In Indian context, limited attempts have been made to estimate the mortality risks among people living with HIV (PLHIV). We estimated the rates of mortality among PLHIV covered under an integrated HIV-prevention cum care and support programme implemented in Karnataka state, India, and attempted to identify the key programme components associated with the higher likelihood of their survival.Retrospective programme data of 55,801 PLHIV registered with the Samastha programme implemented in Karnataka state during 2006–11 was used. Kaplan-Meier survival methods were used to estimate the ten years expected survival probabilities and Cox-proportional hazard model was used to examine the factors associated with risk of mortality among PLHIV. We also calculated mortality rates (per 1000 person-year) across selected demographic and clinical parameters.Of the total PLHIV registered with the programme, about nine percent died within the 5-years of programme period with an overall death rate of 38 per 1000 person-years. The mortality rate was higher among males, aged 18 and above, among illiterates, and those residing in rural areas. While the presence of co-infections such as Tuberculosis leads to higher mortality rate, adherence to ART was significantly associated with reduction in overall death rate. Cox proportional hazard model revealed that increase in CD4 cell counts and exposure to intensive care and support programme for at least two years can bring significant reduction in risk of death among PLHIV  even after adjusting the effect of other socio-demographic, economic and health related confounders.Study confirms that while residing in rural areas and presence of co-infection significantly increases the mortality risk among PLHIV, adherence to ART and improvement in CD4 counts led to significant reduction in their mortality risk. Longer exposure to the intervention contributed significantly to reduce mortality among PLHIV. Globally, it is estimated that 35.3 million [32.2 million–38.8 million] people were living with HIV (PLHIV) by the year 2012.A total of 55,801 PLHIV registered with the programme were included in the analysis, of which, about nine percent (4903 PLHIV) died during the project period, i.e., between 2006–2011. The analysis presented in The study attempted to analyse the expected survival probability of PLHIV post they detected positive by selected characteristics such as sex, ART and CD4 status, and their duration of programme exposure. Considering the variations in accessibility to HIV care services by their place of residence , the survival probabilities were adjusted for their location of usual stay. The effect of programme exposure, ART treatment, and CD4 counts may be confounded by the background characteristics of PLHIV, and hence, survival probabilities can be tentative until they are adjusted for the effects of background factors. The most important result to notice from Based on the data derived from a retrospective cohort of patients living with HIV and registered with an intensive HIV care and support programme for PLHIV in selected districts of Karnataka, this study made an attempt to estimate the mortality rate and the probability of survival post ten-year intervention period among them. Only a few studies in India, till date, have made any effort to determine the mortality risk using the programme-based individual tracking data using a large sample size. Findings of this study documented the death rate of 38 per 1000 person-years, which was little higher than the death rates reported in the other parts of the country.The study reported relatively higher mortality rates among males compared to females. This finding is somewhat contrary to the general belief that men have better access and utilization of health care services including HIV-testing and counseling, thereby, should have lower chances of mortality. However, because the intervention was primarily focussed on rural areas, the social stigma attached around HIV/AIDS may lead to the lower access of services among men. The role of stigma in limiting the access of services may not be so strong among females as the intervention had several focused activities to bring the females to the clinic periodically and serve them various health services that they need. ExistingBoth bivariate and multivariate analysis showed a strong association between higher mortality rates and demographic variables such as age, educational level, and place of residence. The higher death rate among older ages has been found in other studies too., 19–25 FIn agreement with the previous studies, the findings of this study also suggest lower death rate and a higher likelihood of survival among the PLHIV, who were on ART. Globally, in the absence of a cure for HIV, the increased use of ART has been able to improve the survival of individuals infected with HIV–28 by poOne of the significant finding of our study is that the likelihood of survival increases with the high level of CD4 count and it corraborates with the previous studies conducted in India., 38 The Analysis conducted in this paper also focused on analyzing the effect of exposure to care and support intervention on the survival of PLHIV. It is clear that the survival probabilities improved as the duration of programme exposure increased. However, if the programme exposure is more than two years, there is hardly any further decrease in the survival probability post ten years since tested positive. Such relationship, of course, expected to depend upon CD4 count and whether the person is on ART or not. But results of the hazard model indicate that even after controlling for CD4 count and being on ART along with other background characteristics, the programme exposure alone reduces the risk of mortality drastically compared to who did not have any intervention exposure. The intervention exposure should have helped PLHIV to undergo the CD4 count test regularly and to get on ART treatment whenever necessary. However, intensive programme exposure for two years appears to be sufficient to sustain this behaviour.Despite, the study observed various important findings including the minimum duration of intervention exposure required to reduce the mortality risk among PLHIV, the findings should be considered with caution. As the study was taken up using the retrospective data, some of the potential confounders of mortality such as viral load, previous histories of ART uptake, sequencing of co-infection, and side effects during the ART regime under the process of medication could not be included. The information on opportunistic infections, other than TB, was not properly captured. Similarly, the information on distance to ART center was not available. Therefore, our analysis could not use any information pertaining to the previous history of ART uptake presence of other opportunistic infections. Our results on the death rate might be overestimated due to the fact that all causes of death were included in the study and it is possible that certain deaths might have occurred due to non-HIV related causes. Due to a very large sample size, most of the bi-variate and multivarite results are statistically significant at one percent level of significance, and therefore, results should again be considered with caution. However, despite these limitations, many of the findings of this paper have importance from the planning of care and support programme and its implementation.The study revealed several useful results that have potential bearing on reducing the risk of mortality among the HIV-infected population. The most useful findings emerged from our analysis are adjusted hazard risks for CD4 status and duration of programme exposure. The increase in CD4 count from less than 100 to more than 350 reduced the hazard risk by more than 90 percent. An important question that was not properly answered till date was the required level of the CD4 count to reduce the hazard risk to zero. In fact, the even more relevant question to be asked is: what is an optimum level of the CD4 count for ART treatment? Our findings clearly demonstrated that a minimum CD4 count of 100 is required for the survival, whereas, CD4 count of more than 350 enhances the survival chances of PLHIV by multiple times. To maintain a high level of CD4 cell count among PLHIV, it is essential for the national programme to focus on the adherence of HIV-infected persons to ART therapy. Though the efforts are being made to improve the ART adherence among HIV-infected people and provision of free ART medicines at designated government ART centres have already been made under the national programme, still regular follow-up with the HIV-positive patients is required for better results. Further research is required to understand the reasons for non-adherence. Addressing the adherence in the ongoing ART programme in India may bring a notable reduction in the current level of mortality among HIV-infected persons.Another significant finding of our paper is that the programme exposure of at least two years can brings a substantial reduction in the likelihood of mortality among PLHIV. More specifically, a focused care and support intervention with repeated follow-up and strategic use of information for ongoing improvement in the health and well-being of PLHIV has been critical in reducing the mortality. The project like Samastha that focused on medical and psycho-social services, regular follow-up of CD4 counts, and ART adherence contributed significantly to reduce mortality among PLHIV. For policy makers and programme implementers, it is definitely encouraging to know that exposure to a well-designed programme can become a good proxy for monitoring of CD4 counts and ART adherence.


Mobile Visual Location Recognition (MVLR) has attracted a lot of researchers' attention in the past few years. Existing MVLR applications commonly use Query-by-Example (QBE) based image retrieval principle to fulfill the location recognition task. However, the QBE framework is not reliable enough due to the variations in the capture conditions and viewpoint changes between the query image and the database images. To solve the above problem, we make following contributions to the design of a panorama based on-device MVLR system. Firstly, we design a heading  aware BOF (Bag-of-features) model to generate the descriptors of panoramic images. Our approach fully considers the characteristics of the panoramic images and can facilitate the panorama based on-device MVLR to a large degree. Secondly, to search high dimensional visual descriptors directly on mobile devices, we propose an effective bilinear compressed sensing based encoding method. While being fast and accurate enough for on-device implementation, our algorithm can also reduce the memory usage of projection matrix significantly. Thirdly, we also release a panoramas database as well as a set of test panoramic quires which can be used as a new benchmark to facilitate further research in the area. Experimental results prove the effectiveness of the proposed methods for on-device MVLR applications. Mobile visual location recognition (MVLR) Although the research on MVLR has witnessed many achievements in the past few years, the technology is still not mature enough. For example, most existing methods are based on Query-by-Example (QBE) principle which generally requires an example image as a query to search for similar database images. However, the level of retrieval reliability is still insufficient due to the likely variations in the capture conditions  and the viewpoint changes between the query image and the images in the database.We think that the use of panoramas can improve the usability of on-device mobile visual location recognition systems obviously due to following reasons. Firstly, compared with a query image with relatively narrow angular field of view, a panoramic image commonly contains more useful visual information which can be used to generate visual descriptors with higher discrimination power. Secondly, the use of panoramic query image can help users to formulate their visual intent more conveniently, which is useful for enhancing the user experience.While promising, it is not a simple task to realize panoramas based MVLR directly on resource limited mobile devices. For example, it is difficult to fit the panoramas searching engine into the RAM of mobile devices because the memory budget of an on-device MVLR application is only about dozens of megabytes. Secondly, the limited computational power makes the fast and accurate panoramic image searching become a difficult and challenging task on mobile devices.In view of the above problems, we make following contributions in this research to the design of a panoramas based on-device MVLR system. Firstly, we use heading information from digital compass to facilitate the BOF descriptors generation process. Our approach fully considers the characteristics of the panoramic images and can facilitate the panorama based on-device MVLR to a large degree. Secondly, we propose a compressed sensing based encoding method. Our method is fast and compact enough for power limited mobile devices, which makes the storing and searching of panoramic image database directly on mobile devices come true. Thirdly, we also release a panoramas database as well as a set of test panoramic quires which can be used as a new benchmark to facilitate further research in the area.The rest of this paper is organized as follows: Section 2 discusses the related work. Section 3 gives an overview of our panorama based on-device MVLR system. Section 4 gives the details of panoramas database construction. Section 5 introduces the heading-aware BOF method that will be used to generate the descriptors of panoramic images. Section 6 discusses the compressed sensing based visual descriptor code method. Section 7 gives the location recognition method. Section 8 shows some experimental results. Section 9 is a conclusion.In the past decade, MVLR In that case, traditional image describing  While promising, existing methods are not efficient enough because the retrieval reliability of the Query-by-Example based image retrieval principle is still insufficient. In view of that, we propose a panorama based framework in this research to improve the performance of on-device MVLR systems.The proposed panorama based on-device MVLR framework is shown in Offline Panoramic Images compression and indexing: In this stage, we build a panoramic image search engine which will be used for on-device MVLR. We firstly generate the heading-aware BOF descriptor of each database panoramic image and then convert them into binary vectors by using the method given in section 6.Online location recognition: To perform location recognition, the heading-aware BOF descriptor of the query panoramic image will be generated firstly. Then, the method of section 7 will be used to perform panoramic image searching directly on mobile device to fulfill the location recognition task.Subsequent sections describe the method used in detail, present the results, and evaluate the method's performance.We collect the HUST Panorama database by using a mobile mapping vehicle composed of Ladybug3 360°spherical digital video camera system, Global Positioning System (GPS), and Inertial Measurement Unit (IMU). We directly use the panoramic images to generate the database.We collect the street view of the main roads of the Huazhong University of Science and Technology (HUST) and obtain 5081 images captured at 4-meter intervals on average. Our work is permitted by the Huazhong University of Science and Technology. The range (GPS) of our study is between  using heading-aware method.So many kinds of methods such as BOF (Bag-of-features), VLAD  and REVV  can be used to generate the visual descriptors of panoramic images. Obviously, we can directly generate the descriptors of query and database panoramic images to fulfill the searching task. However, it will cause trouble in our case because the database images are complete 360-degree panoramas, while the submitted query may not be. As shown in The ideal situation is that we can extract the query corresponding areas only, filtering out the disturbed areas. Based on this idea, we propose to partition the database panoramas equally. As shown in Suppose that the database panoramas are divided into L parts. The heading-aware visual descriptor is concatenated by L sub-descriptors:Where While capturing the query panorama, two headings from compass are recorded. One heading is recorded when it starts to capture query panoramas, and another heading is recorded when it finishes capturing. While combining the perspective of camera, the query's start and end angles with north direction can be estimated. Suppose that the start angle with north direction is a, and the end angle is b. The query's range is defined as the interval:The range corresponds to the parts:Check the area's endpoints. If the query in this part is less than half of it, the endpoint part is excluded. As shown in Where Given a specific query with included parts Let Where Applying the heading-aware method to panorama based MVLR system can filter out most disturbed areas. Meanwhile, partial spatial information can be retained by dividing the panoramas, which makes up for the shortcoming of traditional visual descriptor methods to some extent. However, it also leads to an increase in the descriptor dimension. More memory space is needed to store the database's descriptors, and more computation time is needed to retrieve. We suppose to address this problem by the compressed sensing based code method, which will be introduced in details in section 6.In this research, we use the BOF method which has been proved to be the most common and effective approach in dealing with the problem of large-scale image retrieval. In BOF method, local image features from sample images are used to train a vocabulary tree Algorithm 1 Heading-aware BOF for databaseInput:Extract local image features from each panorama of Use the local features to train a vocabulary tree, and the number of leaf nodes is Determine the part that the feature belongs to by the feature location. Generate the BOF Output:The vocabulary tree;The heading-aware BOF increase the space and computation time requirements. This section deals with this problem by descriptors coding. In this section, we will first introduce the compressed sensing theory and bilinear projection briefly, followed by the approach of using bilinear method to realize the measurement of compressed sensing.Compressive sensing (CS) has aroused great attention in the signal processing community. Recent theoretical results show that if the signal is sparse (or nearly sparse) in some basis, then with high probability, the observations essentially encode the salient information in the signal. We say that a signal For a K-sparse signal, the observation is obtained by projecting the signal onto a randomly chosen vector, namely random projection, of which the entries are independent and identically distributed (i.i.d.) . Consider an It's inspiring that CS enables the recovery of sparse or compressive signals from a small set of incoherent projections. And recent researches show that the signal's compressive measurements can be more effectively used than first recover the signal, which enable data compression. However, for high-dimension data, the random projection matrix may require too much storage space and computation time. For example, if encoding a Let We reorganize it into a The bilinear projection uses two matrices Where This projection is given by We present a method for visual descriptor coding by using random bilinear projection. As described earlier, we adopt BOF to generate visual descriptor. Considering that the BOF vector is sparse, and the sparsity increases with dimension, we can directly extract the measurements by random matrix. Given a Algorithm 2 Bilinear Compressed Sensing CodeInput:Reorganize Generate two linear projections Compute the embedding of data Compute the binary code Concatenate Output:The comparison of the traditional method and bilinear method is shown in the Given a query, we need to compute the distance to each binary code in the database. The Hamming distance is very effective for binary codes. Taking into account the retrieval accuracy, we adopt the asymmetric distance, in which the database descriptors are binarized after compression, but the query is just compressed. For a query, which is compressed into Since This section introduces the method used to perform location recognition. Before the location recognition process, we generate the heading-aware BOF for database panoramas by Algorithm 1, and encode them by Algorithm 2. The codesThe heading information and GPS are used to generate the heading-aware BOF. In the similarity evaluation process, the GPS information is used to narrow down the retrieval range to improve the location recognition accuracy. The location recognition method is described in detail as follows:Step 1) Narrow down the candidate range set Step 2) Find the included parts Step 3) Generate the heading-aware BOF The code of query isn't binarized after the bilinear compressed sensing for improving the accuracy.Step 4) For each database panorama in set In this section, we first give the result of our location recognition. Then we evaluate the heading-aware BOF algorithm on the HUST panorama database that we release. And we evaluate the performance of bilinear compressed sensing on the HUST panorama database and San Francisco PFI database recall@ R which is defined as the proportion of query vectors for which the correct match is ranked within the top R returned results.The performance of different methods are measured by We extract SURF features from each database panorama. The hierarchical K-means are adopted to train a vocabulary tree which contains To perform the location recognition, we first use the GPS information to find the database candidates within 200 meters from the query. We generate the heading-aware BOF according to the query's heading information and use the algorithm proposed in the section 7 to perform the location recognition. Finally, a geometric verification (RANSAC with a 2D affine model) We also implement the method proposed by Chen et al. In our current system, each database panorama takes 2410 bytes , we propose a method for comparison (HBOF-CMP). The method generates database descriptors separately by part, while query does not. Meanwhile, generate traditional We test the performance of bilinear Compressed Sensing based visual descriptor code on the HUST panorama database and San Francisco PFI database. For HUST panorama database, we divide the panoramas into 12 parts and generate Heading-aware BOF by algorithm 1. The vocabulary tree used contains We compare our method (BCSC) with Compressed Sensing based visual descriptor code (CSC) and Product Quantization (PQ, Comparing our method with Compressed Sensing based method, our bilinear projection based method can reduce memory needed for projection matrix and computation time greatly. Comparing our method with PQ, PQ performs poorly in our experiments. PQ can encode the descriptor into very short code, but it fails to provide a rational accuracy, which proves the necessity of larger code size for high dimensional descriptor to get the highest absolute accuracy. Meanwhile, the memory needed to store the codebooks is 39.1 MB, which is extreme for our application.In this paper, we discuss the MVLR by panoramas images. The traditional visual descriptors perform poorly on the panoramas images. We propose a heading-aware visual descriptor method for panorama image. Experimental results on HUST Panorama database prove the effectiveness of heading-aware BOF. We also design bilinear Compressed Sensing based code which reduces the costs of memory and computation time for projection matrix significantly. Experimental results on HUST Panorama and San Francisco PFI database show that the performance of bilinear projection method is comparable with Compressed Sensing based code with a full projection matrix. We also release a HUST Panorama database. We hope that the released dataset will facilitate further research in the area.


Myocardial infarction leads to changes in the geometry (remodeling) of the left ventricle (LV) of the heart. The degree and type of remodeling provides important diagnostic information for the therapeutic management of ischemic heart disease. In this paper, we present a novel analysis framework for characterizing remodeling after myocardial infarction, using LV shape descriptors derived from atlas-based shape models. Cardiac magnetic resonance images from 300 patients with myocardial infarction and 1991 asymptomatic volunteers were obtained from the Cardiac Atlas Project. Finite element models were customized to the spatio-temporal shape and function of each case using guide-point modeling. Principal component analysis was applied to the shape models to derive modes of shape variation across all cases. A logistic regression analysis was performed to determine the modes of shape variation most associated with myocardial infarction. Goodness of fit results obtained from end-diastolic and end-systolic shapes were compared against the traditional clinical indices of remodeling: end-diastolic volume, end-systolic volume and LV mass. The combination of end-diastolic and end-systolic shape parameter analysis achieved the lowest deviance, Akaike information criterion and Bayesian information criterion, and the highest area under the receiver operating characteristic curve. Therefore, our framework quantitatively characterized remodeling features associated with myocardial infarction, better than current measures. These features enable quantification of the amount of remodeling, the progression of disease over time, and the effect of treatments designed to reverse remodeling effects. A computational atlas of image-derived shapes refers to an alignment of maps that relate individual anatomical geometry and function to the distribution of biological variations across a population, which can be described at different scales from genotype to phenotype http://www.cardiacatlas.org) is a world-wide web-accessible resource, comprising a population atlas of asymptomatic and pathological hearts The Cardiac Atlas Project  imaging is a non-invasive modality, which provides detailed, quantitative data of the heart structure and function. Compared to other imaging modalities, CMR does not use ionizing radiation, and is not dependent on restricted views of the heart. As a result, many large research studies are using CMR to collect phenotypic data on cardiac disease. Model-based image analyses were developed in the last decades from the availability of large-scale data set of CMR images. This has led to the growing number of statistical analysis applications for cardiac shape and motion In this study, we applied principal component analysis (PCA) to characterize the cardiac shape features in a large number of CMR cases. PCA is a widely used dimensionality reduction technique, which has been applied to heart shape analysis CMR datasets of 300 patients with myocardial infarction from DETERMINE and 1991 asymptomatic volunteers from MESA were obtained from the CAP database for inclusion in this study. These represented a random sample of the MESA baseline and DETERMINE CMR examinations contributed to CAP with local Institutional Review Board approval. This retrospective study was approved by the Health and Disability Ethics Committees of the New Zealand Government, under reference MEC/08/04/052. Informed participant consent compatible with sharing of de-identified data was obtained in writing in all cases. Imaging studies and derived analyses were de-identified, prior to analysis, in a HIPAA compliant manner [US Health Insurance Portability and Accountability Act of 1996 ], annotated using standard ontological schema, stored in a web-accessible picture archiving and communication system database, and analyzed using atlas-based techniques 1C continuity,  to the DETERMINE cohort (SSFP). It is known that these two protocols result in small differences in the placement of inner and outer surfaces of the heart. SSFP typically gives rise to larger estimates of left ventricle (LV) cavity volume and smaller estimates of LV mass than GRE. The shape bias has been shown to be regionally variable, and can be effectively removed using a maximum likelihood correction algorithm modes. After the projection, the number of modes retained is typically well below the number of original variables, yet still retains a high percentage of the overall variability in the original set. The first mode accounts for as much of the variability in the data as possible, and each succeeding mode in turn has the highest residual variance possible under the linear orthogonality constraint. The coordinates  of the surface sampling points were concatenated into a shape vector. Shape vectors from all cases were formed into a matrix. The eigenvectors of the covariance matrix formed the principal component modes, and their corresponding eigenvalues indicate the proportion of the total variation explained by each mode. Selecting the number of PCA modes to retain in subsequent analysis is contingent on the application. In this paper, enough modes were retained to explain 90% of the total variance. Three PCA cases were considered, the first using only shape vectors at ED, the second using shape vectors at ES, and the third using a combination of ED and ES (ED&ES). The ED&ES PCA was formed by concatenating the shape vectors from ED and ES into a single shape vector.Principal component analysis P is the probability of the a certain case belonging to the myocardial infarction set, L represents the log-likelihood of the model  of the receiver operating characteristic curves, since this is also an overall measure of goodness of fit .After PCA, a logistic regression model PCA was performed on the shape models at ED and ES as well as their combination (ED&ES). A scree plot Five logistic regression models were studied using all available data. The coefficients (β), standard error, associated p-values, standardized coefficients and odds ratios (OR) were calculated for each model. A p-value of 0.05 or lower was considered significant. The first model included age, sex, height, weight, systolic blood pressure and diastolic blood pressure . This waThe standardized coefficients show which modes have greater effect on the probability that the case is a patient. Mode 1 and mode 4 have greater effect in the classification model at ES. Mode 1, mode 6 and mode 2 have greater effect in the classification model at ED. EDV, ESV and MASS are highly related with the disease, according to The goodness of fit was compared between the five models with the indices of Deviance, AIC, BIC and AUC of each model, which are listed in We have proposed an atlas-based disease analysis framework by means of shape parameters from LV finite element models with a large number of subjects. The framework consisted of three steps: (1) fitting a finite element model to the LV MR images, (2) principal component analysis of the aligned shape parameters, and (3) quantification of the association with disease using logistic regression. We hypothesized that patients with myocardial infarction have significant shape differences with respect to the normal population, due to cardiac remodeling. The results supported this hypothesis, with most modes significantly associated with disease. The PCA analysis also performed better than traditional indices of remodeling (mass and volume). This method can therefore be used as a clinical tool for the characterization of the patterns of change associated with remodeling. These methods can also be used to track individual patients over time, by quantifying the degree to which their shape modes conform to the remodeling spectrum. Patients who are moving toward the adverse side of the spectrum may benefit from more aggressive treatment regimes. Conversely, the reverse remodeling associated with treatment can also be quantified. Although in this study we applied the method to patients with myocardial infarction, this framework is generalizable to any disease group.Note that we did not attempt to correct for colinearity between EDV, ESV and Mass in the MASSVOL model, or between SBP and DPB in the baseline model. EDV and ESV were strongly correlated , as were ESV and Mass , which would affect these coefficient estimates and odds ratios in the model. However, all three were input together in the MASSVOL baseline model to show the combined goodness-of-fit of traditional indicators, in order to assess the improvement given by the PCA modes. SBP, DBP  and other baseline variables were included in all the regression models to control for any differences between the patient and asymptomatic groups .The finite-element method is a powerful representation of the LV model, which also provides traditional indicators such as volume and mass. This method has been used to characterize cardiac motion PCA clusters the variability of the finite element models into orthogonal modes that can be interpreted from a global shape point of view. In Although heart size is known to be dependent on patient body habitus, we did not correct the shape vectors for height or weight, as done clinically using indexing methods. This was because the baseline model already included height and weight, so all PCA logistic regression analyses were automatically corrected for height and weight.Further work is needed in several areas. Although PCA is one of the most common dimensionality reduction techniques, other techniques may be more appropriate, such as independent component analysis


New motor rehabilitation therapies include virtual reality (VR) and robotic technologies. In limb rehabilitation, limb posture is required to (1) provide a limb realistic representation in VR games and (2) assess the patient improvement. When exoskeleton devices are used in the therapy, the measurements of their joint angles cannot be directly used to represent the posture of the patient limb, since the human and exoskeleton kinematic models differ. In response to this shortcoming, we propose a method to estimate the posture of the human limb attached to the exoskeleton. We use the exoskeleton joint angles measurements and the constraints of the exoskeleton on the limb to estimate the human limb joints angles. This paper presents (a) the mathematical formulation and solution to the problem, (b) the implementation of the proposed solution on a commercial exoskeleton system for the upper limb rehabilitation, (c) its integration into a rehabilitation VR game platform, and (d) the quantitative assessment of the method during elbow and wrist analytic training. Results show that this method properly estimates the limb posture to (i) animate avatars that represent the patient in VR games and (ii) obtain kinematic data for the patient assessment during elbow and wrist analytic rehabilitation. This is the focus of this paper;to optimize the rehabilitation processes by using the kinematic (and other) patient models. This optimization includes hybrid technologies . Robotic and VR technologies are important components of the modern neurorehabilitation systems for pathologies such as stroke or spinal cord injury –3. In thdesign and control of the advanced robotic exoskeletons which provide assistance to the patient during motor rehabilitation , 6,animation of realistic avatars representing the patient in virtual reality (VR) scenarios , andacquisition of kinematic data of the patient during the training exercises to assess improvement along the therapy.In the mentioned scenario, the proper estimation of the patient limb posture is a fundamental prerequisite for the following:This paper presents a method for estimation of limb posture from the exoskeleton posture. Notice that such an estimation is not trivial, since the limb is not rigid, is not standard, and has kinematic topology different from the exoskeleton topology.Our method delivers limb postures estimates to strengthen and to enable downstream applications in robotic rehabilitation .The inclusion of robotic devices in motor rehabilitation therapies has been increasing over the last decade. The robot-assisted therapies complement conventional rehabilitation by providing intensive, repetitive, task-specific, and interactive treatment. All these factors contribute to a more effective rehabilitation –9.Robotic-assisted therapy has been shown to improve active movement, strengthening, and coordination in stroke patients . The majCombining these exercises with VR games makes the therapy more attractive to the patient, increasing motivation and treatment effects , 13. It A central element in designing a therapy is the feedback that patients receive. To achieve relatively permanent changes in the capability of producing skilled action, it is crucial to provide the patient with proper feedback in order to produce a positive impact on the neural mechanism promoting motor learning .Feedback includes all the sensory information as the result of a movement and it is divided into two classes: (1) intrinsic or inherent feedback, which is information captured by human sensory systems as a result of the normal production of the movement, and (2) extrinsic or augmented feedback, which is information that supplements intrinsic feedback , 16. RobFrom the perspective of the therapist, robotic devices can be used to obtain quantitative metrics for the assessment of the improvement of the patient. The kinematic information of the affected limb during the exercises is required to compute several evaluation metrics, such as joint amplitudes, speeds, movement smoothness, and directional control.Currently, the gaming platform provides an elementary assessment of the patient performance with metrics such as Hand Path Ratio  and joinCurrently, the games only provide the patient with feedback of his hand position. We propose to provide a 3-dimensional representation of the arm, which would help the patient to immerse in the VR environment.Our proposed therapy uses the Armeo Spring exoskeleton for the upper limb intervention . We findThe kinematic data provided by the exoskeleton samples the angular position of its joints. Such information cannot be used directly to represent the human arm, since the patient limb and the exoskeleton kinematic models differ significantly.This paper presents a method to estimate the posture of the limb by using the kinematic data provided by the exoskeleton. We propose to solve the limb's inverse kinematics (IK) problem extended with the kinematic constraints of the exoskeleton fixations on the limb. This extended problem is solved in real time with standard robotic libraries. In this manner, we aim to overcome the limitations of the Armeo system regarding to the feedback and assessment of the patient.This paper is organized as follows: Several estimation methods and human models have been proposed in the literature to solve the problem of limb posture estimation. Next, we present a brief review of developments in these areas.Most of the existing work on limb posture estimation focuses on free movement scenarios. We define a free movement scenario as a situation in which the patient limb does not wear an exoskeleton or interact with any other robotic interface. Under the mentioned conditions, the literature that addresses upper limb posture estimation considers tasks in which the human subject has to reach a desired object. Therefore, these approaches are designed to estimate the posture of the upper limb based on a given target position and orientation of the hand.Statistical , 19, IK Statistical or data-based approaches model the human kinematics with regressive models from empirical data . FactorsKinematic approaches model the human limbs with links, joints of different degrees of freedom, and end-effectors . The IK Optimization approaches require a nontrivial function to minimize, which actually leads to the desired configuration . When oApproaches combining optimization-based and statistical models have been also proposed to overcome the individual limitations of optimization and statistical methods , 32. Natthe mechanic design of the exoskeleton .the type of assistance that the exoskeleton provides .the performance of the exoskeleton motion controller. Here, using a naive one-to-one mapping between the joint angles of the human limb and exoskeleton leads to poor positioning results .There is a shortage in the literature addressing posture estimation of the human limb while interacting with an exoskeleton. Although exoskeletons are designed with the ultimate goal of minimizing their kinematic differences with human limbs and interact seamlessly with them, the following factors influence the human motion patterns and therefore the posture of the limb:References , 21 propReferences , 21 do nOther common methods to estimate the posture of human limbs cannot be used or are impractical in robotic-assisted scenarios. For example, inertial and magnetic measurement systems (IMMSs) presented in , 36 are If optical tracking systems are used, arrays of markers need to be attached to the patient in order to measure the limb joint angles. Occlusions of such markers are frequently produced by the mechanic structure of the exoskeleton when performing the rehabilitation exercises. To overcome the occlusions of the markers, a redundant setup is necessary . This liA central element in human posture estimation is the human kinematic model itself. Simple models based on hierarchies of links and lower kinematic pairs can be found in , 37–40. The selection of the human kinematics model rests not only on the kinematic statement of the problem, but also on the compromise between accuracy and speed required in a particular application.Although the methods designed to estimate the posture of the upper limb (in absence of a robotic interface) reviewed in On the other hand, the few posture estimation approaches that address limb interaction with an exoskeleton  have beea method that can be applied, in a general manner, to solve the limb posture estimation problem using kinematic data provided by the exoskeleton attached to the limb,the implementation of our proposed method for the upper limb posture estimation using the Armeo Spring exoskeleton, andthe quantitative validation of our proposed method by determining the estimation errors during the training of meaningful upper limb rehabilitation exercises.In response to the mentioned issues, in this paper we present the following:In this section, we state the problem of estimating the joint angles of the patient limb during robotic-assisted rehabilitation therapy from the kinematic information provided by the robot. The elements that are considered inputs to the problem are the following: (1) the geometry and topology  of the This problem can be formally stated as follows.GivenR, where LR and JR are sets of links and joints, respectively,the kinematic model of the exoskeleton LR = {lR0,…, lRf+1};JR = {jR0,…, jRf}:N(jRi) denotes the degrees of freedom (DOF) of jRi;vRi = {θ1,…, θN(jRi)} is a vector that contains the angles of each DOF of jRi;R is an open kinematic chain. Therefore, lRi and lRi+1 are connected by joint jRi, where i ∈ ;qR ∈ Rn, n = ∑i=0fN(jRi), contains the set of independent coordinates that defines a configuration of R uniquely:the vector qR = {vR0,…, vRi,…, vRf};qRt represents the state of qR in instant t and its value is known;H, where LH and JH are sets of links and joints, respectively,a human patient with a kinematic model of his limb LH = {lH0,…, lHg+1};JH = {jH0,…, jHg}:N(jHi) denotes the DOF of jHi;vHi = {θ1,…, θN(jHi)} is a vector that contains the angles of each DOF of jHi  ;H is an open kinematic chain. Therefore, (lHi) and (lHi+1) are connected by joint (jHi), where i ∈ ;qH ∈ Rk, k = ∑i=0gN(jHi), contains the set of independent coordinates that defines a configuration of H uniquely:the vector qH = {vH0,…, vHi,…, vHg};ith element of qH, θi, is subject to hi(θi) = θimin ≤ θi ≤ θimax  ;the qHt represents the state of qH in instant t and its real value is unknown;M = {m0,…, mp} that connect R and H:a set of passive mechanisms mi   connects lRa   and lHb  ;mi imposes a movement constraint of N(mi)-DOF to lHb with respect to lRa;C(M) = {c0,…, cp} contains vector-valued functions ci ∈ RN(mi)   that model the kinematic constraint imposed by mi;the set ci is an equality constraint of the form ci = 0;each D = {d0,…, ds} that intend to represent the performance measures that govern the posture of the limb in a specific situation:a set of vector-valued constraint functions (a) di(qHt)  is an equality constraint of the form di(qHt) = 0;each (b) di vector is denoted by dim(di).the dimension of the Goal is as follows(1) to qHt such thatfind the vector ci = 0  ∀ i ∈ ;hj(θj) = θjmin ≤ θj ≤ θjmax  ∀ j ∈ ;du(qHt) = 0  ∀ u ∈ .To solve this problem, a method based on IK of the limb has been developed. The following sections describe the methodology implemented.The Armeo Spring  is a pasWe built a kinematic model of the Armeo Spring , which cOur implementation models the links and joints of the Armeo exoskeleton and creates a hierarchical structure of them.Although the Armeo exoskeleton presents a parallelogram mechanism in its kinematic chain, the exoskeleton can be modeled with a serial chain extended with a dependency equation among the joints used to represent the parallel mechanism.Our upper body model (33-DOF) includes joints of the spine, shoulder complex, elbow, and wrist. It is based on the ones presented in , 39, 48,Although there are more complex and accurate kinematic models of the upper body, the results obtained in , in a scThe neutral or rest posture of the arm is defined with the arm fully extended along the body as in . The ranThe Armeo provides fixations for the human limb. These fixations introduce constraints on the position and orientation of the coordinate systems attached to the arm, forearm, and hand.There are several factors that affect the satisfaction of the constraints during the execution of the exercises. This set includes (1) deformation of the coupling mechanisms and (2) uncertainty or errors in the modeling of the human upper limb. Therefore, these constraints are exactly met only under ideal conditions and in practice they do not capture all the details of the real interaction. However, as we prove, they suffice to obtain a reasonable accuracy in the estimation of the limb posture.R and H kinematic chains (see The arm fixation imposes a position (3-DOF) constraint on the human arm. The point on the arm that follows the position of the fixation is determined by an initialization process between the ains see .In our model, the fixations are modeled as rigid bodies. However, the exoskeleton fixations are made of flexible materials, such that their geometry is deformed when large forces are applied on them.The arm fixation suffers significant deformation when the arm is moved towards a horizontal configuration . In those cases, the coordinate system at the exoskeleton arm fixation center undergoes a translation, resulting from the deformation of the fixation mechanism that is not reproduced by our model.To deal with this kind of situations, the weights of constraints representing fixations that suffer less deformation than other ones are adjusted such that they receive more importance when solving the IK problem. In this way, the limb posture is estimated meeting the constraints that model with more fidelity the observed behavior. In this case, the weight of the arm constraint is lower than the ones belonging to the forearm and arm restrictions.The forearm fixation imposes a 3-DOF position constraint on the human forearm. The point on the human forearm that moves together with the fixation is determined in the initializing stage. Additionally, the fixation is able to rotate around its longitudinal axis, according to the forearm pronation/supination movement (1-DOF orientation constraint). The rotation angle is measured with an encoder. The forearm constraint forces the human wrist flexion/extension axis to be approximately aligned with the exoskeleton's wrist joint axis.The hand constraint forces the human hand to follow the position and orientation (6-DOF) of the Armeo hand grip. The patient exercises while grabbing the handle of the exoskeleton. The mechanic design of the Armeo avoids the slippage of the hand with respect to the axis of the handle during the execution of the exercises. As with the previous fixations, the point on the hand where the coordinate system of the hand is located is calculated in the initialization stage.The shoulder constraint does not belong to the set of movement restrictions imposed by the coupling mechanisms of the Armeo. Instead, it is related to the restrictions intended to produce a natural posture of the upper limb considering also the influence of the exoskeleton on the patient movements. This constraint helps to choose one of the multiple configurations of the human kinematic chain that comply with the other categories of constraints.jR0 joint represented with symbol A in jR0 comfortable postures for the spine and arm can be achieved.Currently, it is implemented to attract the GH joint to a position (3-DOF position constraint) below the first joint of the Armeo , such that the difference e = Tr − Xr between Tr and the actual pose of the end-effector of r, Xr ∈ R6, approaches zero.Given a desired pose (position and orientation) vector Z(qr), which linearly relates the velocity of the end-effector and the joints byThere are several approaches to solve this problem, including analytic  and numeXr for e in  may not be square  or invertible. In those cases, the pseudoinverse and damped least squares (DLS) methods (among others) can be used to obtain Δqr, such that ||e|| is minimized. The pseudoinverse method is computationally faster than the DLS but tends to be unstable when the robot approaches a singular configuration. The DLS method offers more robustness  at the cost of a slower convergence . Otherwise, ei represents a restriction related to the natural posture of the limb, and therefore ei ∈ Rdi)dim are not reachable. It is important that the method used to solve the IK problem handles this situation robustly, avoiding oscillations. For this reason the DLS method was used.Notice that, due to modeling inaccuracies of the kinematic chains or the constraints, it is possible that for a configuration References , 39 statwJi is the weight of joint JHi and that joints Jc and Jd can contribute to the movement of end-effector i to diminish ei. Then, if wJc > wJd, the displacement that Jc performs is larger than the one done by Jd. This means that Jc is preferred to be moved over Jd to reach a desired target.Let us assume that In our model, the weights of the joints of the upper body were adjusted such that the joints on the spine of the model perform small displacements in comparison with the movement performed by the shoulder, elbow, and wrist joints.e gives more importance to reach a specific target over others. In our approach, this translates into giving some constraints more importance than others. Let us define with wci   the weight of the ci constraint and with wdu   the weight of du constraint.On the other hand, applying weights to the error vector wci ≈ 1.0). Otherwise, low weights (wdi ≈ 0.2) were assigned to the other type of constraints.In our model, high weights were adjusted for the kinematic constraints imposed by the exoskeleton fixations (qHtw = Zw*ew and Zw* = Zwt(ZwZwt + αI)−1. The weighted Jacobian matrix is given by Wq = diag{w0,…, wk−1}. Here, if wa and wb are related to JHi , wa = wb = wJi. The weighted error vector is given by ew = Wee, where We = diag{w0,…, wv−1} and v = ∑i=0pN(mi) + ∑j=0sdim(dj). If wa and wb are related to the same ci constraint, wa = wb = wci. This also applies for weights related to constraints du. However, independent weights can be assigned for the position and orientation components of a constraint.There are different formulations of the DLS method that incorporate weights for the joints and error vector . In V-RTo accurately estimate the limb posture, it is required to properly couple the human and exoskeleton kinematic models. To do so, we require to correctly position the end-effectors of the human kinematic model with respect to the arm, forearm, and hand coordinate systems. These end-effectors must be positioned such that they are able to move together with the coordinate systems of the fixations of the exoskeleton model (targets). Notice that the position of the end-effectors with respect to the links of the human model changes according to the actual patient and exoskeleton dimensions.The initialization of the kinematic chains requires a reference pose of the exoskeleton in which (a) the human joints angles can be determined accurately and (b) the exoskeleton's fixations undergo negligible deformation, reducing the uncertainty about the position of the human model end-effectors.The pose of the exoskeleton that meets the mentioned requirements is the one in which the flexion/extension of the shoulder and elbow take place in the sagittal plane . In thisjR0 lies above the human GH joint. Adjust the height of the exoskeleton model such that jR2 is at the level of the human GH joint. These instructions are prescribed by the manufacturer of exoskeleton to use it with the actual patient.Position the exoskeleton model such that the joint Compute the arm flexion and abduction angles such that the arm passes through the origin of the arm fixation coordinate system. Adjust the origin of the arm end-effector coordinate system to match the origin of the arm fixation.With the position of the elbow joint defined, compute the elbow flexion and the GH internal rotation angles such that the forearm passes through the origin of the exoskeleton forearm fixation. Adjust the origin of the forearm end-effector coordinate system to match the origin of the forearm fixation.Compute the wrist extension angle such that the human hand is able to grasp the exoskeleton's hand grip. Adjust the hand end-effector to match the position of the Armeo's end-effector at the hand grip.Calculate the forearm pronation/supination angle such that the wrist's extension/flexion axis matches the orientation of the Armeo's hand grip longitudinal axis with respect to the human forearm pronation/supination axis.Adjust the human forearm and hand end-effector coordinate systems to match the orientation of the forearm and Armeo's end-effector coordinate systems, respectively.The coupling process involves the following steps.The result of the initialization process is depicted in To implement the proposed method the virtual robot experimentation platform (V-REP) was used , which iThe source code of the simulator was compiled, modified, and integrated into our rehabilitation platform. Custom classes and functions were programmed to allow easy data exchange among the Armeo, the rehabilitation game platform, and the IK module of the simulator.Obtain the angles of the Armeo's joints by using hardware and software interfaces provided by HOCOMA AG .Use the obtained angles to update the joints angles of the Armeo's kinematic model in the simulator.Retrieve the angles of the joints of the human model computed by the simulator's IK module.The limb posture estimation process consists of the following steps.Computing the inverse kinematics of our upper limb kinematic model, once the Armeo model is updated in the simulator with the real joint measurements of the exoskeleton, takes less than 4 ms on a 2.13 Ghz dual-core CPU. Therefore, the implemented method is suitable for real-time posture estimation without using high-performance hardware.After the joint estimates are produced, we use them to update the patient avatar in VR games. We also store them in a database for a posterior patient assessment.reaching exercises, in which the subject recreated the postures of his arm to reach and grab objects that are close to his body . These eextreme region exercises, in which the subject positioned his hand in the boundaries of his arm workspace . These eCurrently, we have implemented two types of games for the robotic-assisted upper limb rehabilitation therapy. The first type of games focuses on the rehabilitation of reaching movements. The second type of games addresses the rehabilitation of analytic movements of the GH, elbow, and wrist joints.Reaching rehabilitation is performed by training the movements that are required to reach and grasp objects with the hand. These exercises involve several joints of the upper limb, and, therefore, they are considered complex.To train these exercises, we have programmed a game in which the patient controls the movement of a virtual human arm by moving his own arm . The tarAccording to motor learning theories, the training of analytic movements constitutes the first step into learning complex motor tasks. In such a step, simple movements involving few DOFs of the limb are practiced –58.For this scenario, we have programmed a game  in whichFor both games, the limitations of the mobility of the patient are identified in a calibration phase, guarantying that the target of the games is properly located. Other game parameters  are adjusted through the medical interface . The medThe VR games were programed with the OpenSceneGraph API , which aDuring the therapy, the patient sees the VR scene. The kinematic models are used for IK computations and they are not displayed.In order to determine the accuracy of our developed method, the joint angles of 4 voluntary healthy male test subjects (average age 34 years) were measured by using an optical tracking system and compared with the angles obtained from our posture estimation algorithm during the execution of typical  robotic-assisted rehabilitation exercises. As discussed in wrist flexion/extension (WFE),elbow flexion/extension (EFE),forearm pronation/supination (FPS),simultaneous elbow flexion/extension and forearm pronation/supination (SEFEFPS).The specific exercises performed by the test subjects wereThe evaluation of our method has been conducted without performing any previous setting or automatic adjustment of the weights or other parameters of the approach in order to reduce the estimation errors. However, algorithm training might be used in the future to improve the method's performance.A detailed explanation of the method that was used to measure the human joint angles would merit an additional manuscript. Nevertheless, a basic description of this method is provided next.In order to measure the limb joint angles of the test subject, we use a Polaris Spectra optical tracking system (OTS) . In ordeOne rigid body (reference rigid body) is used as the coordinate system of reference for the measurements of the OTS. The position and orientation of the other rigid bodies (mobile rigid bodies) are computed with respect to the reference rigid body.The reference and mobile rigid bodies are installed on different arm segments  according to the joint angle to be measured. Compute a reference coordinate system for the joint of interest. A subset of the axes of the resulting coordinate system match the axes of rotation of the joint. The position and orientation of the joint coordinate system are defined with respect to the reference rigid body.Compute the orientation of the mobile rigid body with respect to the joint coordinate system.Compute the joint angles that result from rotations of the mobile rigid body by using Euler-angles decomposition. The rotations of the mobile rigid body are caused by the exercising of the subject joint.In order to measure the human joint angles, we have adapted the method presented in , which iTo build an orthogonal right-handed coordinate system of reference for the joint, we identify each axis of rotation of the joint, as proposed in .To identify each rotation axis of the joint, we use the instant helical axis method described in . A rotatIn contrast to the proposal presented in  to compuAccuracy of the Limb Joint Angles Measurement Method. In motor rehabilitation, goniometry is the standard method to measure the angle at the patient joints. This is a manual method, and, therefore, its efficacy depends on the examiner experience [perience . One of perience . In otheAlternative approaches to measure the patient limb joint angles are IMMS-based methods. One of the methods that provide better accuracy than goniometry is presented in . This meIn tests with an artificial 1-DOF joint, the method to measure the limb joint angles that we have adapted from  allowed Compute the joint coordinate system corresponding to the evaluation exercise .Instruct the subject to perform the corresponding evaluation exercise until the number of desired joint angle measurements is taken.Compute the RMSE in the estimation of each joint angle by comparing the measured angle with the estimation provided by our algorithm.Compute the ROM of the subject movements from the measured angles.For each trial of the evaluation exercises we performed the following steps.During the execution of the evaluation exercises the amplitude, speed and the number of cycles of the movements in each trial were left to the discretion of each test subject. In the evaluation, the VR games were not executed, given that they are not necessary to assess the accuracy of the posture estimation algorithm. Furthermore, in this way the influence of the VR games on the subject movement amplitude, speed, and repetitions is avoided, which derives a richer variety of movement features in the evaluation exercises.However, it is worth mentioning that the joint limits of the exoskeleton, the need to avoid occlusions of the passive markers on the rigid bodies attached to the test subject, and the limited detection volume of the OTS do constrain the subject's movements.In this section, we present the results of the experiments described in N.B.: in this section we compare our results against freely moving subject cases reported in the literature. We resort to such free movement cases since we found no reports concerning estimations errors of the wrist or elbow angles in limbs constrained with exoskeletons.To elaborate this point, we present in These results suggest that the response speed of our algorithm, given a change in the Armeo joint angles caused by the movement of the human subject, allows providing better estimates when the subject moves slowly (as in rehabilitation therapy). In our algorithm, the response speed largely depends on the damping constant used in the DLS method to solve the limb's IK. By using a smaller damping constant in the DLS method, the response speed can be improved, sacrificing some stability.Nevertheless, the average RMSE obtained for all subjects shows a better performance of our method with respect to , an optiIn flexion and extension of elbow , Table 6For all subjects, our method overestimates the amplitude of rotational movements about the flexion/extension axis, when compared against the measured values  provide an estimation of the pose of the human upper limb with enough accuracy to be used for avatar animation in VR games and (b) obtain the kinematic data for the patient assessment during analytic training of the elbow and wrist.Future work includes (a) the exploration of other approaches to model the flexible fixations of the exoskeleton, (b) the definition of a set of weights for the human model joints that represent the movement features of a set of human subjects, and (c) a quantitative assessment of the performance of our method in a functional rehabilitation scenario.


Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets , focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations. Hearth contractions are regarded by many scientists as the foremost example of a physiological system showing predominantly nonlinear behavior, mainly generated through integration of multiple neural signaling at the level of the sinoatrial node Among all nonlinearity and complexity measures, Lyapunov exponents (LEs) have been proven to provide an important mathematical tool in characterizing dynamical properties of a nonlinear system Relying on the approach suggested by Chon et al. In this work, the IG mean is modeled as a third-order nonlinear function of the past RR intervals. In order to perform an effective parameter estimation and retain all the historical information of events, the cubic NAR kernels of the Wiener-Volterra series are expanded using the Laguerre bases A random point process is a stochastic process whose elements are point patterns specified as a locally finite counting measure The general Nonlinear Autoregressive (NAR) formulation can be written as: Due to the autoregressive structure of eq. 3, the system can be identified with only exact knowledge of the output data and with only few assumptions on the input data. In practice, this series will obviously be truncated at some small, finite value. Here, we represent the nonlinear cardiovascular system by taking into account up to the cubic nonlinear terms, i.e. An important practical limitation in modeling high-order nonlinearities using the model in eq. 4 is the high number of parameters needed to sufficiently fit the observed data. An advocated approach to solve such a limitation has been proposed by using the Laguerre functions The computation of the Laguerre Filter output can be simplified by using the following recursive relation Since the Here The coefficients Moreover, as A local maximum likelihood method It is known from point process theory The estimated CIF is used to evaluate the goodness-of-fit of the proposed heartbeat interval point process probability model, which is based on the KS test The Lyapunov Exponent (LE) of a real valued function More generally, let us consider an In our case, the matrix Using the Einstein notation, we obtain: Therefore, the elements of the Jacobian can be computed as follows: Considering The matrix In order to perform a comparison analysis with standard and nonlinear estimates of heartbeat dynamics, we also calculated the standard mean of the RR intervals (Mean RR), the root mean square of successive differences of intervals (RMSSD) and the number of successive differences of intervals which differ by more than 50 ms  Before reporting the implementation of the synthetic datasets, it is important to clarify some important differences from standard definitions that are introduced by our methodology. In fact, standard nonlinear systems such as the Hénon Map and Rössler Attractor are intrinsically defined in the continuos time domain, whereas our methodology deals with stochastic point processes which are a sequence of events. Moreover, additive noise terms have to be considered as well. Therefore, starting from the canonical equations of each nonlinear system, we slightly modify the system equations by adding a noise term. Then, the output of the system is taken as an input of an integrate-and-fire system. The output of such an integrate-and-fire system constitutes the series modeled by the proposed cubic NARL model within the point-process framework.In order to test the efficiency of the proposed cubic NARL model in tracking the complexity of a synthetic stochastic series through the IDLE index, we simulated a modified version of the well-known chaotic Hénon Map as suggested in The time series As a further validation, we simulated a modified version of the well-known chaotic Rössler time series  and upright sessions alternated six times with three possible modality of transition: active stand-up, slow and fast passive tilt. A single-lead ECG was continuously recorded for each subject during the study, and the RR intervals were extracted using a curve length-based QRS detection algorithm http://www.physionet.org/) The second heartbeat dataset was constituted from data gathered from Congestive Heart Failure (CHF) and reference healthy subjects on a public source: Physionet (We performed the IDLE estimation by fitting the NARL model on Considering the noise level *10−4) only for the proposed Considering the noise level We performed the IDLE estimation by fitting the NARL model on the Before estimating the IDLE from the experimental datasets, we first considered a specific time-domain method Using this dataset, we further evaluate the effect of the Laguerre parameter Finally, we report further results on the nonlinearity test separately performed for each of the experimental session, instead of the whole recordings see . As a reThe results of the second experimental dataset (on CHF) are shown in We presented a novel methodology able to instantaneously characterize the complex nonlinear dynamics of a stochastic series of events by using the LEs. The proposed approach relies on the previous literature for the LEs mathematical definition The effective procedure for the time-varying parameter identification is ensured by the combined use of the discrete-time Laguerre expansions for the Wiener-Volterra terms and local maximum likelihood method. In particular, expanding the Volterra terms with the orthonormal Laguerre bases requires a reduced number of parameters to retain the information of all the past events. The nonlinear regression is further performed on the derivative series to better account for nonstationarity complexity variability, i.e., the analysis of complex systems referring to the fluctuations in complexity instead of analysis of central tendency. Within the proposed framework, it is always possible to incorporate physiological covariates (such as respiration or blood pressure measures) and produce further instantaneous indices from their dynamic cross spectrum and cross bispectrum Importantly, the proposed measures also allows for the study of the The novel IDLE index was evaluated in both synthetic and experimental heartbeat series. Estimations on the synthetic dataset were performed on a stochastic version of the well-known chaotic Hénon Map and Rössler attractor. The use of such a modified version of the Hénon Map and Rössler system alongside the obtained IDLE results need to be discussed. We are aware that in purely deterministic Rössler equations the first LE should be zero in the non-chaotic region, whereas it should be increasingly positive in the chaotic region. However, the IDLE results show slightly negative values in the non-chaotic region. Such a behavior may be ascribed to the stochastic input and to the additional integrate-and-fire step which affect the estimation of all complexity measures, including LEs. To this extent, in order to further investigate the effect of noise, results from the Hénon Map equations were gathered as a function of the noise level. We demonstrate that, for small amount of noise  suggest that loss of instantaneous heartbeat complexity as a function of velocity of the postural changes is reasonably due to changes in the nonlinearity of the cardiovascular system . Of note, we have previously reported that the standard HRV indices defined in the time and frequency domain are unable to distinguish the three possible modality of transition through different p-values Moreover, the novel complexity features {Concerning other preliminary applications, the proposed IDLE methodology has been revealed as a powerful tool also in tracking the instantaneous complexity during loss of consciousness induced by anesthetic drugs


In terms of making genes expression data more interpretable and comprehensible, there exists a significant superiority on sparse methods. Many sparse methods, such as penalized matrix decomposition (PMD) and sparse principal component analysis (SPCA), have been applied to extract plants core genes. Supervised algorithms, especially the support vector machine-recursive feature elimination (SVM-RFE) method, always have good performance in gene selection. In this paper, we draw into class information via the total scatter matrix and put forward a class-information-based penalized matrix decomposition (CIPMD) method to improve the gene identification performance of PMD-based method. Firstly, the total scatter matrix is obtained based on different samples of the gene expression data. Secondly, a new data matrix is constructed by decomposing the total scatter matrix. Thirdly, the new data matrix is decomposed by PMD to obtain the sparse eigensamples. Finally, the core genes are identified according to the nonzero entries in eigensamples. The results on simulation data show that CIPMD method can reach higher identification accuracies than the conventional gene identification methods. Moreover, the results on real gene expression data demonstrate that CIPMD method can identify more core genes closely related to the abiotic stresses than the other methods. The changing environmental conditions have a significant impact on the survival and growth of plants. A series of various abiotic stresses can bring about the overproduction of reactive oxygen species in plants, which may damage carbohydrates, proteins, lipids and DNA resulting in oxidative stress With the development of science and technology, the emergence of gene microarray technology Among a variety of methods, feature selection is demonstrated to be a simple and effective method. To obtain the features of gene expression data, feature selection methods firstly calculate a score for each feature, then choose the features which gain high scores Although SVD and PCA have already been used to analyze the gene expression data successfully, they still have some defects. For instance, SVD's left singular vectors and right singular vectors are always dense. In the same way, this drawback exists in the principal components (PCs) of PCA. Thus, it is difficult to explain these singular vectors and PCs objectively. Researchers have proposed a variety of mathematical methods to reduce the complexity of the data and make them more intelligible and interpretable. For example Liu et al. proposed robust PCA for discovering differentially expressed genes The sparse methods mentioned above were proverbially applied on gene expression data analysis and have made many remarkable achievements. But these methods are usually unsupervised while the category label of each sample in gene expression data has been already known. That is, the class information is neglected by these sparse methods when processing gene expression data. For example PMD was used to extract plants core genes by Liu et al. Therefore, we bring in the class information by the total scatter matrix and put forward a novel method to improve the performance of PMD-based gene extraction method for identifying plants core genes responding to abiotic stresses. We called it a Class-Information-based Penalized Matrix Decomposition (CIPMD). The scheme of CIPMD is as follows. Firstly, the total scatter matrix is obtained based on samples of the gene expression data. Secondly, we decompose the total scatter matrix by using SVD, and construct a new data matrix via multiplying the left singular vectors by the singular values. Thirdly, the new data matrix is decomposed to get the sparse eigensamples by PMD. Finally, the core genes are identified according to the nonzero entries in eigensamples.Our main contributions of this paper are as follows. On one hand, it is the first time that it puts forward the CIPMD method via integrating the class information into penalized matrix decomposition. On the other hand, to identify plants core genes responding to abiotic stresses, it provides plenty of experiments on simulation and real gene expression data.The remainder of the paper is organized as follows. Section 2 describes the methodology of CIPMD. Section 3 presents the numerical experiments and discusses the results. The conclusion is shown in Section 4.In this section, the class-information-based penalized matrix decomposition (CIPMD) method is introduced. Then, it is used to identify the core genes responding to the abiotic stresses.In this subsection, we take the class information of samples into account and propose the CIPMD method to gain a better performance than PMD. At first, we bring in the class information via the total scatter matrix There exist many samples which contain different class labels in gene expression data. We take advantage of the class labels of samples via the total scatter matrix. For all the samples of all classes, we define three measures from the mathematical point of view. The first measure is named as a between-class scatter matrix  (b) Step3. In order to obtain the rank-The gene expression data are stocked as the matrix According to subsection 2.1.3, the matrix Our goal is to identify the core genes from the gene expression data. Generally speaking, due to the complexity of Firstly, the number of variables used to denote the sample expression profiles can be reduced by CIPMD. According to eq.(9), Secondly, since the eigensamples Thirdly, the sparse Finally, the core genes responding to abiotic stresses are identified via the sparse The whole scheme to identify the core genes can be summarized in the following:Firstly, the total scatter matrix Secondly, Thirdly, PMD decomposes the data matrix Fourthly, the genes corresponding to nonzero entries in Finally, the core genes are checked by using Gene Ontology (GO) tool.In this section, we evaluate the CIPMD method by applying it to identify the core genes responding to abiotic stresses. Subsection 3.1 and 3.2 provide the results on simulation and real gene expression data sets, respectively. For comparison, the sparse principal component analysis (SPCA) In this subsection, the simulation data are firstly introduced. Then, the parameters of SPCA, PMD and CIPMD are chosen appropriately. Since SVM-RFE method eliminate genes one by one by using Recursive Feature Elimination (RFE) and have no control-sparsity parameters, so we do not consider it in this subsection. Finally, the results on simulation data are shown.The simulation data are generated with The simulation data are in In this subsection, the parameter The determination of parameter : For CIPMD, we need to determine the appropriate parameter The selection of control-sparsity parameters: Except for SVM-RFE, all the other three methods are sparse, whose control-sparsity parameters have a great influence on identification accuracy. The SPCA proposed by Journee et al. has an excellent performance both in computational speed and quality For fair comparison, 500 genes are identified by using these methods with their own appropriate parameters. And the Signal-to-Noise Ratio (SNR) is set to be 0.1 when the simulation data are generated.We randomly generate the simulation data by iterating 100 times to evaluate the performances of the four methods. The specific numerical values of identification accuracies of the four methods with different parameters are shown in supplementary file . For theFor the multi-class case, the graphical depiction of the identification accuracies of these methods with different parameters is shown in The real gene expression data are introduced in subsection 3.2.1. Then, the gene ontology (GO) analysis is adopted to evaluate the performances of the four methods.http://affy.arabidopsis.info/] The raw gene expression data include two classes: shoots and roots in each stress. The Affymetix CEL files are downloaded from NASCArrays [Our method brings in the class information of samples based on the total scatter matrix. Therefore, in our experiments, two stress types of gene expression data are processed simultaneously.http://go.princeton.edu/cgi-bin/GOTermFinderGene Ontology (GO) Term Enrichment tools can be used to describe genes in the input or query set and to help discover what functions the genes may have in common Terms responding to stimulus: The numbers of genes responding to stimulus (GO:0050896), which is the ancestor of all the abiotic stresses, are identified by the four methods in shoot and root samples are listed in As The sample frequencies of the six different stresses response to stimulus in shoot and root samples are shown in From PMD outperforms the proposed method in some case of the experiment, e.g. the UV-B light stress data set in shoot samples and the salt stress data set in root samples, the most likely reason is that the different distributions of data lead to the different performances between methods. This problem also exists in elsewhere, for example Zheng et al. proposed a gene selection method based on Robust Principal Component Analysis (RPCA) to select plants characteristic genes, in their experiments, the number of genes responding to abiotic stimulus (GO:0009628) is selected by three methods in root samples, the performance of RPCA is equal to PMD only in UV-B stress data set, in other data sets, RPCA method is superior to the others Terms responding to stress:As The sample frequencies of response to stress in shoot and root samples are shown in Core genes responding to the stresses: The data of the drought stress in root samples and heat stress in shoot samples are analyzed to evaluate the core genes identified by our method closely related to the stresses.For drought stress in root samples, Response to represents what stresses the genes response to, and the column of Reference denotes the searching results that the authors have already confirmed in their literatures. As Moreover, we compare the genes identified by CIPMD with the ones identified by PMD, SPCA and SVM-RFE to verify the core genes extracted by our method closely related to abiotic stresses. For heat stress in shoot samples, In detail, we compare the genes identified by CIPMD with the ones identified by using PMD, SPCA and SVM-RFE. There are 20 different core genes identified by our method and neglected by PMD, SPCA and SVM-RFE. Among these 20 genes, 14 genes responding to heat have been confirmed in literatures. We show the verified results of the 14 genes in In this study, we proposed a novel Class-Information-based Penalized Matrix Decomposition method for identifying core genes. Our method can achieve a better identification capacity by bringing in the class information of samples based on the total scatter matrix. By integrating matrix decomposition and the PMD method, our method is appropriate to analyze the gene expression data. A large number of experiments on simulation and real gene expression data demonstrate that our CIPMD method outperforms both PMD, SPCA and SVM-RFE. Thus, our approach is effective to identify plants core genes responding to abiotic stresses.In the future, we will focus on the biological interpretation of the core genes.Table S1The identification accuracies of the four methods with different parameters.(XLSX)Click here for additional data file.


As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system. Development of new smart materials like piezoelectric, magnetostrictive and shape memory alloy (SMA) made it possible to produce micro motion and force, and magnetic shape memory alloy (MSMA) is also a new type of material which possesses advantages of smart materials such as fast response frequency, outstanding strain and stress capability Many researchers have proposed a number of control strategies to eliminate the negative effects of hysteresis nonlinearity. Tao G et al. proposed a parameterized hysteresis model, developed a hysteresis inverse, and designed adaptive controllers based on an adaptive inverse model, which improved system performance using a robust adaptive law to update the controller parameters and hysteresis inverse parameters We established a feedforward control to eliminate the negative effects of hysteresis nonlinearity. To achieve feedforward control of MSMA actuators, we used a hysteresis inverse model based on a Krasnosel'skii-Pokrovskii (KP) hysteresis model as a feedforward controller. To further improve the control precision and the performance of the adaptive system, we adopted a hybrid control scheme that respectively combines classical PID feedback control and self-tuning PID feedback control based on the Radial Basis Function (RBF) neural network, and implements high precision control of the output displacement of the MSMA actuator. Simulation results demonstrated the validity of the proposed approach.KP operator and discretization of the KP model. For practical application of the actuator, the hysteresis loop curve of the actuator input-output relationship includes a major loop and a minor loop, and in this paper we establish a hysteresis non-linear model based on the KP model to provide an accurate description of the hysteresis loops in the MSMA actuator. The elementary hysteresis operator selected here is the KP operator (operator  [26], [2where where ers  see  gives thwhere To obtain the appropriate density parameter, this paper employs the variable step-size recursive least-squares method, which reduces the amount of calculations by merging some repetitive operations in the traditional recursive least-squares algorithm Suppose that the algorithm of the recursive weighted least squares is as follows:where The step-size To linearize the entire system, we established an inverse model as the feedforward controller for the MSMA actuator where where The flowchart of the modified solution method of the inverse KP model is given in The previously proposed control scheme makes the inverse KP model a feedforward controller. To further improve the control accuracy and anti-disturbance performance, a hybrid control scheme is proposed by combining feedforward control and feedback control.In this section, a control method is adopted by combining the inverse KP model feedforward controller with a feedback controller using the classical PID control method. The relationship between the output where In this section, classical PID control is exchanged for the RBF neural network self-tuning PID control The RBF neural network is a three-layer forward neural network with a single hidden layer. The structure of the RBF neural network adopted in this paper is illustrated in where the Gaussian basis function where The weight from the input layer to the hidden layer is taken as constant 1 and the weight vector from hidden layer to output layer is taken as The learning performance function of the RBF neural network is chosen as:The gradient descent method is selected as the learning algorithm in the neural network.The PID controller applied in this paper is an incremental PID controller and the control error is the difference between the input and output which is expressed as:The tuning index of the tuning algorithm is defined as:The parameters of proportion, integral and differential in the PID controller are where To sum up, the output of the PID controller can be expressed as:The KP model can be used to describe the hysteresis minor loop and demonstrate the complex input-output relationship. The relationship between the input and output for the MSMA actuators is shown in To verify the validity of the inverse KP model proposed in this paper, the number of discretization lines In this feedforward control experiment, when we make the desired displacement an input signal, in an ideal situation, the input-output relationship should be linear. The feedforward controller designed in this paper compensates for the hysteresis nonlinearity so that the input-output relationship can transform a complex uncontrollable hysteresis loop to a simple controllable linear relationship. Based on a large number of experiments and parameter adjustments, the differential coefficient To verify the effectiveness of the hybrid control scheme based on the RBF neural network self-tuning PID, we performed a simulation experiment. In this experiment, the parameters of the PID controller were set to This paper presents a hybrid control strategy for an MSMA actuator that utilizes the inverse KP model as a feedforward controller with PID feedback control. The proposed hybrid control strategy is applicable for all the type of MSMA actuator whose output displacement is continuous. We identified the density parameters in the KP model using a variable step-size recursive least-squares estimation algorithm. Based on the KP model, an inverse KP model was established by employing the modified explicit solution method, and the inverse model served as a feedforward controller to implement open-loop control for the MSMA actuator. To further improve the control accuracy, we combined PID feedback control and a feedforward control system, and then replaced the classical PID controller with a self-tuning PID controller based on the RBF neural network. The Jacobian information of the controlled object was obtained from the RBF neural network to adjust the PID parameters in real-time, enhancing the adaptive performance of the system. The simulation experiment results illustrated that the inverse model established in this paper possessed good predictive accuracy with a maximum prediction error of 2.09%. In addition, the entire feedforward control system could track the control signal well and the maximum tracking error was only 1.1%, while, when combined with the classical PID control, the maximum tracking error was reduced to 0.61%. Finally, the maximum tracking error decreased to 0.43% when the classical PID control was replaced by the self-tuning PID controller based on the RBF neural network. Therefore, the simulation experiment verified the validity of the hybrid control strategy.