Several studies investigating the use of electromyographic (EMG) signals in robot-based stroke neuro-rehabilitation to enhance functional recovery. Here we explored whether a classical EMG-based patterns recognition approach could be employed to predict patients’ intentions while attempting to generate goal-directed movements in the horizontal plane.Nine right-handed healthy subjects and seven right-handed stroke survivors performed reaching movements in the horizontal plane. EMG signals were recorded and used to identify the intended motion direction of the subjects. To this aim, a standard pattern recognition algorithm  was used. Different tests were carried out to understand the role of the inter- and intra-subjects’ variability in affecting classifier accuracy. Abnormal muscular spatial patterns generating misclassification were evaluated by means of an assessment index calculated from the results achieved with the PCA, i.e., the so-called Coefficient of Expressiveness (CoE).Processing the EMG signals of the healthy subjects, in most of the cases we were able to build a static functional map of the EMG activation patterns for point-to-point reaching movements on the horizontal plane. On the contrary, when processing the EMG signals of the pathological subjects a good classification was not possible. In particular, patients’ aimed movement direction was not predictable with sufficient accuracy either when using the general map extracted from data of normal subjects and when tuning the classifier on the EMG signals recorded from each patient.The experimental findings herein reported show that the use of EMG patterns recognition approach might not be practical to decode movement intention in subjects with neurological injury such as stroke. Rather than estimate motion from EMGs, future scenarios should encourage the utilization of these signals to detect and interpret the normal and abnormal muscle patterns and provide feedback on their correct recruitment. The American Heart Association, the Department of Veterans Affairs and the Department of Defense have recently endorsed the use of robotic therapy to enhance the recovery of upper extremity following a stroke . This enWhile the use of EMG signals for biofeedback in rehabilitation has been quite controversial -27, few Here we investigated whether EMG signals could correlate the activations of the upper arm muscle patterns with goal-directed movements, and whether this kind of information can be used for movement prediction. Our goal was to extract a general model/map of the EMG activation patterns valid for point-to-point reaching movements in a gravity-compensated, horizontal plane environment. This information could potentially be used in future applications to develop an assistive robotic device able to discriminate between the intended  and the generated  movement directions, and eventually to provide assistance when the two are not coincident. In this context different scenarios are possible. In fact, the direction error could be detected by either comparing the real-time EMG signals to a reference model of patterns of activation extracted from the healthy population, or by allowing the patient to establish his own target movements by calibrating the system for every pathological individual.To achieve our goal, young healthy and pathological subjects were asked to perform pointing movements on the horizontal plane while holding the handle of a robotic manipulandum. The EMG signals of several muscles of the arm and of the trunk were recorded. We applied a classical electromyography pattern classification technique used for similar applications . In partNine right-handed young healthy subjects (GROUP I) and seven stroke survivors (GROUP II) of different impairment levels volunteered to participate in the experiment. The following inclusion criteria were applied for patient recruitment: 1) diagnosis of a single, unilateral stroke verified by brain imaging; 2) sufficient cognitive and language abilities to understand and follow instructions; 3) absence of apraxia and severe concurrent medical problems (including shoulder pain). Table Each participant sat on a chair and gripped the handle of a planar manipulandum, the Inmotion2 Robot  . Trunk mExperiments with healthy subjects aimed at understanding potential usage of the SVM classifier and quantifying its accuracy. These experiments allowed for the exploration of normal characteristics of EMG signals in terms of spatial distribution and the definition of a reference model of muscular activations.Participants were instructed to make point-to-point horizontal reaching movements between a central position and one of four outer targets arranged on a 0.14 m circumference at North, East, South, and West locations  at 1000 Hz. Each electrode was connected to an amplifier ; signals were band-pass filtered (20–450 Hz) and then recorded by the robot (position and EMG synchronized). In the case of patients #1, #3, #4, #5 and #7, those who performed the experiments at the Volterra Hospital, EMG signals were recorded with the Noraxon data acquisition system . Sample rate was set at 1500 Hz and total gain was 1000. A synchronization signal was sent by the robot to the Noraxon system both when the cursor exited from the initial target and when it entered in the arrival target. This signal was used in post processing analysis to synchronize position and EMG data.The EMG activities were recorded from a selection of muscles, thought to become active in similar exercises ,33,34: PIn the case of Patients #1, #4 and #7, MT muscle in some cases showed a change in signal amplitude during the experiment, likely resulting from a partial detachment of the electrode from the skin. This muscle was then removed from further analysis.Initial intended movement direction was extrapolated from muscle activity recorded between  ms with respect to the movement onset, represented by the time the cursor left the start target. Due to the stochastic nature of the EMG signal, we evaluated the discrimination capability and robustness of several features used in the literature for myo-control classification (for a detailed review see ). Time d•IAV : •AR coefficients (Auto-Regressive coefficients): time series in which the signal samples are estimated by linear combination of their earlier samples . The ord•ZC (Zero Crossing parameter): the number of times the waveform crosses the zero:•Threshold value was set as 0.025 V.•HIST (HISTogram parameter) . For eacThe quality of the feature space was estimated by means of the Davies Bouldin (DB) parameter applied to the scatter matrix of data from all muscles as in . The DB Where,i and Sj are the dispersion of the ith and jth clusters respectivelywhere Sij is the distance between mean values:and Di is the number of cluster Ci, yi is the ith input pattern vector and mi is the mean vector of pattern ith.with NThe lower the DB parameter, the higher is the degree of class separability. The comparison among all subjects and movement directions showed that HIST parameter presented the best overall performances--see Table http://www.csie.ntu.edu.tw/~cjlin/libsvm ms with respect to the movement onset. The relevance of each muscle in the specific motion direction under investigation for each trial was quantified by means of an information content index, namely the Coefficient of Expressiveness (CoE) .jth trial, each lth muscle, and each rth direction, we computed a k index defined as:For each i,l,r is the correlation coefficient between the ith principal component and the selected muscle for the rth movement direction, λi is the eigenvalue associated to the ith principal component, p is the total number of eigenvalue, J is the numbers of trials. The CoE coefficient for each muscle was given normalizing the kj,l,r index with respect to the maximum among the k indexes of the muscles recorded for the jth trial.where n is the number of principal components that contains 80% of the variance of the system, cMuscle activity during each trial was then summarized via N-component vector of CoE values, where N was the number of the muscles included in the analysis. Only muscles with CoE values larger than 0.7 were considered relevant for motion production; otherwise they were judged non-relevant .For each muscle, the modulation of the CoE across the four directions was evaluated considering the polar distribution of the coefficient. Specifically the patterns of muscle activations identified for the neurological intact participants were used as a baseline for comparison with those of the patients. Thus, different abnormal spatial patterns were evaluated and correlated with the results obtained with the SVM.Table Tables When SVM was trained with data from the healthy subjects and tested separately on each patient, the accuracy rates ranged between 25-45% . The CoE_M ±1.96 · SE (SE = Standard Error) coefficients computed for each direction were connected by periodic cubic spline interpolation curves Figure . The resfirst row). This approach took into consideration modulation of muscle activity reported by Flanders and Georgopoulus [In Figure gopoulus ,23. In aOverall, GROUP I showed highly repeatable and stable patterns of activation across different subjects, trial repetitions and movement velocities as revealed by the narrow confidence interval of the CoE parameter. Conspicuously, in accordance with PCA analysis, muscles of the back--such as MT, LT, TM--were not relevant for motion production as indicated by the lower CoE values.In accordance with previous studies  we obserIn the case of Patient #1, TR contributed to motion toward North, West and East directions; DM and the DP were involved mainly when initiating motion toward the South and West directions and the DA muscle when moving toward the East direction , or tuning the classifier on each individual.Some limitations of the study should be highlighted at this point. For instance, we only recorded a small subset of all the possible trunk and upper limb muscles. In the case of GROUP I, this approach worked quite well. However, in the case of GROUP II the number of trunk and back muscles should have been increased to account for the presence of compensatory strategies in the classifications extracted with the SVM. Proper electrodes placement was a critical issue when dealing with patients due to the weak EMG signals. Moreover, patients were often overweight due to physical inactivity with a subsequent EMG signal decay, which further affected classification accuracy. Additionally, we could not rule out the presence of fatigue at the base of intra-subject variability in the performance of stroke survivors. Finally, in the present study we used a statistical classifier. Neural networks might also have been employed as an alternative, given the good performances in the pattern recognition described in literature ,34. A reThe results of this study are in line with a previous work from Lee and colleagues , which aIt is often speculated that the process of motor recovery either involves spared tissue on the motor and sensory areas in the lesioned hemisphere or it enhances activity in pre-existing motor networks in the unaffected hemisphere. Several solutions employing EMG are possible. For example, it could be possible to calibrate the system on patient-specific characteristics and to have the clinician select the admissible co-activation pattern that represents an effective strategy to inhibit pathological scheme. The control system of the robot could then be implemented in order to train patients to always reproduce the same correct pattern. The rationale underlying this approach is that learning may be elicited providing the subject a feedback on the muscle forces he has to produce to achieve the desired trajectory.The aim of the present study was to investigate the use of EMG pattern recognition approaches, based on statistical classifiers, to decode subject’s intention to move toward a certain direction in the horizontal plane. In the case of normal subjects the approach worked quite well. In the case of stroke patients the approach did not perform well. Our results show the limitation of the use of this technique in robotic-aided neuro-rehabilitation; the findings suggest that rather than using the EMG signals to discriminate patient’s intentions, we could instead use these signals to develop an online procedure that provides a feedback on the error in the muscle activational patterns. Further experiments need to be performed to verify the clinical advantages which can be achieved using this approach.H. I. Krebs is a co-inventor in several MIT-held patents for the robotic technology. He holds equity positions in Interactive Motion Technologies, Watertown, MA, USA, the company that manufactures this type of technology under license to MIT.The other authors do not have competing interests, as defined by the BioMed Central Publishing Group, or other interests that may influence the results and discussion reported in this study.BC conceived and designed the study, carried out the experiments and the data analysis and drafted the manuscript; PT carried out the experiments with patients; SM and HIK participated in the design and the coordination of the study and drafted the manuscript. All authors read and approved the final manuscript.


We measured perceived depth from the optic flow (a) when showing a stationaryphysical or virtual object to observers who moved their head at a normal orslower speed, and (b) when simulating the same optic flow on a computer andpresenting it to stationary observers. Our results show that perceived surfaceslant is systematically distorted, for both the active and the passive viewingof physical or virtual surfaces. These distortions are modulated by headtranslation speed, with perceived slant increasing directly with the localvelocity gradient of the optic flow. This empirical result allows us todetermine the relative merits of two alternative approaches aimed at explainingperceived surface slant in active vision: an “inverse optics” modelthat takes head motion information into account, and a probabilistic model thatignores extra-retinal signals. We compare these two approaches within theframework of the Bayesian theory. The “inverse optics” Bayesianmodel produces veridical slant estimates if the optic flow and the headtranslation velocity are measured with no error; because of the influence of a“prior” for flatness, the slant estimates become systematicallybiased as the measurement errors increase. The Bayesian model, which ignores theobserver's motion, always produces distorted estimates of surface slant.Interestingly, the predictions of this second model, not those of the first one,are consistent with our empirical findings. The present results suggest that (a)in active vision perceived surface slant may be the product of probabilisticprocesses which do not guarantee the correct solution, and (b) extra-retinalsignals may be mainly used for a better measurement of retinal information. The current models of active Structure-from-Motion (SfM) are based on theHelmholtzian account of perception as inverse inference An alternative theory hypothesizes that the visual system estimates the metricproperties of local surface orientation by using retinal information alone. Retinalinformation “directly” specifies the 3D affine properties of the distalobject , but it does not allow a unique determination ofits Euclidean metric properties, such as slant A fundamental difference between these two approaches is that only the first onemakes use of information about ego-motion. This difference is very important. Infact, empirical results show that perceived surface tilt depends critically onego-motion information. A particularly convincing demonstration in this respect hasbeen provided by The purpose of the present investigation is to determine whether observers useinformation about the speed of head motion to estimate surface slant. To thispurpose, we compared the judgments of local surface slant provided by active andpassive observers to the estimates provided by two Bayesian models. The two modelswere constructed (a) by taking into account information about the observer headmotion, and (b) without taking into account information about the observer headmotion. The empirical data were obtained by asking observers to judge the localslant of virtual and physical planar surfaces from the optic flows generated bynormal or slower head translation velocities.Consider a coordinate system centered at the observer's viewpoint, with thelane see .Supposedef)component  of the velocity field –which is zero along the horizontal dimension for our stimuli – is givenbynot sufficient to specify theslant of the surface. In order to specify In the present investigation, we only consider planar surfaces slanted by anangle def could be solved if the visualsystem were able to accurately measure the second-order optic flow, but several studies showthat this is not the case def can be disambiguated by combining the informationprovided by the first-order optic flow and the extra-retinal signals, if someassumptions are met (see next Section).In general, the ambiguity of def can be overcome by the active observerunder the assumption that the object is stationary – a reasonableassumption in many real-world situations The ambiguity of stationarity assumption, that is, they favor thesolutions in which the optic flow is produced by the observer's motiondef value. This further source of uncertainty isdescribed by a Gaussian distribution rigidityassumption, that is, they favor the solutions in whichdef is produced by a rigid rotation. A further assumptionis that the slant of the surface does not depend on the relative motion betweenthe surface and the observer.The Bayesian model presented by Colas and collaborators formalizes this ideadef and Under these assumptions, the problem of estimating local surface slant given theknowledge of def depends only on the distal slantdef are measured with no error,then defare measured: the larger From the definition of the conditional probabilityflow see . If  andapriori distribution of a random variable representing the amount ofrelative rotation between the observer and the surface. In this case, Eq. 14reduces toWe propose that the visual system estimates surface slant without considering theinformation about head translation velocity see . With reDomini and Caudek showed that this account is sufficient for predicting perceivedslant from the optic flow in the case of the passive observer def is a one-parameter family ofdef is not uniform, but ithas a maximum equal to The importance of ith see .Eqs. 14 and 15 provide two alternative models for the perceptual derivation ofsurface slant from the optic flow in active vision. The purpose of the presentinvestigation is to contrast them by comparing their predictions to thebehavioral data obtained when head translation velocity is manipulated.In the present experiments, observers were required to produce two different headtranslation velocities. The first was comparable to the peak horizontal headvelocity during normal locomotion Active and passive observers judged the perceived slants of virtual or physicalplanar surfaces. The results indicate that the judgements made by the observersare systematically biased by the head translation velocity see . The samdef. For the active andpassive viewing of virtual planar surfaces, the observers' judgments ofslant complied with this prediction  and the Euclideanmetric properties  of the visual scene. By usingsophisticated head-tracking techniques with high spatiotemporal resolution, wemanipulated the information content of the stimuli to generate optic flowscorresponding to (a) the active viewing of a virtual surface, (b) the passiveviewing of a virtual surface, and (c) the active viewing of a physical surface. Wealso varied the head translation velocity . The observers'judgments of perceived surface slant were then compared to the Bayesian estimatescomputed with and without taking into account the translational velocity of the head.Thirty-four undergraduate students at the University of Parma, Italy,participated in this experiment. All participants were naïve to thepurposes of the experiment and had normal or corrected-to-normal vision.The orientation of the participant's head and the translational headdisplacements were recorded by an Optotrak 3020 Certus system. Two sensorsrecovered the 3D position data of two infrared emitting diodes (markers on aneyeglass frame) aligned with the observer inter-ocular axis. The signals emittedby the markers were used to calculate the A custom Visual C++ program supported by OpenGL libraries and OptotrakAPI routines was used for stimulus presentation and response recording. The sameprogram also controlled the orientation of a physical planar surface that, in aseparate block of trials, was placed at a distance of 760 mm in front of theobserver. The boundary of the physical surface was occluded by the same maskused for the virtual displays. This aperture was closed when the surface'sorientation was changed.The simulated displays were random arrangements of  consistentwith a slanted 3D planar surface. Given the smaller viewing distance (760 mm),the constant amount of lateral head shift produced a relative rotation of thesurface about the vertical axis of 3.76The physical planar surface was painted black and randomly covered withphosphorescent dots. With respect to the virtual surface, the physical surfacewas covered by larger dots (about 5 mm) having an irregular shape, a lowerdensity (about 13 dots were visible through the irregular aperture), andproviding texture cues , Passive-Vision with a Virtualsurface (PVV), and Active-Vision with a Physical surface (AVP). Participantswere randomly assigned either to the “normal” or to the“slow” head translation velocity conditions. Each AVV and PVV blockcomprised 25 trials (5 repetitions of 5 simulated slants magnitudes). The AVPblock comprised 16 trials (4 repetitions of 4 slant magnitudes). In the PVVblock, the stimuli generated in the AVV block were shown again in random order.The completion of each block of trials required about 30 minutes.Participants were tested individually in total darkness, so that only thestimulus displays shown on the CRT screen, or the luminous dots on the physicalsurface, were visible. In the AVV and AVP blocks, observers viewed the stimuliwhile making back-forth lateral head translations. The observer's head wassupported by an horizontally extended chin-rest allowing lateral movements ofEach experimental session was preceded by a preparatory session in which theparticipant's inter-pupillary distance was measured, the instructions wereprovided, and training about the appropriate head translation velocity and themagnitude estimation task was provided. Participants were trained in themagnitude estimation task by completing two blocks of 20 trials each. In oneblock, they were required to generate an angle between two segments on acomputer screen after being prompted by a random number in the range0–360. In the other block, they were required to estimate a random angledepicted to the screen. The relationship between the response and the testvalues was analyzed with a linear regression. Only participants who metperformance criteria of a slope in the interval  and anintercept in the interval  entered the experimentalsession.def was extracted in each trial from theinstantaneous profile of the deformation component of the optic flow byfollowing the procedure illustrated in def valueswere then used to test the prediction of Eq. 15.The maximum value of e.g., Sun, Zhu,Kramer, Yang, Song, Piepho, & Yu, 2010). Here, we measure the goodness offit as Statistical analyses were performed by means of Linear Mixed-Effects models withparticipants as random effects and


Interactions between individuals that are guided by simple rules can generate swarming behavior. Swarming behavior has been observed in many groups of organisms, including humans, and recent research has revealed that plants also demonstrate social behavior based on mutual interaction with other individuals. However, this behavior has not previously been analyzed in the context of swarming. Here, we show that roots can be influenced by their neighbors to induce a tendency to align the directions of their growth. In the apparently noisy patterns formed by growing roots, episodic alignments are observed as the roots grow close to each other. These events are incompatible with the statistics of purely random growth. We present experimental results and a theoretical model that describes the growth of maize roots in terms of swarming. To exploit soil resources optimally, plants have developed intricate root systems that are characterized by complex patterns and based on the coordinated group behavior of the growing root apices We generated random growing paths by considering an assembly of independent particles separated initially by distance In the model of non-random growth, we consider the root apex or tip as a moving particle, and we treat the length of the root as the temporal history of the particle. Each particle is described by a velocity vector, the orientation of which denotes the direction in which the root apex moves. We assume that each seed produces only one main root and no collateral roots. This simplification is reasonable because the main root provides the longest and clearest history of interaction with its neighbors. The roots can interact with their neighbors at any point along their lengths. We assume that each root grows at a slightly different speed, giving rise to different root lengths. While this feature is clearly observed in experiments, thus motivating its inclusion in the theoretical model, we remark that this is not crucial in determining the growing-roots patterns. We have introduced the variation in speeds in accordance to experimental data which revealed that the variability in root lengths is always observed. Moreover, each plant is assumed to interact with neighboring plants causing spatial attraction or repulsion depending on the individual root responses. As mentioned before electric fields may be a possible mechanism of such interaction. These attractive and repulsive forces become effective when a certain distance separates the roots and leads them to grow closer or far away to together. As two roots approach each other, the mechanisms of direction adjustment  would switch on. The root apices adjust their direction as they detect their neighbors within a certain radius We calculate the velocity vectors associated with root growth rate and direction for 10 experiments and analogously for 10 realizations of the numerical experiments. In numerical simulations, approximately the same number of seeds and temporal data points are considered as in the experiment. The sample growing paths from the experiment, the model of non-random growth and the model of random growth are shown in ibutions . The samibutions . In contibutions . The conperiment  and the periment , whereasperiment . This paAs described in the previous paragraph, the asymmetry in the heights of the bimodal distributions may indicate the existence of a preferred direction of growth or episodic alignments of directions between neighboring roots. To investigate, we calculated the spatial correlations between velocity vectors as a function of the distances between the roots. More precisely, we defined a radius In the non-random model, the mean probability distribution of the velocities tends very slowly to a symmetric shape, and large fluctuations in the differences between the heights of the bimodal peaks are observed between individual experiments. In the random-growth model, different patterns are observed. The effect of noise makes the distributions symmetrical, and consequently, the fluctuations in the differences of the heights of the bimodal distributions are smaller. However, when interactive forces are present, the distributions become asymmetric and the fluctuations larger. These fluctuations arise from the alignment of growing roots and some type of synchronization of growth directions. The results of the experiment and non-random model differ qualitatively from those of the random-growth model, and the experimental results differ slightly from the predictions of the non-random model. This difference may be related to the fact that the non-random model considers only a few of the most essential ingredients that contribute to non-random growth. Other elements which have been neglected for the sake of simplicity contribute to root interactions and behavior: for instance, inhomogeneities in water distribution, initial distances between the seeds, or angle of the support on which the roots are growing. Despite these facts the proposed model allowed us to qualitatively reproduce the observed growing root patterns by making use of few basic ingredients.Concerning the swarming behavior in roots, one of the advantages could be the efficient chemical modification of the soil in their vicinity. This would allow the maintenance of specific root micro-niche which is optimal for their physiological performances, in particular, the extraction of the essential nutrients from the soil and the defense against pathogens.In conclusion, the experiments revealed that the qualitative features of root growth are well explained by a model of swarm behavior. The main insight gained in this study is that the root apices act as decision-making centers, giving rise to correlations in the growth patterns. We have identified a few key ingredients allowing us to explain and reproduce qualitatively the observed phenomenology, in particular, the angle adjustment and the attractive and repulsive interactions. Repulsive forces have been considered in the description of the polymer brushes Maize seeds were germinated at 24Figure S1Probability distribution of the velocities of growing roots. A. Experiment, B. non-random growth model and C. random-growth model. The parameter values used in B are: (EPS)Click here for additional data file.Figure S2Probability distributions of the distances of the root apices from their seeds: . A. Experiment, B. non-random growth model and C. random-growth model. The parameter values in B and C are as in (EPS)Click here for additional data file.Video S1Experiment with a growing group of maize roots.(MOV)Click here for additional data file.Video S2Experiment with a single growing maize root.(MOV)Click here for additional data file.


We found R2 > 86% for the most general models of knee quasi-stiffnesses for the flexion and extension stages of stance. With only subject height and weight, we could predict knee quasi-stiffness for preferred walking speed with average error of 9% with only one outlier. These results provide a useful framework and foundation for selecting subject-specific stiffness for prosthetic and exoskeletal devices designed to emulate biological knee function during walking.Biomechanical data characterizing the quasi-stiffness of lower-limb joints during human locomotion is limited. Understanding joint stiffness is critical for evaluating gait function and designing devices such as prostheses and orthoses intended to emulate biological properties of human legs. The knee joint moment-angle relationship is approximately linear in the flexion and extension stages of stance, exhibiting nearly constant stiffnesses, known as the quasi-stiffnesses of each stage. Using a generalized inverse dynamics analysis approach, we identify the key independent variables needed to predict knee quasi-stiffness during walking, including gait speed, knee excursion, and subject height and weight. Then, based on the identified key variables, we used experimental walking data for 136 conditions (speeds of  Mechanisms that can emulate human-like biomechanics are essential for robust performance of a number of engineered locomotion systems including anthropomorphic bipedal robots Researchers have proposed theoretical models of varying complexity for the whole limb that can generate human locomotion Recently, the concept of quasi-stiffness or “dynamic stiffness” The overall goal of this study was to establish a series of statistical models based on theoretical analysis and experimental data to characterize spring-type behavior of the knee in stance for adult humans spanning body size (height and weight) across a range of walking speeds. A well-developed general model of knee joint quasi-stiffness during walking promises to aid in diagnosis of musculoskeletal dysfunction and the development of biologically-inspired assistive devices (orthoses and prostheses) to improve mobility. For the latter applications, the stiffness of the knee joints will often need to be chosen in advance for specific cases or in a real-time form for employing a more complex active impedance control e.g. , such asWe begin this paper with a description of the modeling and data collection methods used in the study, including an inverse dynamics analysis to obtain a generic expression for the knee moment from which we identify a subset of independent factors that can describe the quasi-stiffnesses of the knee during stance phase. We use an experimental data set (136 conditions across 14 subjects) spanning a substantial range of body size and gait speed of human adults to fit coefficients to these factors and present a series of general-form statistical models for quasi-stiffnesses that can account for the variability of the behavior of the knee among subjects based on body and gait parameters.There are occasions where more simplified models that are primarily based on the body parameters might be favorable. This includes models for the design of compliant prostheses and orthoses, and exoskeletons for the knee that are versatile enough to perform well over a range of speeds around the energetically optimal gait speed. In order to apply the general-form models (described above), the magnitude of excursion for the knee and the speed as the gait parameters must be known. However, there are occasions where knee kinematics cannot be easily and repeatedly characterized , or where it would be undesirably time-consuming or expensive (such as in a prosthetist choosing a prosthesis stiffness for a specific patient). Accordingly, we also develop stature-based models that predict the knee quasi-stiffnesses at the optimal gait speed and for mean values of the knee excursion across the data.–c). In this phase, the knee undergoes a flexion stage (a–b) and an extension stage (b–c) while supporting body weight. Exhibiting a shock damping mechanism To evaluate knee joint quasi-stiffness, we first divide the gait cycle into stance and swing phases  and height (H) as the body parameters, and walking speed (V), and magnitude of knee flexion (X-Y), and 2) Extract theoretical model-forms by investigating the terms of the equation for the knee moment on the sagittal plane and correlate them with body and gait parameters.We used a generalized, analytical inverse dynamics approach to derive an equation for the knee joint moment during human gait. The detailed analysis is documented in the gait , point bThe inverse dynamics analysis outlined in Parameter definitions for equation (1) and the equations that follow are listed in b). At this instant, the ground reaction force  shows a maximum magnitude for normal walking on a level ground. Moreover, since the ground reaction moment (i.e. the moment applied on the foot from the ground) is substantially smaller than the knee moment, we neglect it  and (5-b) in equation (4) results in:Assuming the knee behaves nearly linearly in the weight acceptance phase of the gait Combining (6) and (7) constitutes the following analytical forms for the quasi-stiffness of the knee in the weight acceptance phase, and its flexion and extension stages:V, H, and W); and similarly for These equations suggest that, in its most general form, 67.7–94.0 kg) and height (1.43–1.86 m). These data were provided to us by other researchers from previous studies from two labs:We extracted knee joint angle and moment data from 14 subjects including unimpaired male and female adults spanning a reasonably wide range of weight  were used to calculate the knee joint angular position and torque through the stance phase of walking in each trial from the linear position and ground reaction force data.Five subjects (subjects 10 to 14 in a), the end of flexion stage as the point of maximum moment (point b), and the end of extension stage as the point of minimum moment before the toe leaves the ground (point c). In other words, the flexion stage is composed of the data points between a and b; and the extension stage between b and c. Then we applied linear fits between the angle and moment data points in flexion and extension stages (as described in the previous section). The slopes of the fits were correspondingly reported as a was subtracted from the angle at point b to obtain b and c. We averaged First, for each subject, we plotted the knee moment and angle data against each other,  when working with subjects with different body size It is preferred to use the non-dimensional Froude number  at the non-dimensional gait speed of We found high values of From a design point of view, our results suggest that a device  can approximate the behavior of the human knee by utilizing a spring with stiffness equal to the quasi-stiffness of the knee at the preferred gait speed. For other gait speeds, the stiffness of the device might ideally be tuned based on the equations presented in a priori knowledge of the knee quasi-stiffness variability for the users. To size the stiffness of the prosthetic and orthotic devices, the designers utilize the average quasi-stiffness extracted from the kinetic and kinematic data of sample healthy subjects Nm/rad to ∼430 Nm/rad, depending on the sample population that the designers have chosen and the tuning process Recently, researchers in the field of prosthetics have moved toward quasi-passive systems and implemented impedance control methods in their designs To examine the differences between a model that is based on the average data and the models developed here, we found the average values of Applications of the models presented in this study are not restricted to the field of medical orthoses and prostheses. These models could also be used for the design of knee exoskeletons that are meant to augment the performance of a healthy knee. Researchers have proposed a range of sophistication in the design of exoskeletons from quasi-passive to fully active systems Our study had a few limitations worth noting. First, we only addressed the behavior of the knee during stance phase of normal walking on level ground. Our approach could be extended to other joints of the lower-limb, other gait regimes (e.g. running) and also account for variable terrain or carried loads. For example, the quasi-stiffness of the ankle significantly increases as the ground slope changes Another limitation was that in order to establish the current models, we used 136 gait trials for 14 adult subjects. Therefore, our analyses could be generalized only to the range of age, height, weight, and gait speed that the subjects represent and as much as the statistical significance supports. Similar statistical analyses could be carried out on other groups of subjects such as children or older adults and other locomotion regimes such as running to establish similar models. We employed several simplification and estimation steps to identify the important predictors that only hold when the subject walks on the sagittal plane with no pathologies in the gait. A more sophisticated model could take the eliminated terms and confined parameters into account. For example, researchers have shown significant dependence of the ankle quasi-stiffness on the gender and age Taken together, we have established a family of models with different levels of sophistication that predict the quasi-stiffnesses of the knee in stance. From an applied standpoint, our models could be used in gait analysis, modeling, and simulations, and also in the fields of orthotics, prosthetics, and bipedal robots.Figure S1A schematic model of the support shank and foot for a subject walking on the sagittal plane. The figure depicts the proximal force and moments of the shank and foot segments, and the center of masses ((TIF)Click here for additional data file.Table S1Description of mathematical expressions.(DOCX)Click here for additional data file.Appendix S1Inverse dynamics analysis.(DOCX)Click here for additional data file.


Suicide attempts constitute a serious clinical problem and have important implications for healthcare resources. The aim of the present study was to evaluate the effectiveness of case management using crisis postcards over a 6-month follow-up period.A randomised controlled trial was conducted in Kaohsiung, Taiwan. Prevention of further suicide attempts was compared between two groups with and without the postcard intervention. The intervention group consisted of 373 participants . The control group consisted of 388 participants . A survival analysis was used to test the effectiveness of the crisis postcard intervention for the prevention of suicide reattempts. Per-protocol and intention-to-treat analyses were conducted.The intention-to-treat analysis indicated that the crisis postcard had no effect , whereas the per-protocol analysis showed a strong benefit for the crisis postcard .Although the results of the present study indicated that the postcard intervention did not reduce subsequent suicide behaviour, our study provides an alteration to the postcard intervention. Further studies need to be conducted to clarify whether this type of intervention can reduce subsequent suicidal behaviour, with a particular focus on reducing the rate of loss to follow-up. Suicide is a global challenge and a major public health problem worldwide. Suicide accounts for almost 1 million deaths annually, and an estimated 10 million suicide attempts occur every year . This diThe repetition rate of self-harm reported in a review of findings from Western countries is 15-16% at 1 year with a slow increase to 20-25% over the following few years . In TaiwCognitive behavioural therapy is a pragmatic, action-oriented intervention for major mental disorders, and its methods are modified for use in many other conditions . One parThe gold standard used to evaluate the efficacy of an intervention is a randomised controlled trial, but few studies have successfully tested suicide interventions using a randomised controlled trial design . Due to Based on these constraints, we added a crisis postcard intervention to case management services to treat individuals who had repeatedly attempted suicide. The aim of the present study was to evaluate whether the use of crisis postcards in addition to case management is more effective than case management alone in preventing suicide reattempts over a six-month follow-up period.Kaohsiung City is located on the southwest coast of Taiwan and is the second largest city in Taiwan. It features a highly developed manufacturing industry and is home to the largest commercial harbour in Taiwan. Kaohsiung City plays a pivotal role in commercial industry and shipping in Taiwan and is an important port between the Indian Ocean and northeast Asia.When individuals who had attempted suicide within the previous month were found by suicide prevention gatekeepers in medical or non-medical organisations in Kaohsiung, gatekeepers filled in the relevant information about the suicide attempters on the national suicide prevention reporting sheet and faxed them to the suicide prevention centre in Kaohsiung according to our national suicide prevention policy. The eligible participants in our study were recruited from July 2011 to December 2011. Referred cases included hospitalised patients, patients identified by the Bureau of Police and the Bureau of Fire, and patients identified and referred by suicide prevention gatekeepers.After receiving the participants’ documented informed consent, they were randomly assigned to either the intervention group or the control group according to the last digit of their National Identification (ID) Card. In Taiwan, every citizen, when he/she is born, is randomly assigned an ID number by the National Department of Internal Affairs, regardless of sex, race, skin colour and place of birth. A valid National Identification number consists of one English letter and is followed by nine digits. Because the last digit of the ID (from 0 to 9) has the same probability of being chosen, it was used for randomisation during the sampling process in this study. Participants with an ID card ending in an odd number were assigned to the intervention group, and those with an ID ending in an even number were assigned to the control group.The process of enrolment is illustrated in Figure The case managers of the suicide prevention centre in Kaohsiung are typically psychiatric nurses, but our team also includes psychologists and social workers. After receiving the subjects’ information from the national suicide prevention reporting sheets, we contacted the suicide attempters via telephone or a home visit within one week and provided case management services at least six times in the following three months. The case management services included psychological support, providing proper coping strategies, follow-ups to increase adherence to the referrals provided for psychiatric treatment, and individualised casework, including the coordination of social resources and brief crisis intervention if needed .Case managers at the suicide prevention centre gathered the subjects’ individualised information related to the crisis and discussed it with the subjects during the case management services. Afterwards, the case managers listed the necessary coping strategies and appropriate resources on the crisis postcard. There were two major components included on our crisis postcards:  individuVariables on the national suicide prevention reporting sheet consisted of categorical variables and continuous variables. The categorical variables were sex, referral source , employment , living conditions  and suicide method. High lethality suicide methods included hanging, charcoal burning or jumping from high altitudes. The continuous variable was age. The history of suicide attempts was acquired from the record of the National Suicide Prevention Reporting System in our study.χ2 test and the independent samples T test.The primary outcome measure was the occurrence of a suicide reattempt during a 6 month follow-up period. The primary objective of this study was to examine whether the time period until recurrent suicidal behaviour of participants in the intervention group was significantly different from that of the control group. The primary endpoint was based on a survival analysis and determined using the Cox proportional hazard model to test the effectiveness of the crisis postcard intervention on the prevention of suicide reattempts. The length of follow-up for each subject was represented by the number of days between the baseline evaluation and the date of either a suicide reattempt or the end of the follow-up period, depending on which came first. The results are reported as hazard ratios, 95% confidence intervals (CIs) and p-values from the Cox proportional hazard regression model. Statistical significance was considered to be p < .05. Survival and Cox regression analyses were conducted using the Statistical Package for the Social Sciences (version 17.0). Per-protocol  and intention-to-treat (ITT) analyses (control group vs intervention group) were conducted in our study. The differences between the demographic characteristics of the present study were tested using the We assessed 1,218 participants for eligibility, of whom 457 failed to give consent , but the per-protocol analysis showed a strong benefit for the crisis postcard .A survival analysis Figure  was usedAlthough the per-protocol analysis showed a strong benefit for the crisis postcard, the primary finding of the present study was that the crisis postcard intervention did not significantly reduce subsequent suicidal behaviour in the intention-to-treat analysis. Excluding non-adherent suicide attempters might introduce bias because suicide attempters who adhered to treatments tend to have better outcome regardless of whether the treatment was effective. Although there were no significant differences between subjects receiving full case management services who read the crisis postcards in the intervention group and those receiving full case management alone in the control group, precautious measures should be taken when considering the per-protocol analysis. The 106 subjects excluded from the intervention group had a significantly higher proportion of patients with a previous history of suicide attempt. This might contribute to a pre-existing difference and produce potential biases in a per-protocol analysis. In addition, excluding those who did not read the postcards could bias the apparent effectiveness. Suicide attempters who would like to read the crisis postcards might have better outcomes than those who would not read the crisis postcards, regardless of treatment. Because the per-protocol analysis removed the balance of randomisation, the results were more similar to those of an observational study than a randomised trial and should be interpreted with caution.When analysing data from randomised clinical trials, intention-to-treat analysis provides the highest level of evidence. However, the intention-to-treat analysis almost certainly underestimated the effectiveness of the crisis postcard. Because the intervention group was “contaminated” with participants who received the crisis postcard but did not read it, the groups appeared more similar, and it was harder to detect a difference between them (if one existed). Thus, the intention-to-treat analysis might have had only a slim chance of detecting a true difference between the groups.The results of the present study are similar to those of a previous study conducted by Beautrais and colleagues, who reported that a postcard intervention did not significantly reduce self-harm reoccurrences . HoweverA limitation of this study was the relatively high rate of loss to follow-up in the intervention group, which was problematic when analysing the results. The elimination of patients lost to follow-up from the per-protocol analysis overestimated the effect of the crisis postcard, whereas the estimation of the treatment effect was generally conservative because of dilution due to non-compliance in the intention-to-treat analysis.The individualised crisis postcard in the current study altered the physical appearance and the wording of the card for each patient. Although the present study indicated that the postcard intervention did not reduce subsequent suicide behaviour, our study provided an alteration to the postcard intervention. Further studies are needed to clarify whether this type of intervention can reduce subsequent suicidal behaviour, with particular emphasis on reducing the rate of loss to follow-up.The authors declare that they have no competing interests.WJC: The first author, who collects, analyses data, writes and reedits this manuscript. CKH: The second author, who helps first author to collect data and give suggestions and comments on the manuscript. SSS: The third author who helps first author to collect data and reedit the manuscript. CCC is equally shared with corresponding author with FHC, GGL, LSC, YJF, PYY, TCC who helps to collect data, participant in this study and give some suggestions on this manuscript FHC is the corresponding author who analyses raw data, writes partial paper and instructs the authors to write this manuscript. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-244X/13/191/prepub


Conserved motifs in biological sequences are closely related to their structure and functions. Recently, discriminative motif discovery methods have attracted more and more attention. However, little attention has been devoted to the data imbalance problem, which is one of the main reasons affecting the performance of the discriminative models. In this article, a simulated evolution method is applied to solve the multi-class imbalance problem at the stage of data preprocessing, and at the stage of Hidden Markov Models (HMMs) training, a random under-sampling method is introduced for the imbalance between the positive and negative datasets. It is shown that, in the task of discovering targeting motifs of nine subcellular compartments, the motifs found by our method are more conserved than the methods without considering data imbalance problem and recover the most known targeting motifs from Minimotif Miner and InterPro. Meanwhile, we use the found motifs to predict protein subcellular localization and achieve higher prediction precision and recall for the minority classes. Biological sequence motif is the over-represented pattern in biopolymer (nucleotide or protein) sequences relative to a background model Representation of biological sequence motifs can usually be classified into two categories: fixed-length motif representation and variable-length motif representation Up to now, most of the discriminative methods have been used in discovering the DNA motifs. DIPS Few investigations have been done on the discriminative motif discovery methods in protein sequences. DEME To the author's knowledge, there is little information available in literature about the data imbalance problem in discriminative motif discovery, although it is an important issue in the field of machine learning In this article, we focus on the data imbalance problem in discriminative motif discovery inspired by DiscHMM which employs MMIE, a discriminative HMM training method, to discover targeting motifs and uses the found motifs for predicting protein subcellular localization. There are two types of data imbalance problems to be solved. The first data imbalance problem is the multi-class imbalance problem that has more than two classes with uneven distributions. The second one relates to the imbalance between the positive and negative datasets at the stage of HMMs training. A lot of methods have been proposed to solve the data imbalance problem such as sampling methods, cost-sensitive methods, kernel-based methods and active learning methods A biological benchmark dataset has been used to characterize the efficiency of our method compared with other methods. The results indicate that our method has superior precision and recall for minority classes because of its ability to use phylogenetic knowledge imported by simulated evolution and information in the negative training set. In addition, our method recovers the most known targeting motifs from Minimotif Miner Our method is described below in the following aspects: problem formulation, combining strategy of sampling, protein subcellular localization prediction, datasets and implementation.We represent the motifs by HMMs and use the following notations: Generative training of HMMs is to optimize the maximum likelihood estimation (MLE) criterion with the Baum-Welch algorithm While discriminative training of HMMs is to optimize the MMIE criterion with the extended Baum-Welch algorithm The assumption of one occurrence per sequence (OOPS) model After a motif (represented by HMM) is found, top motif instances will be retrieved from protein sequences by posterior decoding: for each candidate motif, we scan all protein sequences, identify all possible positions (motif instances) of the begin state and the end state of the motif and compute the product of the posterior probabilities of the begin state and the nearest end state for ranking. Then, all positions in all sequences are ranked by this product. Finally, when the number of the top positions is given, they are selected according to the ranking.The targeting motifs discovered by DiscHMM are more discriminative according to their effect in the overall accuracy of predicting protein subcellular localization than the generative motifs. However, the precision and recall of the relative minority classes are very low, even zeros. Therefore, a combining strategy of resample is adopted to solve the data imbalance problem. This strategy applies the over-sampling method via simulated mutation to generate new sequences for the minority classes and random under-sampling method in MMIE for HMM training.The first kind of data imbalance problem is the multi-class imbalance, which is the main reason for the low precision and recall of minority classes. To solve this problem, we try to use over-sampling method to add new sequences into the minority classes. In order to avoid over-fitting, we do not use the random over-sampling method that randomly selects sequences from the minority class sets, replicates them and adds the replicated ones into the original sets We use the BLOSUM (BLOcks SUbstitution Matrix) matrix as the model of evolutionary mutations. The BLOSUM matrix is a substitution matrix used to measure the similarity between protein sequences for alignment of them. BLOSUM matrices are derived from about 2000 blocks of aligned sequence segments characterizing more than 500 groups of related proteins Input: Training sequences Sizes of classes Mutation rate Calculate the largest size of classes ForFordoRandomly select a sequence Obtain the length Randomly pick Replace the amino acid in every one of the Add the new sequence into the set of classOutput: The new training datasetsAfter building the new training datasets by simulated evolution, we can use it and the extended Baum-Welch algorithm to optimize the MMIE criterion to get discriminative motifs represented by HMMs. Although the found motifs by the above methods are discriminative and useful for classification, both the percentage and significance of the conserved motif instances retrieved by those HMMs are low, which will be described in details later. The results may be attributed to the one-vs.-all strategy adopted for MMIE, since we have used the simulated evolution method to generate so many new sequences and the negative training set becomes so large that the extended Baum-Welch algorithm is affected.Therefore, the random under-sampling method is applied to make the size of negative training set as large as the positive one. Moreover, we don't intend to randomly select a set of the original negative set before the training of HMMs as usual machine learning methods do, which may cause the extended Baum-Welch algorithm to miss important sequences of the negative set resulting in less discriminative HMMs The main evaluation of the discovered motifs is based on their classification performance, so the log-likelihood ratio The found motifs are ranked by using one-step backward feature selection to further evaluate their contributions for predicting subcellular localization. For the SVM and the feature vector consisting of log-likelihood ratios, the accuracy after removing each feature (corresponding to a motif) is recorded and the motifs are ranked according to the ascending sort of the accuracies.Saccharomyces cerevisiae proteins with curated localization annotation in UniProt We apply our discriminative motif discovery method via simulated evolution and random under-sampling to the PSLT2 dataset Five sets of experiments are implemented: (i) generative training of HMMs, (ii) discriminative training of HMMs, (iii) generative training of HMMs with simulated evolutionary mutation, (iv) discriminative training of HMMs with simulated evolutionary mutation, (v) discriminative training of HMMs with simulated evolutionary mutation and under-sampling. In addition, all the algorithms above are executed on the flat and hierarchical structure respectively. For the sake of clarity, the above algorithms are marked as Gen, Disc, GenM, DiscM and DiscMU respectively. The evolutionary mutation rate for GenM, DiscM and DiscMU is selected as 20% as it has been shown in To make a fair comparison, we set similar options for all five algorithms: motif length is set to 4 that the number of match states is 4 for HMM. For generative HMM (Gen and GenM), we run the Baum-Welch algorithm with 10 random initialization and at most 50 iterations. For discriminative HMM , the generative HMM algorithm is executed firstly with the same options described above, then the extended Baum-Welch algorithm is implemented on the HMM with highest likelihood with 50 iterations at most. In order to obtain multiple non-redundant motifs for each compartment, after a motif is found we mask the amino acids assigned to match states by Viterbi algorithm The reasons for setting the motif length to be 4 are: firstly, the average length of functional eukaryotic linear motifs validated experimentally, including ligand sites, post-translational modification sites, proteolytic cleavage and processing sites and subcellular targeting sites, is approximately 6 (6.3) residues. Simultaneously, the 6.3 residues contain 3.7 defined positions  on average The SVM is trained and tested by the software SVMlight We compare the results of the five sets of experiments with the same evaluation criteria as the DiscHMM and focus on the impact of the data imbalance on the motif discovery and classification. In order to prevent the impact brought by excessively high sequence similarity, all the results are obtained on the original PSLT2 dataset not the augmented dataset after simulated mutation.The primary goal of our work is to identify novel discriminative targeting motifs which are occurring frequently in the positive set while scarcely or not occurring in the negative set. Since there is still a little current knowledge about targeting signals, finding a discriminative targeting motif based on its effect of classifying positive and negative sequences may be a useful and effective way. As a result, we use the found motifs to predict localization and further apply the prediction results to evaluate motif finding methods. The evaluation criteria used here are recall, precision and accuracy, and they are given by the following formulas:The overall accuracies of this prediction comparison are shown in The total accuracy of GenM, DiscM and DiscMU are higher than Gen and Disc, this is probably due to the application of over-sampling via simulated evolution, as a result, the multi-class imbalance problem has been solved, so that the precision and recall of minority classes increase substantially which will be described in detail later.The hierarchical structure, that mimics the cellular sorting pathways and may provide another layer of biological information, leads to great improvement in classification results for Gen and Disc which has been shown in DiscHMM, but it has a little effect on DiscMU and even worse than flat structure for GenM and DiscM. The reasons for the above situations may be that we use over-sampling method based on a simple simulated evolutionary model to generate new sequences and don't consider embodying the information of the cellular sorting pathways in that model, therefore, some of the new sequences may contain more targeting information of the negative class than their own class, so that it is affected when using the hierarchical structure of compartments for training and classification. These have greater impact on GenM and DiscM than DiscMU since in DiscMU we use under-sample to reduce this impact to some extent.The method Disc doesn't outperform Gen as it is presented in GenM and DiscM, versions of Gen and Disc respectively combining over-sampling, receive high prediction accuracies. Specifically the DiscM with flat structure which reaches the highest accuracy (62.5%). However, both the percentage and significance of the conserved motif instances discovered by these two methods are lower than Gen and Disc which will be shown in detail later. This indicates that the motifs found by these two methods are very helpful in classifying, but them may be not potential sorting signals or involved in other functions that proteins in a given compartment need to carry out. Further, we will discuss later that the motifs found by DiscMU method, versions of Disc combining over-sampling and under-sampling, are not only beneficial to classification, but also can find more conserved motifs.The above discussions on overall accuracy don't adequately reflect the negative impact of data imbalance problem and the superiority of our algorithm. Therefore, we do a further test on dataset I to illustrate the performance of Disc and DiscMU on each compartment. The results are displayed in As we can see, the precision and recall of almost all compartments are improved by our method, except the precision of Membrane (7.1) reduces from 67.13% by Disc on flat structure to 66.26% by DiscMU on tree structure, the recall of Membrane (7.1) reduces from 43.30% by Disc on tree structure to 34.32% by DiscMU on tree structure and the recall of Nuclear (37.6) reduces from 73.62% by Disc on flat structure to 73.36% by DiscMU on flat structure. However, the precision and recall of the relatively minority classes, such as Secreted (0.8), Peroxisome (1.4) and Golgi (2.1), improve greatly. The results imply that the discriminative HMMs training with the strategy of combining over-sampling with under-sampling is an effective method for protein subcellular localization prediction.The three most discriminative motifs found by Disc and DiscMU using hierarchical compartment structure are shown in After evaluating the found motif by precision and recall of localization prediction, we would like to identify how many of motifs discovered by different methods were previously known.A list of known targeting motifs collected by Lin The previous discussion shows that methods with over-sampling by simulated evolution were able to recover the most known motifs. However, they recover only a few known targeting motifs, even the most effective method recovers only 4 from 56. This is probably due to that there have been many real targeting motifs that are unknown up to now. Moreover, since the found motifs are very useful for protein subcellular localization predicting, some of them may play an as yet unidentified role in localization or other different biological interpretations of sequence signatures that differentiate between proteins that reside in different compartments. The key problem is how to validate them as potential sorting signals or involved in other functions that proteins in a given compartment need to carry out. One way is using the analysis of motif conservation: the found motifs that are expected to be potential sorting signals are more conserved among evolutionarily close species Saccharomyces Genome Database (SGD) fungal alignments Saccharomyces cerevisae protein sequences is defined as four conservation states: no conservation versus weak, strong, and identical conservation (across seven species). Second, for each of the five methods, 20 most discriminative motif candidates defined by backward feature selection as described previously are chosen. Third, for each of the 20 motifs, the top 30 positions based on likelihood or posterior probability are retrieved. Finally, for each motif instance, it is considered conserved if all sites in that instance are labeled as having strong or identical conservation by ClustalW First, according to The percentage of conserved motif instances for different methods and the corresponding statistical significance are presented in These results clearly indicate that motif instances discovered by all methods are significantly conserved when compared to conserved 4-mers. Moreover, For GenM and DiscM, versions of Gen and Disc respectively combining over-sampling, both the percentage and significance of the conserved motif instances are lower than Gen and Disc, although they are very useful in predicting locations. As we mentioned before, since we have used the simulated evolution method to generate a large number of new sequences, when we adopt the one-vs.-all strategy for MMIE, the negative training set becomes so large that the extended Baum-Welch algorithm is affected for training HMM. Consequently, HMM trained by GenM and DiscM cannot reflect the common characteristics of the positive training sequences. However, DiscMU, incorporating simulated mutation and random under-sampling into discriminative HMM training, achieves relatively high percentage, significance of the conserved motif instances and prediction accuracy. This suggests that the proposed method is not only contributing to classify proteins, but also more useful for discovering conserved motifs.We have developed and used a new method that applies a simple strategy of combining over-sampling with under-sampling method in discriminative HMM training to discover protein targeting motifs. The combining strategy contains over-sampling method via the simulated evolution for multi-class imbalance problem at the data preprocessing stage and random under-sampling method for the imbalance between the positive and negative datasets at discriminative HMM training stage. It successfully deals with these data imbalanced problems and assists in identifying more discriminative motifs in terms of prediction precision and recall for all compartments especially the minority classes. According to the conservation analysis, most of the novel motifs discovered are considered to be potential sorting signals or involved in other functions that proteins in a given compartment need to carry out. The advantage of our method is probably due to two aspects: first, the over-sampling method via simulated evolution contains phylogenetic knowledge obtained from the information in the BLOSUM62 matrix Our method provides a way to solve the data imbalance problem in discriminative motif discovery with multiple-class. Although we take the discovery of protein targeting motifs as an example to show the power of our method, our method can be easily applied to other problems of motif discovery and can contribute significantly to finding efficient, discriminative and conserved motifs, e.g., DBDs, post-translational modification sites and protein-protein interaction sites.β-Strand mutation model for beta-structural motifs Although the results presented in our paper show that the proposed method is relatively efficient in solving the data imbalance problem in discriminative motif finding, there are still same inadequacies in our work. For example, we select the 20% mutations in our experiment since it performs better for building profile HMMs to recognize G-protein coupled receptor proteins and SCOP super-family proteins, however, it is very important to research on how different mutation rates affect the establishment of profile HMMs for targeting motifs and how to build different mutation models for different subcellular compartments, such as the In addition to the cases mentioned above, it is helpful to take advantage of the attributes of short linear motifs File S1Supporting Information. Figure S1. Hierarchical (tree) structure of compartments based on cellular sorting. Figure S2. Accuracy of predictions based on simulated evolution by using BLOSUM45, BLOSUM62 and BLOSUM80 respectively. Figure S3. Number of known motifs recovered based on simulated evolution by using BLOSUM45, BLOSUM62 and BLOSUM80 respectively. Figure S4. Percentage of conserved instances of the top 20 candidate motifs based on simulated evolution by using BLOSUM45, BLOSUM62 and BLOSUM80 respectively. Table S1. The known motifs of InterPro recovered by DiscMU. Table S2. The sequences that contain IPR00426. Table S3. The known motifs of Minimotif Miner recovered by DiscMU.(DOC)Click here for additional data file.


Independent component and canonical correlation analysis are two general-purpose statistical methods with wide applicability. In neuroscience, independent component analysis of chromatic natural images explains the spatio-chromatic structure of primary cortical receptive fields in terms of properties of the visual environment. Canonical correlation analysis explains similarly chromatic adaptation to different illuminations. But, as we show in this paper, neither of the two methods generalizes well to explain both spatio-chromatic processing and adaptation at the same time. We propose a statistical method which combines the desirable properties of independent component and canonical correlation analysis: It finds independent components in each data set which, across the two data sets, are related to each other via linear or higher-order correlations. The new method is as widely applicable as canonical correlation analysis, and also to more than two data sets. We call it higher-order canonical correlation analysis. When applied to chromatic natural images, we found that it provides a single (unified) statistical framework which accounts for both spatio-chromatic processing and adaptation. Filters with spatio-chromatic tuning properties as in the primary visual cortex emerged and corresponding-colors psychophysics was reproduced reasonably well. We used the new method to make a theory-driven testable prediction on how the neural response to colored patterns should change when the illumination changes. We predict shifts in the responses which are comparable to the shifts reported for chromatic contrast habituation. In this paper, we propose a new method to analyze several data sets jointly and use it to relate properties of chromatic natural images to properties of the primary visual cortex: We show that the new method provides a parsimonious statistical explanation of both spatio-chromatic processing and its adaptation to changes in illumination.Statistical modeling of natural images under fixed, or uncontrolled, illumination reveals that “Gabor-like” features  are basic building blocks of natural images. These features are robustly obtained if statistical methods are used that take higher than second-order statistical information into account, for instance sparse coding However, the statistical methods in Statistical modeling of tristimulus pixel values of images under different illuminations provides an explanation of chromatic adaptation for spatially flat stimuli However, the statistical methods in Thus, the aforementioned statistical methods account for the different aspects of neural processing in V1 with which they are primary concerned, but neither of these approaches generalizes well to explain both aspects at the same time. We aim here at explaining both spatio-chromatic processing and adaptation using a single statistical method.In this paper, we present a novel statistical method to jointly analyze multiple data sets  Sparsity of the estimated canonical coordinates (Relation between data sets) The canonical coordinates can have linear or higher-order (variance) correlations across the data sets.In addition to the coupled features The above properties are in stark contrast to canonical correlation analysis (CCA). CCA represents the data using related features as in (1), but sparsity of the canonical coordinates is not a criterion, and CCA is sensitive to linear correlations between the two data sets only, see HOCCA is performed by solving an optimization problem. The features The objective function We show in We show here that HOCCA is a nonlinear generalization of CCA: For large values of The objective in (1) considered as a function of the features isWe illustrate here properties of HOCCA and provide some intuition by means of a simple example. We assume that We generated data according to the probabilistic model underlying HOCCA , with variable levels of correlation and sparsity of the canonical coordinates We analyzed the results using three measures of performance  between the two data sets was identified. For that purpose, we measured the mutual information between the coupled pairs of sources. In The results reported above validate the theoretical properties of HOCCA: We found that HOCCA led to a more efficient representation of the two data sets than CCA, as measured by sparsity or gain in independence, and that the recovery of the correspondence between the two data sets was also better, as measured by mutual information.Next, we apply HOCCA to chromatic natural images that were acquired under two different illumination conditions, daylight and yellowish light. We analyze the learned coupled representations, show that they account for known experimental results and make a theory-driven prediction. Two properties of the learned representations are of particular interest: First, the representation of the two data sets individually, that is, the spatio-chromatic processing for a given illuminant. Second, the coupling (correspondence) between the representations across the two data sets, that is, the adaptation to changes in the illumination. We also compare the representations learned by HOCCA with those from other statistical methods, namely ICA, CCA, and whitening by principal component analysis, see Applying HOCCA, or one of the alternative methods considered, to the two sets of images produces two sets of coupled filters (sensors), each one adapted to one of the two lighting conditions. The filter outputs yield an internal representation of the images in terms of canonical coordinates, see We analyzed the learned representations of natural images statistically using the same measure as for the artificial data. We used multi-information reduction and sparsity to assess the individual representation of each data set; to assess the coupling we used mutual information between the coupled canonical coordinates.Taken together, Regarding the features per data set, we use the finding that neurons in V1 are dominantly tuned to spatially localized oriented Gabor-like features with achromatic, red-green and yellow-blue chromatic content as plausibility baseline Visual inspection of the features shows that for whitening and CCA, the achromatic and the chromatic oscillations in the high frequency features do often not match spatially. They have different fundamental frequencies. For ICA and HOCCA, however, there is no such mismatch between achromatic and chromatic parts. Further, the ICA and HOCCA filters seem chromatically less saturated than the whitening and CCA filters. This means that in order to elicit a comparable response, ICA and HOCCA filters would require a stronger amplitude for chromatic than for achromatic gratings.Regarding the coupling, the sorting according to mutual information shows that for ICA, HOCCA and CCA, low-frequency features are more related than high-frequency ones. Further, for non-zero frequencies, the achromatic features are more related than the chromatic ones.We analyzed the similarity of the corresponding features, using the mean squared error as distance measure. Direct application of this distance would, however, be strongly biased by the chromatic shift due to the different illuminations. Therefore, Von-Kries color compensation We further investigated the learned coupling by assessing the ability of the different representations to reproduce psychophysical data on color corresponding pairs (color constancy). In the color psychophysics literature, physically different stimuli are referred to as corresponding if they give rise to the same perceived color when viewed under different conditions We show in A qualitative comparison of these predictions with the experimental data in the left column shows that HOCCA and CCA led to a better performance than whitening or ICA-based correspondence methods: For whitening, the arrangement of the points is rather different from the experimental data. For ICA, the predictions are often over-saturated such that many of the predicted colors fall outside the chromaticity diagram, which means that they are physically unrealistic. For HOCCA and CCA, however, this was much more rarely the case.A quantitative comparison was performed by computing the root mean squared error between the predicted and the experimental colors in the XYZ color-space. The results are given in In the previous sections, we used different criteria to analyze the learned representations per data set and the coupling across the data sets. The criteria used assessed the two aspects of the learned representations separately. Here, we consider both aspects at the same time.The learned filters map the images We investigated how the different representations perform in an adaptation task in the presence of neural noise: We compared the different methods in their ability to predict the representation of an image under illumination CIE D65 from its representation under CIE A. The mean squared prediction error is derived in We analyzed the learned representations of HOCCA, ICA, CCA, and whitening from both statistical and biological points of view using multiple criteria, see The previous sections showed that HOCCA provides a single (unified) statistical framework to study both efficient representations and adaptation. In this section, we use HOCCA to make a testable prediction about the response of human spatio-chromatic sensors (neurons) to colored patterns under change of illumination.HOCCA produced pairs of filters optimized for illumination CIE A and D65. Considering the two corresponding filters to be instances of the same  physical sensor when adapted to two different illuminants, we can investigate how adaptation changes the response to the same stimulus.For the prediction, we used six representative HOCCA filter-pairs, three pairs with chromatic content in the red-green (RG) direction , to jointly analyze multiple data sets. HOCCA combines desirable properties of canonical correlation analysis (CCA) and independent component analysis (ICA). HOCCA seeks independent and sparse sources inside each data set which have linear or variance correlations across the data sets. HOCCA is as widely applicable as CCA. Moreover, it generalizes CCA because it is not only sensitive to linear correlations but also to higher-order dependencies. We validated HOCCA on artificial data and proved that CCA emerges as a special case.Second, we showed that HOCCA provides a single (unified) statistical framework to study visual processing under fixed lighting conditions and adaptation to new ones. Results on chromatic natural images demonstrated the benefits of jointly maximizing efficiency of representation and coupling across the data sets, as opposed to first maximizing efficiency and then finding a suitable coupling, or focusing on coupling only. We found that HOCCA features are consistent with the spatio-chromatic tuning properties of neurons in the primary visual cortex and that HOCCA reproduces corresponding colors psychophysics reasonably well. HOCCA provided us with a specific, experimentally testable prediction on how the response to colored patterns should change when the illumination changes.We showed that HOCCA provides a generalization of CCA. CCA has been extended in many ways. Kernel CCA is a nonlinear extension of CCA that is sensitive to nonlinear dependencies across the data sets, see Section 3.2 of CCA was also combined with ICA In ICA, there is an ambiguity in the ordering of the column vectors of the mixing matrix. The joint estimation of In our simulations on natural images, we used a postprocessing stage after ICA where the mixing matrices We applied HOCCA to two sets of images acquired with different illuminants, namely daylight-like CIE D65 and yellowish CIE A. HOCCA produced two sets of coupled filters, each one adapted to one of the illuminants. We compared HOCCA with three other statistical methods: Whitening by principal component analysis, ICA, and CCA. For HOCCA and CCA, the filters are learned together with their correspondence. For whitening and ICA, however, the filters are learned separately for each data set. We sought a correspondence after learning of the filters by finding pairs which had maximal mutual information.Regarding the representations per data set, the mutual information reduction achieved by ICA and HOCCA is consistent with previously reported reductions for ICA in achromatic images Regarding correspondence, we found that, as HOCCA, CCA yielded a large amount of mutual information between the corresponding canonical coordinates even though CCA is only sensitive to linear correlations. The reason for this is two-fold: First, linear correlations contribute strongly to mutual information, see Corresponding colors have been inferred from properties of natural images before A and D for the labeling). Furthermore, the objective function optimized in HOCCA consists of a sample average over several such observations. The visual system, however, is exposed to only one scene under one illumination at a time. While a sample average can be computed in an online fashion, assuming that the visual system has access to labeled input data is more problematic. However, information about the labels is often implicitly available and the labels can be inferred from it. For the inference of the labels, it is enough that the brain “knows” that an object under either of the two illuminations is the same (kind of) object. Such information about the identity of an object could be provided by top-down processes. For instance, when leaving a house with a red apple in the hand, the brain “knows” that the apple was not switched out but that the same object is in the hand both inside and outside, even though the radiance sensed by the eyes is different. This means that HOCCA should not be considered a mechanistic model of visual processing and adaptation; its neural implementation is left unspecified. Instead, HOCCA should be considered a normative theory based on statistical principles. It tells us what we can expect if efficiency and correspondence are optimized jointly, in case the same images under two different illuminations were available.In the joint learning of the features and the correspondence between them, HOCCA (and CCA) had access to the same images under two different illuminations. That is, the input data came labeled in terms of the illuminant  cannot reproduce effects from eventual non-linear interactions. Therefore, our adaptation predictions cannot straightforwardly be compared to the habituation results reported in We construct here HOCCA such that it takes higher-order statistical dependencies both within and across the data sets into account, in contrast to CCA. This allows us to find a both related and efficient representation of the data. The new method is based on a probabilistic generative model which we outline next. In In order to find an efficient representation for each of the two data sets, we assume that each of the two vectors of canonical coordinates The independence assumption for the canonical coordinates within a data set makes the whitened data Let While Sources While different choices are possible for The family We used artificial data to validate HOCCA. We give here details for the data generation and the performance measures used in the assessment and in the comparison with CCA.The data was generated according to (1). The dimensionality was We analyzed the estimation results of HOCCA and CCA using three measures of performance. The first measure assesses how well the mixing matrices (features) were recovered, the second the efficiency of the learned representation, and the third how well the coupling (correspondence) between the two data sets was identified. We assessed the efficiency of the representation from a sparsity and a related information theoretical point of view. Note that the first two measures are insensitive to the coupling between the data sets.In order to quantify the accuracy of the estimated matrices In order to quantify the sparsity of the recovered canonical coordinates In order to measure the efficiency of the learned representation from an information theoretical point of view, we computed by which extent the mutual information between the recovered coordinates was smaller than the mutual information between the original (white) data. This difference in mutual information is called multi-information reduction. We can here compute it by comparing the entropies of the marginal pdfs of the (white) data and the recovered canonical coordinates In order to assess how well the coupling between the two data sets was identified, we computed the mutual information between the inferred corresponding sources http://isp.uv.es/data_color.htm and a detailed description was given before The data used for the learning consists of pairs of images (image patches) that we extracted from a set of 50 larger natural images acquired under CIE D65, daylight, and under CIE A, yellowish light. We used We then performed whitening and reduced the dimensionality of each individual data set by principal component analysis (PCA). Dimension reduction is worthwhile if there are strong correlations in the data, that is, if the data is essentially located in a subspace of lower dimensionality than We used HOCCA to learn the coupled representation by maximizing the objective CCA is briefly reviewed in Comparing HOCCA with the whitening-based approach is interesting since whitening is the first step in all methods. Comparing HOCCA with CCA and the ICA-based approach is interesting since these methods can be considered to represent limiting cases of HOCCA: ICA features are obtained by maximizing the efficiency (sparsity) of the representation of each data set individually, without concern for a possible correspondence between them. CCA features are obtained by maximization of correspondence (measured by linear correlation), without concern for the efficiency (sparsity) of the individual representations. HOCCA, on the other hand, is jointly maximizing the efficiency of the individual representations and the correspondence between them.The representations were statistically analyzed by assessing their efficiency and the coupling between the corresponding canonical coordinates (feature outputs) For the visualization of the learned features, the features were first scaled to have unit norm and then contrast-normalized by applying a global scaling factor to the deviation from the average. The scaling was chosen so that the feature colors are reproducible in conventional displays: Too small scaling factors lead to chromatically uniform features while too large factors give rise to non-reproducible imaginary colors, that is, to negative luminance or to colors outside the reproducible gamut.We reproduced corresponding-colors based on the learned representations as follows: Given a spatially uniform patch of a certain color under illumination CIE A, we identified it with For the noise-distortion curves, the setup of the corresponding-colors was modified in two aspects: First, we used image data with spatial structure. Second, the internal representation by means of the canonical coordinates was subject to noise. The noisy version of For the stimuli used in the prediction, we changed the chromatic contrast and color content as follows: In a achromatic red-green yellow-blue representation, the color Text S1Details of Higher-Order Canonical Correlation Analysis.(PDF)Click here for additional data file.Text S2Background Material from Multivariate Analysis.(PDF)Click here for additional data file.Text S3Calculations for the Noise-Distortion Analysis.(PDF)Click here for additional data file.