal node  as normal, the faulty node  as faulty, the normal node as faulty and the faulty node as normal. The sum of the probability of the two former cases is called fault detection accuracy.Node's failure ratio: the probability of a node's failure in sensor network.iS is Neighbor (iS) and the total number of neighbors of node iS is noted as Num(Neighbor (iS)).Neighbor node: The two nodes are neighbor nodes if the distance between them is within a single-hop's communication scope. The set of all neighbors of node 3.2.iS and jS, a test result ijC is produced by the data (such as temperature) sensed by each of them. The data at the moment t should be very close to each other because they are near, and the difference θ1; besides, at another moment t+1, the difference of the data of the two neighbor nodes is θ2. If one of these two conditions is not met, at least one of iS and jS is determined as a failure, and the test result ijC = 1, otherwise ijC = 0. For any node iS, its test result with each node in Neighbor(iS) can be obtained. If there are more than Neighbor(iS), then the initial detection status iT of node iS is possibly faulty (LT), otherwise, it may be possibly normal (LG). Thus, initial detection status of each node iS in the network is available.DFD node fault detection scheme proposed by Jinran Chen determines the status of node by testing among neighbor nodes mutually. For two neighbor nodes jS in Neighbor(iS), its actual status may be normal or faulty, so it may be not correct to determine the initial detection status of iS by the test result ijC which cannot be used to verify the status of iS. When the initial detection status of all nodes in the network is obtained, the following detection criterion is used for any node iS: for the nodes in Neighbor(iS) whose initial detection status is LG, subtract the number of nodes whose test result with iS is 0 from the number of nodes whose test result is 1. If the result is not less than iS is normal, otherwise, the status of iS is faulty.For any node 3.3.normalS, if the number of its neighbor nodes with initial detection status of LG is less than normalS is misdiagnosed as faulty, reducing the fault detection accuracy. The conditions of diagnosing the normal node as “normal” are too harsh in DFD node fault detection scheme. Besides, the node fault accuracy of DFD scheme will decrease rapidly when there are not many neighbors of the nodes to be diagnosed or the node's failure ratio of network is high.From the realization of DFD node fault detection scheme, for a normal node iS and the nodes in Neighbor(iS) whose initial detection status is LG, if the nodes whose test result with iS is 0 are not less than the nodes whose test result is 1, then the status of iS is normal (GD), otherwise, the status of iS is faulty (FT).The improved DFD node fault detection scheme proposed in this paper changes the detection criterion of DFD scheme as follows: for any node iS and any node jS in Neighbor(iS), set ijC as 0 and calculate For node ijC as 1 and turn to the next node in Neighbor(iS);If ijC as 1 and turn to the next node in Neighbor(iS);If Neighbor(iS) with iS are all obtained.Repeat above steps until the test results of each node in iT of iS as possibly normal (LG), otherwise iT is possibly faulty (LT).If Num(Neighbor(iS)T-LG) is the number of neighbor nodes of iS whose initial detection status is LG. If iS as normal (GD), otherwise it's faulty (FT).iS whose initial detection status is LG, and if the initial detection status iT of iS is LG, then set the status of iS as normal (GD), otherwise as faulty (FT).If there are no neighbor nodes of Check whether detection of the status of all nodes in network is completed or not. If it has been completed, then exit. Otherwise, repeat steps of (I), (II), (III) and (IV).Improved DFD scheme takes the following steps:iS can also be correctly determined by improved DFD scheme when the number of nodes in Neighbor(iS) whose initial detection status is LG is small (node's failure ratio of network is high). Improved DFD scheme also can be applied in the sensor network where the neighbors of the nodes to be diagnosed are less.From the steps of improved DFD scheme, the status of node p and the average number of neighbors of each node is k. Set the probability of initially diagnosing the actual faulty (FT) node as possibly faulty (LT) is flfP, the actual normal (GD) node as possibly faulty (LT) is glfP, actual faulty (FT) node as possibly normal (LG) is flgP, and the actual normal (GD) node as possibly normal (LG) is glgP, then:i is the number of failed nodes in the neighbors of the node to be diagnosed. According to the detection criterion of DFD scheme, the faulty nodes  can be initially diagnosed as possibly faulty  when i is not larger than half of the number of neighbors of the node to be diagnosed which is m-1. Simultaneously, in j is the number of normal nodes in the neighbors of the node to be diagnosed. According to the detection criterion of DFD scheme, the normal nodes (faulty nodes) will be initially diagnosed as possibly faulty  when j is not larger than half of the number of neighbors of the node to be diagnosed which is m-1.We suppose the node's failure ratio is In improved DFD scheme, the possibility of diagnosing the actual faulty node as normal is:The possibility of diagnosing the actual normal node as faulty is:The possibility of diagnosing the actual normal node as normal is:x is the number of nodes in the neighbors of the node to be diagnosed which is initially diagnosed as possibly normal (LG). In y is the number of actual normal (GD) nodes initially diagnosed as possibly normal (LG) in x nodes. According to the detection criterion of the improved DFD scheme, mistakes will be made to the detection of status of nodes when y is not larger than half of x, n-1. Simultaneously, in z is the number of actual faulty (FT) nodes initially diagnosed as possibly normal (LG) in x nodes. According to the detection criterion of the improved DFD scheme, the actual status can be diagnosed only when z is not larger than half of x, n-1. In The possibility of diagnosing the actual faulty node as faulty is:From x is the number of nodes in the neighbors of the node to be diagnosed which is initially diagnosed as possibly normal (LG). DFD can diagnose the actual normal (GD) node as normal only when x is larger than half of the number of neighbors of the node to be diagnosed which is m-1. The fault detection accuracy of DFD scheme is:k and nodes' failure ratio p, the fault detection accuracy of DFD and improved DFD scheme calculated by k and increasing of p. For the same k and p, the fault detection accuracy of improved DFD scheme is obviously higher than DFD scheme. Besides, improved DFD scheme can also keep high fault detection accuracy even with high node's failure ratio and small average number of neighbor nodes.For different number of neighbor nodes 4.The improved DFD scheme will be applied in a real wireless sensor network system. It is expensive to run schemes on the hardware of the system, so the feasibility and accuracy of the schemes should be verified before being applied. Therefore, simulation becomes the best alternative way of testing, evaluating and verifying. We programmed the DFD scheme and improved DFD scheme using Visual C++ and Matlab. We compared the change of fault detection accuracy of the two schemes with varying node failure ratios for different average numbers of neighbor nodes. Two hundred nodes are randomly deployed in the network, as shown in With 200 randomly deployed nodes, the node fault detection accuracy trend with various average numbers of neighbor nodes is shown in The node fault detection accuracy of the DFD and the improved DFD scheme for different network size is also analyzed and compared. From Figured 4 to 7, we can see that for the same total number of nodes deployed, the average number of neighbor nodes and the nodes' failure ratio, the improved DFD scheme distinctly outperforms the DFD scheme. The fault detection accuracy of the DFD scheme sharply decreases with an increase of the nodes' failure ratio. However, the improved DFD scheme retains a high fault detection accuracy.Comparing In Therefore, compared with the DFD scheme, the improved DFD scheme greatly increases the node fault detection accuracy and high fault detection accuracy can be obtained even with high node failure ratios and small average number of neighbor nodes.5.For the node whose actual status is normal, if the number of nodes which is initially diagnosed as possibly normal (LG) in its neighbor nodes is less than half of the total neighbor nodes, the DFD node fault detection scheme will misdiagnose the normal node as faulty. Modification is made to the detection criterion of DFD scheme and an improved DFD scheme is proposed to address this shortcoming. Simulation results show that the fault detection accuracy of the improved DFD scheme outperforms the DFD scheme for different average numbers of neighbor nodes and node failure ratios. The improved DFD scheme can also be applied to wireless sensor networks where there are less neighbor nodes and the node failure ratio is higher.


Animals alter their locomotor mechanics to adapt to a loss of limb function. To better understand their compensatory mechanisms, this study evaluated the changes in the fore-aft ground forces to forelimb lameness and tested the hypothesis that dogs unload the affected limb by producing a nose-up pitching moment via the exertion of a net-propulsive force when the lame limb is on the ground. Seven healthy Beagles walked and trotted at steady speed on an instrumented treadmill while horizontal force data were collected before and after a moderate lameness was induced. Peak, mean and summed braking and propulsive forces as well as the duration each force was exerted and the time to reach maximum force were evaluated for both the sound and the lame condition. Compared with the sound condition, a net-propulsive force was produced by the lame diagonal limbs due to a reduced braking force in the affected forelimb and an increased propulsive force in the contralateral hindlimb when the dogs walked and trotted. To regain pitch stability and ensure steady speed for a given locomotor cycle, the dogs produced a net-braking force when the sound diagonal limbs were on the ground by exerting greater braking forces in both limbs during walking and additionally reducing the propulsive force in the hindlimb during trotting. Consistent with the proposed mechanism, dogs maximize their double support phases when walking. Likely associated with the fore-aft force adaptations to lameness are changes in muscle recruitment that potentially result in short- and long-term effects on the limb and trunk muscles. Animals have evolved behavioral plasticity to cope with a partial or total loss of a limb’s function. The associated lameness results from unloading the affected limb to relieve the pain, protect it from further damage and allow healing. Among other parameters such as kinematics or muscular recruitment, kinetic parameters change when a limb is unloaded and the animal adapts its locomotor mechanics to the new situation.Ground reaction forces (GRF) are, for analytical reasons, described by orthogonal vectors; each component –mediolateral (Fx), craniocaudal (Fy), vertical (Fz)– having its own characteristic waveform and magnitude that reflect gait, speed and limb function. Therefore, many studies have analyzed GRF to determine limb function in clinically normal and abnormal dogs  evaluate the changes in the fore-aft forces in all four limbs that are associated with a moderate forelimb lameness, 2) determine whether the braking or the propulsive forces are affected more by a distal load-bearing lameness, and 3) test the hypothesis that dogs produce a nose-up pitching moment about the CoM by exerting a net-accelerating force when the lame diagonal limb pair is on the ground. For heuristic reasons, we will focus on the craniocaudal component of the GRF in this study, although, as mentioned above, splitting the GRF into its orthogonal vectors is primarily a conceptual tool.The present study is part of a larger investigation, which aimed at a better understanding of the compensatory mechanisms of walking and trotting Beagles with induced load-bearing forelimb lameness. Therefore, the same subjects and experimental design as in the previous study were used  and propulsive (Fy+) component. In Vicon, touchdown and liftoff events of 10 consecutive strides were manually defined for each limb based on the vertical force curves. Because each stance phase varied slightly in duration and consequently in the number of recorded data points, the force curves were time-normalized to 100% stance duration  using linear interpolation. These time-normalized force data (in N) were averaged across the ten strides to obtain mean±SD for each dog and exported to Excel. Then, the data were normalized to the dog’s body weight using the following equation:Peak and mean force as well as the area under the curve  in percent body weight (%BW) were determined for Fy− and Fy+. We used summed force (in N) instead of impulse (in N/s) because the force data were time-normalized. Additionally, the duration during which braking force was applied and the time to peak force for braking and propulsion relative to the duration of the stance phase were determined. Note that because the braking force that the hindlimbs exert is small and may oscillate around zero before the propulsive phase begins, we determined braking duration by determining the last moment before the propulsion began  and the contralateral (c) limb from the 10 strides.To test whether the analyzed strides were at steady speed, we integrated the fore-aft force to determine the net-change in forward velocity of the CoM for each dog. This net-change in forward velocity was 5.2% of the total impulse produced by the dogs in the sound walking trials, 3.2% in the lame walking trials, 3.3% in the sound trotting trials, and 2.7% in the lame trotting trials. Except for the sound walking trials, in which a slightly greater net-forward acceleration occurred, all values were within the 5% range that has been found to be acceptable as steady-state locomotion in previous studies e.g., .A Wilcoxon signed-rank test for paired observations was performed to detect differences in peak, mean and summed force as well as the temporal parameters between the sound and induced lameness conditions. P values p<0.05 were considered significant. All statistical tests were performed using GraphPad Prism .No significant differences in peak, mean and sum of the braking and propulsive forces were observed between the two fore- and the two hindlimbs during walking and trotting  and 2. AWith regard to the braking component, peak, mean and summed force were significantly decreased in the forelimb in which lameness was induced  and significantly increased in the contralateral forelimb (Fc) during both walking and trotting compared with the control data ; Fig. 2.During both walking and trotting, the time to peak braking and propulsive force was comparable between the sound and the lame conditions. The only significant difference was observed in the affected forelimb in trotting dogs; thereby, maximum braking force occurred significantly earlier during stance ; Fig. 2.After lameness was induced, symmetry indices changed significantly for the peak, mean and summed braking force in the forelimbs during both walking and trotting, while they were unchanged for the propulsive force (except peak force during trotting; At steady state, the forelimbs impart a net-braking force while the hindlimbs impart a net-propulsive force (e.g., walking dogs The evaluation of the net fore-aft acceleration showed that the dogs enrolled in this study walked and trotted at steady speed. Furthermore, the exerted braking and propulsive forces of the two fore- and the two hindlimbs were similar before lameness was induced. This together with the previous evaluation of the vertical load distribution among the limbs Compared to the sound condition, both braking and propulsion were reduced in the affected forelimb but the braking force was more affected than propulsive force during walking. This is in contrast to results from dogs with unilateral fragmented coronoid process disease, in which primarily the propulsive force was altered During steady speed locomotion, braking and propulsive forces must be equal and opposing to prevent the body from undergoing a net rotation about its pitch axis A net-propulsive force in a diagonal limb pair can result from a reduced braking force of the fore- or the hindlimb or both, an increased propulsive force of the fore- or the hindlimb or both or a combination of thereof. Conversely, a net-braking force may result from increased braking and/or decreased propulsive forces of the diagonal limbs. Therefore, the amplitude and/or the time to apply the force may change. The results of this study show that in dogs walking and trotting at their preferred speed and with lameness induced in a forelimb, net-acceleration in the lame diagonal pair results from reduced braking forces in the forelimb with no changes in timing and increased propulsive forces in the hindlimb due to an earlier transition from braking to propulsion but also greater forces exerted by the limb. Net-deceleration in the sound limb pair during both walking and trotting was associated with greater braking forces in the fore- and the hindlimb due to both changes in timing and amplitude. Additionally, during trotting, the propulsive force exerted by the hindlimb was reduced.Assuming that the locomotor adaptations to induced distal, load-bearing forelimb lameness observed herein are comparable to clinical load-bearing forelimb lameness, some implications follow from our results. In dogs with chronic forelimb lameness, the cyclic changes in fore-aft speed of the CoM are likely associated with muscular and potentially also skeletal stress of the locomotor system. For example, the nose-up pitch when the lame diagonal limbs are on the ground results, additionally to a lower braking force of the affected forelimb, from a greater propulsive force of the contralateral hindlimb. This, together with the greater moment at the hip, which has been proposed previously based on the increased vertical force exerted by this limb The trot is considered a two-beat gait in which, within each stride, two functional steps can be distinguished because the two diagonal limbs are closely coupled. This tight coupling likely facilitates the use of the herein proposed strategy of lame dogs ‘doing wheelies and stoppies’ because it enables the separate exertion of net-propulsive and net-braking forces by the diagonal limb pairs. During walking, however, for a good part of the cycle, three legs are on the ground. Three-legged ground contacts interfere with the production of a nose-up pitching moment as only for a short time the affected forelimb and the contralateral hindlimb are solely on the ground. Previous evaluation of the temporal gait parameters under the same experimental condition as used herein has shown that dogs walking with induced forelimb lameness significantly prolong the stance duration of the contralateral hindlimb and shift it forward relative to stride cycle so that the hindlimb’s touch down occurs earlier relative to the stance phase of the ipsilateral forelimb Additionally to the well-established adaptations in limb loading via changes in the vertical ground reaction force, this study shows that walking and trotting dogs with induced forelimb lameness also profoundly alter the craniocaudal force exerted by their limbs. By producing net-acceleration when the diagonal lame limb pair is in ground contact, dogs produce a nose-up pitching moment and thereby temporarily unload the affected forelimb. To regain pitch stability and ensure steady speed during the respective locomotor cycle, the produced net-deceleration results in a nose-down pitch when the sound diagonal limb pair is on the ground. As no clinical study has evaluated the fore-aft force adaptations to forelimb lameness in dogs, it remains open whether diseased dogs also use the proposed mechanism. Assuming they do, the likely associated changes in the recruitment of limb and trunk muscles will potentially lead to short- and long-term orthopedic consequences for the locomotor apparatus. Furthermore, our results show that evaluating the fore-aft component may be helpful in understanding the interdependencies between cause and degree of lameness and ground force adaptations.


Oncorhynchus tshawytscha) were investigated. Disease-induced mortality of juvenile salmon has become a serious concern in recent years. However, the overall effects of disease mortality on the asymptotic and transient dynamics of adult spawning abundance are still largely unknown. We explored various scenarios with regard to the density-dependent process, the distribution of survivorship over the juvenile phase, the disease mortality rate, and the infusion of stray hatchery fish. Our results suggest that the sensitivity to the disease mortality rate of the equilibrium adult spawning abundance and resilience  varied widely and differently depending on the scenario. The resilience and coefficient of variation of adult spawning abundance following a large perturbation were consistent with each other under the scenarios investigated. We conclude that the increase in disease mortality likely has an effect on fishery yield under a fluctuating environment, not only because the mean equilibrium adult spawning abundance has likely been reduced, but also because the resilience has likely decreased and the variance in adult spawning abundance has likely increased. We also infer the importance of incorporating finer-scale spatiotemporal information into population models and demonstrate a means for doing so within a matrix population modeling framework.The effects of an increased disease mortality rate on the transient and asymptotic dynamics of Chinook salmon ( Oncorhynchus tshawytscha) die from various infectious diseases including those caused by viruses e.g. The effects of infectious disease on salmon populations are a serious concern. Studies suggest that Chinook salmon . With respect to transient dynamics, we evaluate the deviation of the adult spawning abundance from equilibrium over time following a large perturbation. These quantities are evaluated under various scenarios with regard to the density-dependent process, the distribution of survivorship over the juvenile phase, the disease mortality rate, and the infusion of stray hatchery fish.Ceratomyxa shastaC. shasta has been documented in a stretch of the Klamath River main stem  are infected by the myxozoan parasite ain stem  [19], [2C. shasta requires two hosts. The spores of C. shasta that infect juvenile salmon are released from the polychaete Manayunkia speciosa, the secondary host of the parasite The lifecycle of Stage-structured population models are used to investigate the effects of an increased disease mortality rate on the transient and asymptotic dynamics of salmon populations. We employ matrix population models that are tributary-specific and include a juvenile survival rate that is dependent on the tributary's juvenile abundance. An alternative specification would be a juvenile survival rate that is dependent on the total juvenile abundance of several tributaries, or perhaps all tributaries and hatcheries. However, this specification would amount to a competition model in which groups of individuals compete for a common resource such as food or space. Under a competition model, the competitively weaker tributary populations would be eliminated, unless the strength of competition between the populations was weak Recently, Worden et al. A stage-structured matrix population model C. shasta. In addition, hatchery-produced fish are released from Iron Gate and Trinity River Hatcheries into the Klamath and Trinity Rivers, respectively, and these fish are thought to migrate to the ocean relatively quickly. However, fish released from Iron Gate Hatchery pass through the infectious zone, and they are known to be infected by C. shasta. On their return from the ocean some of the hatchery-produced fish “stray” into natural areas to spawn instead of returning to the hatchery. In particular, some of the fish released from Iron Gate Hatchery spawn in Bogus Creek and the upper main stem of the Klamath River below Iron Gate Dam, and some from the Trinity River Hatchery spawn in the upper main stem of the Trinity River below Lewiston Dam  is significantly greater than the number straying into the Shasta River. The dynamics for the Klamath River upper main stem spawning population are expected to be similar to that of Bogus Creek, while the remaining natural populations of the river system are minimally affected by the disease.A stage-structured matrix population model was used to characterize the life cycle of a single spawning population (tributary) of fall-run Chinook salmon in the Klamath River basin . Stage 1t, with T denoting the transpose operator. Absent stray hatchery fish, the abundance at time t+1 isLet ecundity . The pert+1 isStray hatchery-origin fish contributing to a natural spawning population were combined with the natural-origin fish in the model at stage 2 . The str stage 2 .The effects of disease mortality on natural production and the contribution of stray hatchery fish are incorporated into the model as described in the next section.It is generally thought that cohort strength in salmon is established by the end of early ocean life The distribution of survivorship over the juvenile phase and the timing of disease infection were incorporated into the ion rate , Table 1We chose to re-parameterize The survival rate of hatchery-produced fish from release to stage 2, on which the contribution of stray hatchery fish,  depends , was assDiscussion).Our disease submodels consider two simple alternatives with regard to the timing of the density-dependent compensatory process relative to the disease mortality. However, there are other possibilities. For example, density-independent survival could occur both before and after the density-dependent process. Or, the disease mortality could occur during the density-dependent process, resulting in the density-dependent term being partitioned . Although these alternatives may more closely represent the natural course of events, we believe that our simpler models provide insights into these more complex situations without the complications introduced by the additional model structure whereResilience has been defined as the asymptotic rate of return to equilibrium abundance  along with the tributary-specific density dependence. If there are two density-dependent processes acting on salmon populations, one tributary-specific and the other affecting aggregate juvenile abundance, the former is likely to have the greater effect. Otherwise, one or more of the component populations would likely be eliminated because of the aggregate competition Density dependencies that are more complex than those explored in this study may occur in nature. For example, the density dependence may be operating during a shorter period of time. If so, this would effectively add density-independent survival terms before and after the density-dependent term in our model. Additional density-independent survival would be expected to simply increase the survival rate that the density dependence is acting upon. Alternatively, the disease mortality may act in the middle of the compensatory density-dependent process, splitting the effect in two . This could be accommodated by combining our two density-dependent survival terms in the five-stage model. With this combination, it would be likely that an increased disease mortality rate would reduce the resilience of the system and also would reduce the equilibrium adult spawning abundance. However, the magnitude of the reduction would depend on how the reduced survival was distributed among the two density-dependent terms and on the density-independent survival rate.C. shasta to the disease-induced mortality of salmon is a key next step towards developing a predictive salmon/disease population dynamics model. The lack of historical monitoring of the disease-causing agents  will likely prevent construction of a statistically-based model Along with obtaining a better understanding of the distribution of survivorship over the juvenile phase and the timing of density-dependent mortality, relating the infection processes of An important message from our study is that simple population models such as standard spawner-recruitment models and standard matrix population models alone are not fully adequate to assess the impact of an increased disease mortality rate at a particular time within a stage because of the time-scale mismatch between these models and the process. It is important to know how survival is distributed throughout the stage within which the increased mortality rate acts, and potentially the location within a spatially stratified population or meta-population in which it acts. The effects of an increased disease mortality rate may also be countered to some degree by the infusion of stray hatchery fish to a natural spawning population. This coupled with the likely expression of density-dependent effects at the local level suggests that, for some situations, the modeling of salmon population dynamics is likely more appropriate at the tributary scale than at the basin-wide scale.


In many everyday situations, humans must make precise decisions in the presence of uncertain sensory information. For example, when asked to combine information from multiple sources we often assign greater weight to the more reliable information. It has been proposed that statistical-optimality often observed in human perception and decision-making requires that humans have access to the uncertainty of both their senses and their decisions. However, the mechanisms underlying the processes of uncertainty estimation remain largely unexplored. In this paper we introduce a novel visual tracking experiment that requires subjects to continuously report their evolving perception of the mean and uncertainty of noisy visual cues over time. We show that subjects accumulate sensory information over the course of a trial to form a continuous estimate of the mean, hindered only by natural kinematic constraints (sensorimotor latency etc.). Furthermore, subjects have access to a measure of their continuous objective uncertainty, rapidly acquired from sensory information available within a trial, but limited by natural kinematic constraints and a conservative margin for error. Our results provide the first direct evidence of the continuous mean and uncertainty estimation mechanisms in humans that may underlie optimal decision making. Success is only achieved when one is prepared with a large enough net to accommodate the variability in both the butterfly’s trajectory and the movement of one’s arm.Uncertainty is a fundamental property of the world, as any avid butterfly collector will attest. To anticipate the fluttering flight of maximum-likelihood ideal observer . Recently, it was shown that humans are not only able to predict the position of objects moving along random or noisy trajectories, but also that they are able to report a level of confidence in this prediction subjective perception of uncertainty is closely related to the objective uncertainty (the measured variability in performance) The theory of statistical optimality in the brain relies crucially on the fact that humans must somehow accumulate statistical information from unpredictable stimuli. For example they may need to estimate not only the The forced-choice paradigm is classically used to compare decisions under uncertainty e.g. . Howevermean of “fluttering” visual cues ; and (ii) indicate the range in which they believe the mean of the cues to lie (viz. choosing an appropriate size of net).To achieve these aims we present a novel experimental paradigm that requires subjects to explicitly track the mean and variance of noise-perturbed visual cues. We control the arrival of noisy visual stimuli over time, allowing us to monitor the behavioural consequences as sensory evidence accumulates. In two variants of our “butterfly catching” task we ask subjects to (i) track the From trial-to-trial we modulate the underlying distribution of the cues, allowing us to observe the evolution of mean and confidence estimates with respect to the visual cues responsible for their formation. Using a sensorimotor model we show the extent to which the observed trajectories are statistically-optimal under the kinematic limitations of human motion, while computation of the weights allocated to each visual cue over time allows us to expose the mechanisms of sensory integration underlying the processes of continuous estimation.Materials and Methods.In this paper we introduce the “butterfly catching” paradigm, illustrated in Materials and Methods). The perceived uncertainty of clusters of noisy visual samples changes as a predictable function of their number The fluttering visual cues are a sequence of blurry dot-clouds, with cloud locations distributed in time according to a pseudo-Normal distribution with mean left). We modulate the variance of the visual cues, In Task 1 we examine subjects’ ability to estimate the mean, aperture , left. Wright), with width determined by the distance between the thumb and forefinger. From Task 1 we establish a linear mapping from objective uncertainty (by optimising the trade-off between accuracy and point-scoring). We assume subjects can acquire this mapping during the 450 trials preceding Task 2.In Task 2 subjects must instead indicate the range of values in which they believe the mean to lie, using a variable cursor aperture , right, Task 2 demands subjects to report their mean and confidence estimates simultaneously, providing a unified paradigm to evaluate the mechanisms underlying the formation of these statistical estimators. To expose these mechanisms we manipulate the distributions of the stimuli from trial-to-trial in two ways: (i) we modulate the variance of the visual cues, low, medium and high) we hypothesised that subjects would estimate the mean and  and shifted cues in a given block by negative, positive, neutral). All other cues were shifted in the opposite direction by To induce perturbations we divided the sequence of cues on a given trial into three blocks  we conducted a within-subjects analysis of variance (ANOVA) on the mean endpoint error , with a two-level factor of task (Task 1 and Task 2) and three-level factor of low, medium, high). This revealed a significant main effect of We found that subjects were equally good at mean estimation in both tasks, shown in In a); (ii) trajectory deviations shortly after the onset of the perturbation ; (iii) spontaneous changes in direction ; and (iv) endpoint errors . The model observer integrates the visual cues in a statistically optimal fashion (by computing the maximum likelihood mean estimate). This estimate manifests itself through the movement of the cursor, which we constrain by introducing three parameters, namely sensorimotor latency, Materials and Methods). This model accounts both qualitatively and quantitatively for the key features of the empirical data, such as the magnitude and timing of direction changes, and the magnitude of endpoint deviation and endpoint error , but these parameters are global to all conditions and have no capacity to explain the role of individual cues on decisions, nor the effects of cue perturbations or variance (see Discussion). In We devised a model of motor behaviour to account for the latencies observed in decisions .To understand the mechanisms by which subjects estimate the mean we can infer the contribution of each of the visual cues to the evolving estimates. These are computed per-subject by linearly regressing the cue locations to the decision made at each time-step, over all trials  are equally weighted . We find a close qualitative and quantitative match , to the reported (subjective) confidence window. These quantities are identical for the ideal-observer.Thus far we have analysed continuous mean estimation behaviour. In this section we analyse subjects’ ability to estimate sensory unperturbed vs perturbed, grouping over the perturbation conditions) and low, medium and high). This revealed a significant main effect of To assess the effect of task manipulations (objective uncertainty), we conducted an ANOVA on the objective error range with within-subject factors of perturbation  and low, medium and high). This revealed a significant main effect of To assess the subjective effect of task manipulations (perception of uncertainty), we also conducted an ANOVA on the confidence window range, with within-subject factors of perturbation ; and (iv) final decisions vary with variance and perturbation onset (6B and 6C). From the interval of the standard error across subjects it is apparent that these phenomena are robust.We have seen above that subjective confidence can reliably discriminate perturbation-induced and variance-induced objective uncertainty at the end of the trial. This behaviour also holds for continuous confidence perception. In Materials and Methods and We devised a kinematic model to account for these observations (see Discussion).This model accounts both qualitatively and quantitatively for the key features of the empirical data, such as the magnitude and shape of variance-induced differences, the magnitude and timing of perturbation-induced inflexions, and the magnitude of the final decision for each condition. The per-subject model parameters were optimised to ensure the best possible fit to the data, but nevertheless have no capacity to explain the within-condition effects of perturbations or variance. While the safety margin parameter b, c and d), occur at the same time as mean estimation changes of direction . The mean estimation and uncertainty estimation tasks appear to be coupled, though our model treats them separately. This could explain the initial discrepancy between our model and the data (a): presumably subjects do not adjust their confidence window until they have first navigated toward the target (after about 1 second). The model provides a good fit to the remainder of the trajectory.It is interesting to note that the increase in perceived uncertainty resulting from cue perturbations  we find that the empirical weights do not reflect optimal performance . We see empirically that each cue deviation contributes to the final decision, but the resultant weight profiles are noisy and difficult to interpret. This may indicate that subjects are sub-optimal at estimating uncertainty from time-evolving visual cues .In computing the weight matrix to explain the evolution of cue weights . In the mean estimation model the cue contributions are chosen optimally (i.e. according to the ML estimate of the mean). The resultant close match between the empirical and observed trajectories for each of the conditions indicates optimal cue weighting. In contrast, in the confidence estimation model a suboptimal “safety margin” is used to explain the magnitude of the estimate and thus a match between empirical and model trajectories does not indicate optimality. This safety margin causes subjects to significantly over-estimate uncertainty, resulting in less than optimal performance in the task.Could the finding of optimal mean estimation and suboptimal confidence estimation be explained by subjects relying on a simpler heuristic? For example, subjects may position their thumb and forefinger on the extremes of the cues seen so far, or choose an aperture size proportional to this range. This was our primary motivation for computing the weights assigned to each cue in the sequence, which revealed that each cue was approximately equally weighted for the mean-estimation task. This would not be the case for subjects relying on subsets of the cues: as the mean of the cues is not equal to the median due to perturbations, the suboptimal heuristic strategies would result in different endpoint decisions, different trajectories and different weight profiles. We therefore posit that mean estimation trajectories are indeed based on optimal cue weighting. In contrast, uncertainty estimation empirical weights do not match the optimal model weights. The presence of a consistent overestimation of uncertainty indicates that subjects may be relying on a subset of the observed cues to form their estimate. Nonetheless, subjects still increase their aperture in response to uncertainty increases and perturbations, indicating that subjects do have access to some measure of their objective uncertainty.A number of studies have observed underconfidence in forced-choice tasks e.g. see , consistMaterials and Methods, and In addition to the possibility of suboptimal uncertainty estimation, from the present results there are a number of alternative potential causes of over-estimated uncertainty: (i) It is not known if subjects fixate on the jittering stimuli or on the cursor, which may effect their ability to accurately judge (or anticipate) the stimulus location see ; (ii) SuOur experiment design utilised a grasping task within a fixed plane. As the task does not abstract the cursor or targets to a computer screen, it maintains many aspects of ordinary grasping , keeping the task as natural as possible. As detailed in the methods, feedback of the fingers was aligned with the true finger locations see . The desindirect evidence of subjective representation of objective uncertainty direct evidence of continuous mean- and confidence-estimation mechanisms that may underlie the observation of optimal integration. In contrast, there are a number of studies in which optimal behaviour was not observed. Multisensory integration studies have demonstrated a significant under-weighting of sensory uncertainty for texture information safety-margin in subjects estimating their uncertainty. By extending our experimental paradigm to multiple sensory modalities we would predict different integration weights for subjects using either subjective or objective uncertainty to form multimodal estimates. By allowing for simultaneous measurement of mean and confidence our experimental paradigm readily lends itself to the testing of such hypotheses.Our results are consistent with a number of studies that report optimal multisensory integration, .Discussion).Subjects were instructed to place their left forearm under a horizontal mirror onto an array of tactile markers, serving as a tactile reference frame consistent and veridical with the visual display. Using the rear-projection mirror setup as illustrated in Stimuli were anti-aliased and projected using a high resolution video projector with latency To enable accurate 3-D tracking of the arm and fingertips we used a Polhemus Liberty 240 Hz 8-sensor motion tracking system . Every 50 ms we sampled the arm and fingertip positions and logged data using custom personal computer (PC) software. The same PC software was responsible for displaying and logging the stimuli, ensuring that our data and stimuli were temporally calibrated.mean of a sequence of visual stimuli, using a fixed-aperture cursor (left). The cursor location was computed as the mean of the orthogonal projections of the thumb and forefinger position vectors onto the forearm.In Task 1 subjects were instructed to indicate the e cursor , left. T1A), followed by a block of trials to assess mean estimation performance as we varied the visual uncertainty, 1B).Each subject underwent an initial training period to become familiar with the task  determined by orthogonal projections onto the arm of their thumb and forefinger. The average position of the projections was interpreted as their mean estimate and the range as their confidence in this estimate.In Task 2 subjects were instructed to indicate the e cursor , right d2A), followed by a larger block of trials to assess their combined mean and uncertainty estimation performance as we varied 2B).Again, each subject underwent an initial training period to familiarise them with the task ; and (ii) we added perturbations  to subsets of the cues . We manipulated the distributions of the stimuli from trial-to-trial in two ways: (i) we modulated the variance of the visual cues . Subjects completed several sessions each with different sets of cue sequences. The order of all trials and sessions were randomised, and on every trial the target location, In order to interpret the subtle effects of these manipulations robustly we used sets of pseudo-random cue sequences which were counterbalanced across 15 trials for each manipulation . One-sixth of trial were of this nature, but these trials did not contribute to our analyses. They were included to ensure subjects would not be able to predict when each trial was going to end, encouraging continuous behaviour.expected objective uncertainty determined in Task 1, encouraging them to estimate and report their objective uncertainty. We exploit the finding that subjects can learn to maximise expected reward In Task 1, 10 points were awarded if the trial was successful. To motivate subjects in Task 2, subjects were awarded less points if their chosen confidence interval was greater than the On a given trial 1B. We first compute the objective error as the mean absolute endpoint deviation for each objective error function for each subject, We then define an The target aperture size for the confidence estimation task could have been chosen to be any quantity proportional to the objective variability. Regardless of the choice of target aperture size, subjects are required to learn the mapping from stimulus to confidence interval in order to succeed at the task. It was an assumption of our approach that this could be done so as to maximise the expected score as per . We deciobjective error range. Further details can be found in If subjects pick an aperture smaller than Each visual cue comprises 5 frames. On each frame for the based on . Blob-clFigure S2 and described in further detail in Text S1) to generate a matrix of cue indices Each To generate each This is repeated using the same ideal observer to accurately estimate the sample mean and sample variance of the cues thus far seen and make decisions based on this available evidence. Given During a trial, as samples accumulate we would expect an In Task 1 the observer’s ideal strategy is to select One can show that the variance of the sample mean estimator is given byPerformance Feedback).Thus, in Task 2 the ideal observer strategy at time The ideal observer can perform instantaneous computations and act on sensory information immediately, but human beings can not. In the presence of inevitable sensory, processing and motor delays and noise we consider how the ideal observer would now perform. We define an ideal-observer model constrained by the three global parameters, Suppose the observer has witnessed In Task 1 subjects can compute objective error functionIn Task 2 we expect subjects to estimate their objective uncertainty. From equation 10 the ideal-observer can calculate the time-delayed variance estimate reported estimate (i.e. the position of the cursor) as perceived estimate  as In addition to sensory delays we introduce motion constraints. At time Note that the model applies to both mean and confidence judgements: For Task 1 we set bias term, We add one additional parameter to the confidence estimation model, a Text S2.To compute the contribution of each cue in the trial to the empirical trajectory observed we perform a multiple linear regression at each time-step using the non-negative weight least-squares algorithm described in location of the cues in the trial (including those not yet seen), plus an additional constant, to the position of the cursor at that time.For Task 1 we regress the pixel absolute deviation of the pixel locations of the cues in the trial from the sample mean, plus an additional constant, to the width of the cursor at that time.For Task 2 we regress the Sensorimotor Delay Model) has relatively few parameters. We optimise these parameters to achieve the best fit to the data, but note that this process does not confound our claims. The model does not modify the magnitude of weights assigned to each cue, it merely constrains the trajectory through which a decision manifests itself.Our model Click here for additional data file.Figure S2Pseudo-Random Cue Sequence Generation. In this figure we illustrate the Saundoku Algorithm for generating pseudo-random cue sequences. The purpose of this method is to ensure that cues are counterbalanced across trials so as to minimise systematic biases to the data, while at the same time presenting no additional information to subjects to aid their success at the task. (A) Cue generation. The sequence of cues to be used for a trial are generated from a pseudo-Normal distribution, created by sampling the Inverse cumulative Normal distribution function at equally spaced intervals (red blobs). The output (black blobs) is distributed pseudo-Normally, i.e. as the number of samples increases the histogram of the samples converges on the Normal probability density function. These samples are shuffled (blue blobs) to provide a cue sequence. The method of shuffling is illustrated in sub-plots B-E. (B) Initial Cues. We create a square shuffle matrix with rows for cue number (in time) and columns for trial number. Each matrix entry corresponds to a cue generated in sub-plot A. We initialise the matrix with diagonals as shown to ensure that each cue appears only once in each trial, and once in every trial. In the figure for clarity we show 60 cues per trial and therefore 60 trials per condition, but in practice we have only 15 cues per trial and 15 trials per condition. (C) Trial Shuffle. We randomise the order of trials to reduce the correlation between neighbouring trials. This does not violate the constraint that each cue appears only once in each sequence, and in every trial. (D) Partial Cue shuffle. We then randomise the order of cues within each trial, but we limit the shuffling to within the first, second and final third of the sequence. This maintains the constraint that each cue appears only once in each sequence, and in every trial, and adds the additional constraint that each third contains all cues an equal number of times. (E) Random Seed. Finally, each entry of the matrix indexes into the shuffled pseudo-Normal sequence in sub-plot A. The resulting plot appears completely random, but we know the correlations between trials, and we know the average mean and variance for the first, second and third block of trials across all trials.(TIF)Click here for additional data file.Figure S3Confidence-Estimation Model Weights. To measure the evolution of cue weights we perform a linear regression of the deviation of each cue in the sequence from the current mean estimate to the confidence window width, using data over all trajectories . In this figure we illustrate the poor match between the empirically observed weights and the model predictions. (A) Empirical Data Integration Windows. At different time-steps in the trial (indicated by coloured arrows) we compute the weight allocated to all cues in the sequence (coloured curves) (B) Empirical Data Cue Evolution. An alternative visualisation of cue weight evolution shows how the weight allocated to the cues at each of the time steps evolves over the time-course of a trial. We do not show the weight allocated to the cue prior to it being seen. This plot reveals that, shortly after being seen, each cue’s weight increases as it contributes to the estimate, then gradually decays. These weight profiles do not match the model and rise much more slowly (as we see in F). (C) Empirical Weights. The weight matrix Materials and Methods). When visualised in this way, using colour to represent cue weight, we can see the initial response delay and the evolution of cue combination, as summarised in A and B. This weight matrix only roughly matches the model (as we see in the plot of (D) Empirical Systematic Bias. In computing the regression of cue to decision we allow for a systematic component to capture the variability in the trajectory that is not explained by the cue weights. Our model roughly predicts the shape of the systematic component (E-F) Model Predictions for comparison, with four parameters ((TIF)Click here for additional data file.Text S1Shuffled pseudo-Normal cue sequence generation. Further details of the cue sequence generation process.(PDF)Click here for additional data file.Text S2Cue weight regression algorithm. Further details of the method used to compute the contribution of each cue in the trial to the empirical trajectory observed.(PDF)Click here for additional data file.Video S1Video showing the evolution of the weights contributing to the mean estimate in Task 2. The contribution of each weight forms an integration window which changes as evidence arrives. Note that at the final time step the integration window is flat for both the empirical data and the model, indicative of optimal integration weights.(AVI)Click here for additional data file.