Cells constantly sense many internal and environmental signals and respond through their complex signaling network, leading to particular biological outcomes. However, a systematic characterization and optimization of multi-signal responses remains a pressing challenge to traditional experimental approaches due to the arising complexity associated with the increasing number of signals and their intensities.We established and validated a data-driven mathematical approach to systematically characterize signal-response relationships. Our results demonstrate how mathematical learning algorithms can enable systematic characterization of multi-signal induced biological activities. The proposed approach enables identification of input combinations that can result in desired biological responses. In retrospect, the results show that, unlike a single drug, a properly chosen combination of drugs can lead to a significant difference in the responses of different cell types, increasing the differential targeting of certain combinations. The successful validation of identified combinations demonstrates the power of this approach. Moreover, the approach enables examining the efficacy of all lower order mixtures of the tested signals. The approach also enables identification of system-level signaling interactions between the applied signals. Many of the signaling interactions identified were consistent with the literature, and other unknown interactions emerged.This approach can facilitate development of systems biology and optimal drug combination therapies for cancer and other diseases and for understanding key interactions within the cellular network upon treatment with multiple signals. Understanding how multiple signals affect cellular functions is necessary in order to be able to understand and control these functions. Extensive studies have been done to address how the activation/inhibition of a particular cellular signaling pathway leads to a specific response. Several challenges limit the ability to study the simultaneous effects of multiple signaling. The complexity and lack of detailed knowledge of cellular systems prevent, in many cases, accounting for the effects of some unknown interactions among pathways or among non-primary signal targets. In addition, genetic or epigenetic alterations between otherwise similar cells can cause a significant difference in their responses. This places additional constraints on the experimental outcomes obtained by analyzing individual components. Furthermore, a critical challenge in the investigation of the effects of multiple signals is the arising complexity associated with the increasing number of signals and their various intensities. Without a systematic approach to replace a large number of time and resource consuming experimental tests, it is difficult to characterize the effects of these signals, to identify appropriate signal combinations.There has been an increasing interest in examining how various biological activities are regulated by multiple interacting signals -4. BerenOther recent work on identifying drug combination focuses on identifying mixtures of drugs where the the search space is reduced to use only a single concentration while the search space is increased by searching through a larger number of potential drugs ,13. The in silico experiments, the model enables analyzing the response of the system to various combinations and determining or selecting subsets of signal combinations that can yield desired cellular responses. The determination of these subsets can be achieved using tools such as stochastic search algorithms and cluster analysis. The proposed approach will facilitate the understanding of fundamental cellular responses, which are system responses reflecting the activity of a complex signaling network controlled by multiple internal and external signals. This approach can promote efficient understanding of cellular functions without intermediates. In addition, the approach allows multiple cell types or other biological systems to be quantitatively characterized, modeled, and compared in parallel. The maximal difference or similarity can be identified using a computational search. It can facilitate the development of drug combination therapies for various types of cancers . The trained models can predict the responses to all 512 combinations with high fidelity. The correlation coefficients between the predicted normalized ATP levels and their corresponding experimentally measured values are higher than R = 0.91 Figure . LookingExperimental testing of all possible combinations can be a costly process. Whenever the response of the biological system is smooth enough, we can utilize a smaller number of combinations to map the entire response surface. In this regard, we have examined the effects of using varying numbers of points to fit the models on the accuracy of prediction. The four methods discussed above were considered and models using 10, 20, 40, 80, 160, and 320 points were fitted. To mimic an actual experimental setup, the points were randomly selected out of the 512 possible combinations using a uniform distribution. The mean square error of prediction for each of the methods and fitting data for both cell types indicate that increasing the number of points reduces the mean square error . Models representing the relationship between the four drugs and the ATP-levels of A549 and AG02603 cells were generated based on 148 experimentally tested combinations. We fitted a single-layer neural network with four neurons using the experimental data. The correlation coefficients between the predicted data from this model and the experimental data were 0.98 for A549 and 0.97 for AG02603 . The drug combinations resulting in the highest performance are considered the best drug combinations of a given set of drugs with corresponding concentrations.Identification of the best performing subset is achievable through various methods. Enumeration and sorting of all possible combinations and their corresponding performances is one method. Alternatively, we can use a clustering algorithm such as a k-means clustering algorithm to group combinations with similar performances ,21.Clustering the points into 20 different groups Figure , we findAdditionally, we investigated the effects of pairwise combinations of drugs on the responses of both A549 and AG02603 cells. The remaining two drugs were fixed at one of two cases, zero or a selected optimal concentration , , and  showed that the experimental ATP levels of A549 and AG02603 were 0.2 and 0.65, 0.13 and 0.51, and 0.13 and 0.5 respectively. This is in agreement with the predicted values for A549 and AG02603 of 0.21 and 0.59, 0.08 and 0.51, and 0.2 and 0.58 respectively.X can be achieved using principal components analysis. Partial least squares can also be used and in this case the reduction in the regressors matrix takes into account variation in the output. However, the components obtained with principal component analysis or partial least squares models would be hard to interpret given the large number of regressors. Instead, we pursue a subset selection algorithm based on all the possible subset regressions [15 - 1 possible models.Modeling of multi-signal induced cellular responses can also be used to study key system-level signaling interactions between the applied signals and their effects on the system outputs. To that end, consider the linear regression model with interaction terms. This model uses a total of 15 regressors that are the concentrations of the drugs, six pairwise interaction terms, four three-drug interaction terms, and one four-drug interaction term. This is a large number of regressors and, potentially, only a portion of these regressors are necessary to describe the variation in the data. Reduction of the regressors matrix ressions . The algThe residual sum of squares of the best models shows that there is no significant reduction in the residual sum of squares for models with more than 10 regressors for the A549 data, and for models with more than 7 regressors for the AG02603 data Figure . The regWe demonstrated the integration of an efficient mathematical approach for a systematic quantitative characterization of the effect of multi-signal combinations in two different cell types. Our method enables the establishment of accurate models to directly connect multi-signal combinations and their effects through a learning process. Only a small percentage of total data points are required to be experimentally tested to establish a predictive model that is capable of simulating the effect of all possible signal combinations.The resulting predictive model is also able to systematically reveal the inter-drug interactions which are often non-linear relationships. Such a model is necessary for multi-drug combination optimization as the optimal combination, upon the addition of a new drug, cannot be achieved simply by testing various amounts of the new drug added to the previously optimized combination. Moreover, the approach allows for examining all lower order mixtures of the drugs and for evaluating the effectiveness without added experimental overhead. This enables efficient selection of drug combinations of different drugs particularly as the interactions between the different drugs vary. The approach enables systematic selection of input signals (drug combinations) that can achieve desired therapeutic goals. Experimental validation of selected top performing combinations presents additional evidence of the validity and utility of the approach introduced.Our approach requires a relatively small number of experimental measurements. With the development of large scale-high throughput measurement systems, our approach will be necessary and more efficient, e.g., when the number of inputs increases. Additionally, it will allow for integration into automated machines for testing and analysis of various biological systems. The addition of other cellular outputs can be another factor in favor of using this approach.We demonstrated the utility of various mathematical modeling approaches for the purposes of modeling and predicting multi-signal induced cellular responses. Linear regression with models including interaction and quadratic terms were capable of producing powerful predictive models. The usefulness of linear regression methods and subset selection algorithms was also demonstrated as they enabled determination of key system-level signal interactions that result in the observed cellular responses. Alternately, neural network models performed generally better for fitting the data particularly when fewer data points were available to fit the models. Additionally, different structures of neural networks were almost equally powerful in producing the models. This present ample opportunity to exploit different structure of networks to mimic more realistic interactions within the cell given such a priori data. The choice of the best method for fitting the model is dependent on many factors. While in some cases simple linear regression can be used, in other cases nonlinear regression methods are necessary to get satisfactory models. Neural networks represent powerful computational models with great flexibility. Different types and configuration renders them useful for a wide range of problems including dynamic prediction using, e.g., recurrent neural networks. This presents an additional use for neural network to build on a wide range of applications in biological and medical research -34.in vivo therapies, in which case the limited experimental scale imposes restrictions on the number of possible drug combinations to test. By largely reducing the number of tests required, our approach can greatly facilitate the development of clinically applicable treatments.It is important to note here that the novelty in this work is not this particular use of artificial neural networks. Rather, it is the use of a system-level model-based approach to study the effects of a large number of signals on various cellular processes and to use that as a basis for selection of the retrospective optimal input signals. Our method resembles a general systems biology approach that can be utilized to address a broad range of biological questions. The method enables comparison of multiple system performances through modeling of their responses. The advantage of our method becomes critical when input signal combinations are characterized for the development of effective For the drugs and cell types chosen, our results showed that four drugs did not provide a significant improvement over three drugs. However, this is not a general result and the causes of this observation are not well known and pose an interesting problem to be examined in a separate study. A potential cause is that the signaling pathways affected by some of the drugs are saturated potentially due to sharing of a common target between two of the drugs. In other studies we are working on with different drugs and cells, four drugs result in an improvement over three drugs and five drugs also improve on four drugs.Our modeling approach enabled identification of key system-level signaling interactions that contribute to the observed responses. These interactions highlighted potential differences in the signaling networks of different cell types as demonstrated. While some signaling interactions were common to the two cell types studied, there were other interactions that were specific to each cell type. Many of these interactions were known a priori. For example, the interactions between U0126 and GF109203X, I-3-M and GF109203X, AG490 and I-3-M, as well as AG490 and U0126 and GF109203X. There are other interactions that were not known a priori such as the interaction between U0126 and I-3-M. Thus the prediction of such interactions can guide experimental identification of the molecules mediating the interactions.In the work presented, we used mathematical tools to construct a predictive model of cellular outcomes. The method was developed in experimental systems that only involved single output measurements. However, the method is a general method that can be used to construct models of the effects of multiple signals on various cellular outcomes, including signaling intermediates. Molecules from various cellular pathways, "intermediates", can serve as candidates for measurement and quantification ,35,36. MCombinational therapies have attracted significant research efforts. Combination therapy for cancer is one example. The challenges associated with cancer treatment range from a lack of understanding of fundamental pathogenic mechanisms to practical experimentation limitations. Cancer is usually caused by multiple mutations and alterations of multiple signaling pathways which pose an extra challenge when defining the mechanisms underlining cancer development . In addiHowever, the design of combination therapies based on studies of the response to individual drugs might not lead to the desired outcomes as interactions between the various drugs can lead to unknown outcomes. The emerging toxicities can be a major hurdle to the development of combination therapies. Therefore, it is important to consider system level signals or outputs that are representative of the state of the cell in addition to cellular intermediates targeted by the drugs. As such, it is important to investigate whether and how a combination of drugs can lead to a better system response compared to any of the individual single-drug responses.Development of drug combination therapies for cancer can lead to more effective therapies to overcome drug resistance and achieve maximal drug efficacy. The demanding task is to find a combination that is maximally effective on cancer cells with minimal effect on non-cancer cells. The method introduced in this work provides the ability to study the system-level effects of combinations of drugs and use the data to select combinations that can lead to desired outcomes by comparing the mathematical models of multiple cellular types. Furthermore, the method is capable of studying and characterizing experimental problems of higher complexity such as the order and timing of administration of multiple inputs into the system, which may help further reduce cytotoxicity and enhance efficacy with the same drugs utilized in clinical treatment of diseases. Moreover, employing our method with emerging technologies such as micro-fluidic devices or "lab-on-chip" will enable high-throughput investigation of multi-drug combinations, and become a promising platform for developing personalized medicine.A549 cells were cultured in RPMI1640 medium (CellGro) supplemented with 10% heat-inactivated FBS, 100U/ml penicillin and 100g/ml streptomycin (CellGro). AG02603 cells were in MEM (Gibco) supplemented with non-essential amino acid (Gibco), 15%heat-inactivated FBS, 100U/ml penicillin, and 100g/ml streptomycin. Cells were seeded one day before drug treatment at a density of 1000cells/well for A549, and 8000cells/well for AG02603, in 96 well plates. ATP assays were conducted with the ATPlite 1step assay system (PerkinElmer) following the manufacturer's instructions and the luminescence signal was measured by Lmax microplate luminometer (Molecular Devices).We used two types of neural networks to fit the data. The first is a single layer four-neuron multilayer perceptron and the other is a two-layer cascaded neural network with a single neuron per layer. The networks were constructed and trained using the neural network toolbox of MATLAB . The traWe used two linear regression models to fit the data. The two models arexnc be the ATP-level of AG02603 and xcc be the ATP-level of A549 cells. Then, the performance function used is given by PerfIn our work, we used a single performance function reflecting the relative importance of each criteria to our setup. The criteria are: maximize AG02603 cellular ATP-level and minimize AG02603 cellular ATP-level. The performance function used is defined as follows. Let whereμ is the column vector IA, FY, and RS wrote the paper. IA, FY, and RS analyzed the data. IA, CMH, and JSS devised the mathematical solutions. FY, JF, and KY conducted the wet experiments. IA carried out the computational experiments. IA, FY, SD, CMH, JSS, and RS conceived the idea. All authors read and approved the final manuscript.


It has been reported that the direction of the guidewire J-tip is associated with misplacement of a central venous catheter. We hypothesized that real-time ultrasound-guided infraclavicular subclavian venous cannulation would be less influenced by the direction of guidewire J-tip compared to landmark method.Sixty adult patients who required subclavian venous catheterization for neurosurgery were enrolled in this prospective randomized controlled study. Patients were randomly divided into a landmark group (n = 30) or an ultrasound group (n = 30). After the subclavian vein was punctured, the guidewire was advanced with the guidewire J-tip directed cephalad. Misplacement or advancement failure of the guidewire was regarded as an unsuccessful placement. Postoperative chest radiography was performed to confirm pneumothorax and the location of the catheter tip.The two groups were comparable with respect to age, gender, height, and weight distribution. The incidence of unsuccessful guidewire placement was lower in the ultrasound group than in the landmark group . Among the unsuccessful guidewire placements, the incidence of misplacement were comparable between the groups and were all located in the ipsilateral internal jugular vein (7% vs. 7%). However, the incidence of advancement failure was significantly higher in landmark group . There were no complications such as pneumothorax or hemothorax.The proper placement of guidewire was less influenced by the direction of the guidewire J-tip with ultrasound-guided subclavian venous cannulation than with the landmark approach. Aberrant placement of a subclavian venous catheter tip may result in incorrect central venous pressure readings or serious complications such as vascular erosion and thrombosis. Various techniques have been suggested to avoid aberrant location of a catheter -5. The dCompared with the landmark approach, real-time ultrasound-guided cannulation results in a higher success rate, requires fewer attempts, and has a lower rate of mechanical complications; thus, it increases the safety of central venous access via the subclavian route .With ultrasound-guided approaches, the course of needle approaching the vein and the tip of needle properly located in the subclavian vein (SCV) can be visualized, which allows more distance from the tip of needle to vessel wall of opposite site. The usual point of skin puncture is more lateral than that of landmark method and the point entering the lumen of the vein is either at the axillary vein or at the point where it continues as the SCV , which aWe hypothesized that in ultrasound method, the proper positioning of the guidewire would be less influenced by the direction of a guidewire J-tip compared to landmark one during SCV cannulation. We evaluated the success rate of proper guidewire placement while the guidewire J-tip directed cephalad before insertion into a needle hub in ultrasound group and landmark group.With approval of the Institutional Review Board of Seoul National University Bundang Hospital (IRB Number E-1006/050-003), informed consent was obtained from all patients. The study protocol was registered with the Korean Clinical Trials Registry (Number KCT0000083).In this prospective randomized controlled study, patients between the age of 18 and 75 years , who required subclavian venous catheterization for neurosurgery at Seoul National University Bundang Hospital throughout October 2010 to November 2011 were included. Patients with chest deformities or significant coagulopathy were excluded. Patients were allocated to two groups, the landmark or ultrasound group, by using a block randomization technique. Randomization was determined with random number tables, and the assignments were concealed in sealed envelopes until immediately before induction of anesthesia.After the induction of general anesthesia, right subclavian venous catheterization was performed using a double-lumen central venous catheter  under aseptic conditions. Patients were placed in the supine position, with the head and shoulder in the neutral position. In the landmark group, the skin was punctured at 2–3 cm below the right clavicle, along the mid-clavicular line, toward the upper border of the suprasternal notch; the puncture needle was advanced until the right SCV was punctured. In the ultrasound group, the real-time ultrasound-guided technique was performed using a SonoSite S-nerve  equipped with a high-resolution 7.5 mHz transducer. The transducer was covered with a sterile sheath, and ultrasonic gel was used. A colour Doppler technique was used to confirm the vein. The right SCV to be catheterized was located in the longitudinal plane, and the needle was directed at the vein in real time. In both groups, when the free flow of non-pulsatile venous blood appeared, the guidewire was advanced with the J-tip directed cephalad. The ipsilateral IJV and contralateral SCV as well as ipsilateral SCV were scanned to confirm the proper position of guidewire. If the guidewire could not be advanced due to resistance or was seen in the IJV under ultrasound examination, it was regarded as an unsuccessful placement, which was the primary outcome of this study. Patients in whom the SCV catheterization failed or arterial puncture occurred were excluded from the analysis.Postoperative chest radiography was performed on all patients to visualize a pneumothorax or hemothorax, which was the secondary outcome measures, and the location of the catheter tip.U test was used to compare mean values between the two groups, and a χ2 test was performed to compare the gender difference and the incidence of failure of proper guidewire placement. A value of P < 0.05 indicated statistical significance.The sample size calculation was based on the results of a previous study, which reported the incidence of catheter tip malpositioning during infraclavicular subclavian venous cannulation to be 43% when the J-tip was directed cephalad [Of the 66 patients enrolled for randomization, six patients were excluded from the study Figure . Three pP = 0.01). Of the unsuccessful guidewire placement, the incidence of advancement failure was significantly higher in landmark group . The incidence of misplacement among the rest of the patients were comparable between the groups and were all located in the ipsilateral internal jugular vein  (Table The incidence of unsuccessful placement of catheter tips was lower in the ultrasound group than in the landmark group (13% vs. 47%, Our study showed that the incidence of unsuccessful guidewire placement was significantly lower during subclavian venous cannulation when ultrasound is used compared to landmark method even when the guidewire J-tip directed cephalad before insertion into a needle hub.We suggest several explanations for lower incidence of unsuccessful guidewire placement in the ultrasound group. First, the different angle of the venipuncture between the two techniques might be related. With the ultrasound-guided technique, the direction of needle pointed along the long axis of the SCV, facilitating proper guidewire advancement. In contrast, with the landmark technique, the angle of the needle was much flatter against the skin, and the needle pointed toward the suprasternal notch, which can lead to the advance of the guidewire into the IJV. Second, the point of vascular puncture is usually at axillary vein or at the junction where it continues as SCV and is more lateral compared to that of landmark method, which allows the longer path for guidewire before entering superior vena cava. Third, more accurate placement of a needle tip in the vessel is possible and the distance from the tip of needle to the vessel wall of opposite side might be longer because the course of needle passage and the tip of needle can be visualized in real time.It is recommended that the direction of the guidewire J-tip should be adjusted caudad before fitting into the subclavian puncture needle hub . HoweverThe head or shoulder position appears to be important for the central venous catheter direction during the infraclavicular subclavian approach -10. TurnIn this study, the incidence of failure to thread the guidewire was high. Failure to thread the guidewire can occur when the J-tip is directed cephalad . If the The use of ultrasound for subclavian venous cannulation has been controversial for anatomical reasons ,12. It hThere were some limitations to our study. First, this investigation was not-blinded because the catheterization could not be disguised; therefore, there was a possibility of a bias. Second, the ultrasound-guided technique failed in three patients. The real-time ultrasound technique has been rated as technically difficult by participating physicians . As prevWe demonstrated that the rate of unsuccessful guidewire placement was significantly lower in real-time ultrasound guided SCV cannulation compared to landmark one even though the guidewire tip was directed cephalad before insertion into a needle hub. We suggest that the guidewire placement is less influenced by the direction of guidewire J-tip in ultrasound method compared to landmark method. From this result, together with the fact that the guidewire placement could be monitored in real time, we concluded that a considerable portion of problems related to the direction of guidewire tip could be resolved with ultrasound method. This could be another benefit of ultrasound-guided SCV cannulation, making the procedure easier, which could be added to already known benefits.The authors declare that they have no competing interests.AYO contributed to conception and design of the study, wrote the manuscript. YTJ contributed to conception and design of the study, revised the manuscript. HPP contributed to conception and design of the study. EJC, JHR, and JWH contributed to acquisition, analysis, and interpretation of data. SHD revised the manuscript. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2253/14/11/prepub


Papio papio) and examined the structure and usage of the animals’ vocal signals. Guinea baboons live in a complex multi-level social organization and exhibit a largely tolerant and affiliative social style, contrary to most other baboon taxa. To classify the vocal repertoire of male and female Guinea baboons, cluster analyses were used and focal observations were conducted to assess the usage of vocal signals in the particular contexts.To understand the evolution of acoustic communication in animals, it is important to distinguish between the structure and the usage of vocal signals, since both aspects are subject to different constraints. In terrestrial mammals, the structure of calls is largely innate, while individuals have a greater ability to actively initiate or withhold calls. In closely related taxa, one would therefore predict a higher flexibility in call usage compared to call structure. In the present study, we investigated the vocal repertoire of free living Guinea baboons , they frequently used vocal signals during affiliative and greeting interactions.Our study shows that the call structure of primates is largely unaffected by the species’ social system , while the usage of calls can be more flexibly adjusted, reflecting the quality of social interactions of the individuals. Our results support the view that the primary function of social signals is to regulate social interactions, and therefore the degree of competition and cooperation may be more important to explain variation in call usage than grouping patterns or group size. The signal design of animal calls and the resulting morphology of their vocal repertoire is assumed to be shaped by several factors, including phylogenetic history,2, habitWhat is less well understood to date is the interplay between social and vocal systems. In recent years, the idea that more complex social systems may generally lead to higher vocal complexity has attracted increasing attention,12,35,36Loxodonta africana, applied with a blowpipe. We measured the individuals with a standard commercial measuring tape and weighed them with a hanging scale. The length and width of the snout and the skull were measured with a vernier caliper. During the whole process we regularly controlled the body temperature, respiration and the corneal reflexes. The head was covered with a cloth, and the cornea was continuously wetted with medical tear supplement. For six individuals body measured were repeated two times in a row, revealing a rather moderate measurement error:F1 – F3). Only a limited number of calls fulfilled this criterion, hence, after visual inspecting our calls merely 3–5 calls per individual were suitable to analyse . We derived the formant spacing (∆F) from the frequencies of the first three formants by finding the best fit to the equationFor statistical analysis, we applied a principal component analyses (PCA) to extract a single compound body measurement. Table which relates individual formant frequencies to average overall format spacing in the vocal tract, approximated as a uniform tube closed at one end (the glottis) and open at the other (the mouth). A detail description of this procedure is given in.Sc) represents the summarized distance of all within-cluster data points (ai) subtracted from the summarized distance to the data points of the successive cluster (bi) and finally divided by the sum of the larger distance:To statistically describe the vocal repertoire we used a two-step cluster analyses on the selected acoustic variables, which has been already successfully applied in other bioacoustic studies,104. We Sc exceeding 0.5 are usually considered to be solid[Sc for each solution. We further compared the formal categorization results to the audio-visual pre-classification of the calls and calculated the percentage of accordance between both classifications.Subsequently, the average value across all call clusters of the respective solution is calculated and gives a number between −1.0 and 1.0; cluster solutions with a be solid. Hence, Afterwards, we ran a discriminant function analyses  with the same acoustic parameters and the calculated call-clusters as grouping variable to evaluate the selected cluster solution and to estimate how the acoustic parameters contribute to the classification. We used a stepwise DFA and the assignment of calls was cross-validated by the leaving-one-out method of SPSS 20.p-values using Simes correction.To analyse sex and context differences of grunts we carried out a linear mixed model analysis (LMM) on the same acoustic variables as used for the cluster analysis, with animal ID as random factor and sex and context as fixed factors, respectively. To identify significant differences between the contexts we applied univariate least significant differences (LSD) post-hoc tests. The influence of body size on the call structure we investigated by conducting a Pearson correlation analysis between the body component and fundamental frequency as well as formant spacing. All statistical tests were two-tailed and conducted with SPSS 20 or the statistical package R (R Development Core Team). We corrected for multiple testing by adjusting all The authors declare that they have no competing interests.PM recorded the data, conducted the analyses and wrote the paper, IN did the veterinary work in the field and collected body measurements, KH designed the study and contributed to the acoustic and statistical analyses and assisted by drafting the paper, JF designed the study and wrote the paper. All authors read and approved the final manuscript.


So far, all the well-known statistical reconstruction algorithms require exactly known system probability matrix a priori, and the quality of such system model largely determines the quality of the reconstructed images. In this paper, we propose an algorithm for PET image reconstruction for the real world case where the PET system model is subject to uncertainties. The method counts PET reconstruction as a regularization problem and the image estimation is achieved by means of an uncertainty weighted least squares framework. The performance of our work is evaluated with the Shepp-Logan simulated and real phantom data, which demonstrates significant improvements in image quality over the least squares reconstruction efforts.In Positron Emission Tomography (PET), an  It utilizes the idea of injecting chemical compounds tagged with positron emitting isotopes into a body to acquire complete coincidence data, which records the concentration information of the isotope distributions at specific locations within the body. The radioactivity images are then reconstructed based on these photon counting measurements.Positron Emission Tomography (PET) is one of the most important medical imaging modality which provides The reconstruction of isotope concentration distribution is an ill-posed inverse problem. Most of current approaches to tackle this problem can be classified into two general categories, namely the analytical methods, which rely on the inversion of Radon transform, and the iterative approaches, which are based on a statistical description of the physical problem a priori. In real situations, however, it is almost impossible to have the exact system model information because real imaging systems are subject to a number of complicated physical effects  However, so far, the common feature of all statistical-based methods for PET image reconstruction is that the system response model is assumed to be exactly known In this paper, we investigate the application of the uncertainty weighted least squares principle to PET image reconstruction. Our algorithm, which is based on a min-max formulation, allows the simultaneous incorporation of system model and measurement statistical uncertainties, thus providing a more robust and accurate solution.In the PET measurement, initially, when a positron-emitting nuclide decays in the body, the nucleus rids of itself of excess positive charge by emitting a positron, which almost immediately loses its energy by collisions in the surrounding tissues and then combines with an electron and annihilates. Two back-to-back gamma rays of equal energy are then generated. These photon pairs can be detected externally by two opposite detectors using a coincidence technique, forming a coincidence event. These acquired coincidence data record the concentration information of the isotope distributions at specific locations within the body. However, in reality, the coincidence events may also include those that the two gamma rays originating from two unrelated position annihilations are detected within the coincidence resolving time and those that the annihilation photons have an interaction of Compton scattering and lose their directional and energy information before they arrive to the detector system. The former are referred as random coincidences and the latter are called scattered coincidences. To recover a reasonable image, random and scattered photon pairs should be subtracted from coincidence events.In practice, the emission sinogram data ideal known noisy measurementssystem modelrandom errors.It is typically difficult or even impossible to obtain an A way to solve the reconstruction problem is to use the statistical principles, where the objective function is:In order to handle the uncertainty issues of the system and the measurements, a min-max cost function formulation can be adopted to achieve robust solution Directly solving (4) will take too much storage space and computational time. Similar to the penalized weighted method proposed by Fessler measurement noise. Here we treat Here, the stationary PET inverse problem is considered. In static imaging case the concentration Now, let us consider the case of uncertainty in matrix priori estimate For above uncertain state space description, once having a To solve the objective function (15), we model uncertainties in system and measurement with a norm-bounded structure Consider about the min-max cost function (15), by setting a corresponding relationship asIn practice, we can choose a reasonable approximation for For any determined Given the uncertain model:Initialization: with given initial state estimation Update step froma prioriestimation  and :Correction step with given measurement :The well-known and widely used Shepp-Logan synthetic emission phantom  with knoThe images of the mean pixel values obtained by the three algorithms EM , UPWLS bA detailed statistical analysis on the estimation results against the ground truth phantom map is performed. Let The bias and variance of errors are averaged over the 50 reconstructions to give the estimates bias and variance at different noise levels which are summarized in The real data set used in this study was acquired on Hamamatsu SHR-22000 scanner There are many different approaches for PET image reconstruction from projections, most of which are based on exactly known system model or system matrix. Several attempts were made to tackle this problem based on a specific type of modelling error, such as positron range, non-colinearity of the photon pair, and depth of interaction effect et al. Unlike these existing efforts that are limited to single type of modelling error, we propose an UPWLS method to handle statistical uncertainties of the system.The P (0), In our current implementation, the parameters are set to some empirically fixed values in all experiments: On the other hand, current methods requires huge storage and expensive computation as today's PET scanners have a large set of detector pairs and the inversion of the system matrix. With the method mentioned in the As a continuation of this work, based on the tracer kinematics equation coming from compartment model, we can recover dynamic changes of tracer density in a continuous time domain for dynamic PET with an uncertain system model.Detailed investigations on these issues are underway.In this paper, we have developed an uncertainty weighted least squares framework for the estimation of activity distribution from PET measured data. The approach enables us to incorporate the system uncertainties into PET image reconstruction, thus providing more robust and stable results. Analytical and experimental results with Shepp-Logan simulation phantom data and real PET measurements demonstrate the power of the proposed method.Appendix S1Derivations for UPWLS solution.(PDF)Click here for additional data file.Appendix S2The iterative expression for state variable and variance.(PDF)Click here for additional data file.Appendix S3Inversion of a large sparse matrix - GMRES method.(PDF)Click here for additional data file.


The network-based approach has been used to describe the relationship among genes and various phenotypes, producing a network describing complex biological relationships. Such networks can be constructed by aggregating previously reported associations in the literature from various databases. In this work, we applied the network-based approach to investigate how different brain areas are associated to genetic disorders and genes. In particular, a tripartite network with genes, genetic diseases, and brain areas was constructed based on the associations among them reported in the literature through text mining. In the resulting network, a disproportionately large number of gene-disease and disease-brain associations were attributed to a small subset of genes, diseases, and brain areas. Furthermore, a small number of brain areas were found to be associated with a large number of the same genes and diseases. These core brain regions encompassed the areas identified by the previous genome-wide association studies, and suggest potential areas of focus in the future imaging genetics research. The approach outlined in this work demonstrates the utility of the network-based approach in studying genetic effects on the brain. The human diseasome network by Goh et al. Organizing existing data and analysis results for such networks, needless to say, is far more economical compared toactually conducting a genomics study. A typical study for genetic associations may require data collection and assays, which can be time consuming and labor intensive. In addition, statistical analyses of such data often require special techniques to account for unique characteristics of the data, such as the family structure, massive multiple comparisons, population biases, or non-normality. On the other hand, the network-based approach requires far fewerresources in terms of costs and manpower involved. Most of the effort is focused on culling multiple databases and organizing findings in the form of a network. The network-based approach enables combining of data from multiple populations together, thus allowing investigators to focus on a large number of genes and/or phenotypes simultaneously.Such a network may represent consolidated results from multiple separate studies, but each of the studies does not have to be as extensive as, for example, a genome-wide association study (GWAS).http://www.ncbi.nlm.nih.gov/pubmed) Some of the disease classes in the human diseasome network k, in the three layers of the tripartite graph were examined, and tremendous heterogeneity in the degree was observed. The degree distribution of the brain area nodes can be seen in F(k). The distribution closely follows an exponentially truncated power law distribution  test), a long-tailed distribution indicating a few highly connected nodes witha large number of connections (k>200). This is in contrast with the vast majority of other nodes with just a few dozen connections; the median of the degree distribution is 32, and 75% of edges are connected to the top30% highest degree nodes. Connections originating from the disease nodes were also heterogeneously distributed. A small number of diseases affect a large number of brain areas extensively .Connections between genes and genetic disorders were based on the network data reported in Goh et al. http://www.pubbrain.org/). The PubBrain website searches a user-provided search term on the PubMed database together with over 300 brain anatomical terms Connections between genetic disorders and brain areas were based on text mining of the PubMed database. The text mining search was interfaced by the PubBrain search engine  test. However, a KS test may not be uniformly sensitive over the wide range of degrees covered in a typical long-tail degree distribution. Even if the tails of the observed and theoretical distributions may appear close to each other on a log-log scale, a KS test statistic is likely dominated by the difference between the observed and theoretical distributions among low degree nodes. This is because the difference between the observed and theoretical is a few orders of magnitude smaller near the tail of the degree distribution compared to the difference near the lower end of the degree range. Although we provide p-values based on KS tests for the observed degree distributions from the tripartite graph by comparing them to exponentially truncated power law and power law distributions, lack of good fit does not imply a lack of heterogeneity in node degrees. The instability of the KS test statistic near the tail of long-tailed distributions was noted by Stumpf et al. Among the brain areas represented in the tripartite network, some may be affected by the same set of diseases, or may be associated with the same set of genes. To understand how brain areas share the same connections to diseases or genes, the tripartite network was collapsed as a set of connections between brain areas representing shared genes or diseases. In particular, a common disease network and a common gene network were constructed. The common disease network was organized by connecting two brain areas that are connected to the same diseases see , left. TIn the common disease network and the common gene network, edge weights were further examined in order to identify brain areas sharing a large number of diseases or genes. To do so, first the distribution of edge weights was examined to identify any heterogeneity in the number of shared diseases or genes among the brain areas. We also formed the core networks, the networks of brain areas formed by the connections with top 10% of edge weights in the common disease and gene networks, accentuating the commonality among the brain areas sharing the same diseases or genes.One of the goals of the core networks is to extract meaningful information from the common disease and gene networks, which are almost fully connected see . AnotherGene-disease connections and disease-brain connections in the tripartite network were based on the data from publicly available databases. However, the data in those databases may be biased toward diseases that are highly studied among researchers. For example, some diseases may be investigated more often than other diseases. Or some diseases may be studied more widely due to favorable availability of research funding for those diseases. To examine such potential biases, the diseases from the tripartite networks were queried in PubMed to gauge the research activity associated with those diseases as the number of publications. The number of PubMed hits and the degrees for the corresponding diseases were plotted to assess any association. In addition, a potential funding bias was investigated among 69 diseases selected from the tripartite network to cover the entire range of disease degrees. For each of these diseases, the amount of total research funding was searched on the RePORTER (Research Portfolio Online Reporting Tools Expenditures and Table S1A list of 65 brain anatomy terms used in the PubBrain searches.(DOCX)Click here for additional data file.Data S1A node list and an edge list of the disease-brain network in Pajek format.(NET)Click here for additional data file.


By anal neurons . Here, tThough the neuronal firing rate may fluctuate with external stimuli, this does not necessarily mean that the rate is extrinsic and perfectly controllable; there could be some uncontrollable intrinsic aspect in the firing rate fluctuation. In this contribution, we go contrary to the above-mentioned studies, and attempt to characterize neuronal spike trains solely in terms of the firing rate, ignoring the firing irregularity. The key feature of neuronal spike trains we now pay attention to is dynamic mode of rate fluctuation, such that the rate either fluctuates smoothly in time or changes abruptly between several stationary states.a posteriori (MAP) estimate for the rate We compare two different models of a fluctuating rate process for their goodness-of-fit with respect to spike trains recorded from single neurons in several cortical areas of rats. The first model is the state space model constructed under the Empirical Bayes method ,4. The ge states -7. The nIn this way, two different estimations of the firing rate are obtained using the continuous state space model and the discrete HMM. We compare them for each spike train obtained from a neuron, and examine whether the continuous or discrete representation of the state transition is more plausible. Then, we examine how the different preferences are distributed in different cortical areas.


Owning to its clinical accessibility, T1-weighted MRI (Magnetic Resonance Imaging) has been extensively studied in the past decades for prediction of Alzheimer's disease (AD) and mild cognitive impairment (MCI). The volumes of gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF) are the most commonly used measurements, resulting in many successful applications. It has been widely observed that disease-induced structural changes may not occur at isolated spots, but in several inter-related regions. Therefore, for better characterization of brain pathology, we propose in this paper a means to extract inter-regional correlation based features from local volumetric measurements. Specifically, our approach involves constructing an anatomical brain network for each subject, with each node representing a Region of Interest (ROI) and each edge representing Pearson correlation of tissue volumetric measurements between ROI pairs. As second order volumetric measurements, network features are more descriptive but also more sensitive to noise. To overcome this limitation, a hierarchy of ROIs is used to suppress noise at different scales. Pairwise interactions are considered not only for ROIs with the same scale in the same layer of the hierarchy, but also for ROIs across different scales in different layers. To address the high dimensionality problem resulting from the large number of network features, a supervised dimensionality reduction method is further employed to embed a selected subset of features into a low dimensional feature space, while at the same time preserving discriminative information. We demonstrate with experimental results the efficacy of this embedding strategy in comparison with some other commonly used approaches. In addition, although the proposed method can be easily generalized to incorporate other metrics of regional similarities, the benefits of using Pearson correlation in our application are reinforced by the experimental results. Without requiring new sources of information, our proposed approach improves the accuracy of MCI prediction from  Alzheimer's disease (AD) is a progressive and eventually fatal disease of the brain, characterized by memory failure and degeneration of other cognitive functions. Pathology may begin long before the patient experiences any symptom and often lead to structural changes of brain anatomies. With the aid of medical imaging techniques, it is now possible to study in vivo the relationship between brain structural changes and the mental disorder, providing a diagnosis tool for early detection of AD. Current studies focus on MCI (mild cognitive impairment), a transitional state between normal aging and AD. These subjects suffer from memory impairment that is greater than expected for their age, but retain general cognitive functions to maintain daily living. Identifying MCI subjects is important, especially for those that will eventually convert to AD , because they may benefit from therapies that could slow down the disease progression.Although T1-weighted MRI, as a diagnostic tool, is relatively well studied, it continues to receive the attention of researchers due to its easy access in clinical settings, compared with task-based functional imaging The determination of the Region of Interest (ROI) is the key for region-based analysis methods. Once ROIs have been determined either by pre-definition The correlation value measures the similarity of the tissue compositions between a pair of brain regions. When a patient is affected by MCI, the correlation values of a particular brain region with another region will be potentially affected, due possibly to the factors such as tissue atrophy. These correlation changes will be finally captured by classifiers and used for MCI prediction. An early work was presented in a conference Without requiring any new information in addition to the baseline T1-weighted images, the proposed approach improves the prediction accuracy of MCI from relative speeds of disease progression in different regions, providing a different pathological perspective complementary to spatial atrophy patterns.Before introducing our proposed approach, it is worth highlighting the advantages of the hierarchical brain network-based approach over the conventional volume-based approaches. Firstly, as mentioned above, our proposed method utilizes a second-order volumetric measurement that is more descriptive than the conventional first-order volumetric measurement. Secondly, compared with the conventional volumetric measurements that only consider local volume changes, our proposed hierarchical brain network considers global information by pairing ROIs that may be spatially far away. Thirdly, our proposed method seamlessly incorporates both local volume features and global network features for the classification by introducing a whole-brain ROI at the top of the hierarchy. By correlating with the whole-brain ROI, each ROI can provide a first order measurement of local volume. Fourthly, although our current approach uses Pearson correlation, it can be easily generalized to any other metrics that are capable of measuring the similarity between features of ROI pairs. Fifthly, the proposed method involves only linear methods, leading to easy interpretations of the classification results. Finally, for the first time, we investigate the www.loni.ucla.edu/ADNI) www.adniinfo.org. The ADNI protocol included a sagittal volumetric 3D MPRAGE with Both the normal control and MCI subjects used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database . More information about the ADNI investigators is given in Acknowledgement.In this study, The T1-weighted MR brain images are skull-stripped and cerebellum-removed after a correction of intensity inhomogeneity using N3 algorithm The overview of the proposed method is illustrated in In this paper, a four-layer ROI hierarchy is proposed to improve the classification performance of volumetric measurements. Each layer corresponds to a brain atlas with different resolution. To make the explanation of our method clear, the bottommost layer that contains the finest ROIs is denoted as With the ROI hierarchy defined above, an anatomical brain network can be constructed for each subject, from which informative features are extracted for classification. For each brain network, its nodes correspond to the brain ROIs, and its undirected edges correspond to the interactions between two ROIs. There are two types of nodes in our model -left: thectively -right.The brain network may be quite complicated. For instance, Firstly, let us consider the bottommost layer For any other layer  matrix   is used Given the ROI interactions in the bottommost layer Represented in the form of matrix, the correlation matrix The correlation matrix that reflects between-layer interactions can be defined similarly to that of within-layer interactions. First, let us consider the correlation matrix for two different layers Now, let us consider the correlation matrix for two layers Note that the hierarchical anatomical brain network may not have the property of small-worldness as shown in DTI and fMRI networks Since a hierarchical fully-connected brain network is used in our study, the dimensionality of the network features is very high: originally more than 10,000 features for each subject. To address this issue, in this paper, we propose a classification scheme to efficiently learn discriminative information from this large amount of network features. The scheme involves feature dimensionality reduction and classification. The overview of the whole process is given in In the rest of this section, our proposed classification scheme is explained in detail. Firstly, in Section “Problem on identifying discriminative features”, we justify the necessity of incorporating both feature selection and feature embedding into the dimensionality reduction module in When the number of predefined ROIs is large, the traditional volumetric-based approaches encounter the high feature dimensionality problem. Therefore some preprocessing steps are conducted to reduce the feature dimensionality before classification. There are usually two ways: i) select a subset of the most discriminative features from the original feature set, known as feature selection, or ii) combine the original features linearly or non-linearly to get a lower dimensional feature space, known as feature embedding. Both methods have been reported in the literature. In Compared with volumetric features, the dimensionality of our proposed network features is even much higher. To address this problem, we propose to use both feature selection and feature embedding to efficiently reduce the feature dimensionality. The reason is two-fold. Firstly, feature selection alone may still give rise to many informative features for the classification. For example, suppose that only 10 ROIs really contribute to the discrimination. The dimension of volumetric features may be maximally reduced to 10 if the feature selection method is effective. However, the number of the corresponding network features that model the pairwise interactions of the 10 ROIs might be up to alone may not be sufficient to identify the discriminative network features with respect to classification. Therefore, a dimensionality reduction process is proposed, which couples feature selection and feature embedding via Partial Least Square (PLS) analysis In short, either feature selection or feature embedding PLS models the relations between the predictive variables  In Step 3, using the features selected in Step 2, a new PLS model is trained to find an embedding space which best preserves the discrimination of features. The embedding is performed by projecting the feature vectors in the matrix In Step 4, after PLS embedding, a small number of features in the new space are able to capture the majority of the class discrimination. This greatly reduces the complexity of relationships between data. Therefore, these features are used to train a linear SVM for predicting MCI patients and normal controls. In our case, a linear SVM can achieve better or at least comparable classification accuracies as a non-linear SVM.The advantages of PLS for our network features over some commonly used unsupervised and supervised nonlinear methods, such as Laplacian eigenmap embedding and Kernel Fisher Discriminant Analysis (KFDA), have been evidently shown in our experiment in Section “Comparison of Classifiers”.In our study, we conduct two kinds of comparisons, that is, to compare the discrimination power of the network and the volumetric features, and to compare the performance of different classifiers for the network features. The discussion of the classification results are given at the end of this section.Please note that, as MCI patients are highly heterogeneous, the comparison of the absolute classification accuracy with the existing works in the literature is meaningless. Therefore in our study, we evaluate the improvement of our proposed approach over the conventional volumetric features by comparisons on the same data set with the same experiment configuration. Furthermore, to investigate the generalization of the proposed method, we conduct experiments repetitively on different random partitions of training and test data sets with different partition ratios. The average classification accuracy estimated in this way tends to be more conservative than the traditional Leave-One-Out approach. More discussions are given below.Firstly, we compare the efficacy of different features with respect to classification. The data set is randomly partitioned into 20 training and test groups with 75 samples for training and 75 samples for test. For a fair comparison, our proposed classification process is applied similarly to both the volumetric and the network features.As aforementioned, our network features differ from the conventional volumetric features in two aspects: i) the network features model the regional interactions; ii) the network features are obtained from a four-layer hierarchy of brain atlases. The contributions of these two aspects are investigated separately. To test the advantages of using regional interactions over local volumes, we compare the network and the volumetric features on the same hierarchical structure (either single-layer or four-layer). To test the advantages of using the hierarchical network structure, we compare network features obtained from different layers  in the hierarchy. Moreover, we compare the networks with and without the cross-layer connections to further explore the function of the hierarchial structure. In summary, five methods are tested in the experiment:Method I is the proposed method in this paper, using the four-layer hierarchical network features.Method II only uses the network features from the bottommost layer Method III uses the network features from all the four layers, but removing the edges across different layers. It tests how the cross-layer connections in the hierarchy contribute to the classification.Method IV uses the volumetric features  from the bottommost layer Method V uses volumetric measures from all four layers. It tests if the volumetric features obtained from the hierarchy can achieve similar classification performance as the hierarchical network features.The results are summarized in Combining the results from Our proposed hierarchical network features in Method I outperform the conventional volumetric features in Method IV. The advantage may come from using both regional interactions and the hierarchical structure.To demonstrate the benefit purely from using the regional interactions, the same atlases in the hierarchy are applied to volumetric features as in Method V. It can be seen from To demonstrate the benefit purely from the hierarchy, we compare the classification performance of the single-layer network features in Method II and the four-layer network features in Method I. The advantage of the four-layer structure is statistically significant over the single-layer. Moreover, the result that Method I statistically outperforms Method III indicates the necessity of using the cross-layer edges in the network.It is noticed that different ratios of training and test partitions may lead to a variation in the classification accuracy. To reflect the influence of this factor, we test seven different numbers of training samples, occupying It is worth noting that the influence of different ratios of training-test partitions on the classification result is often ignored in many existing works. One possible reason is that a Leave-One-Out validation is used when the size of the data is small. This often leads to the use of more than The classification performance of our proposed classification scheme is compared with other six possible schemes shown in To clarify the settings of our experiment, the Laplacian embedding used in P7 is described as follows. The embedding is applied on a connection graph that shows the neighboring relationship of the subjects. Based on the connection graph, the distance between two subjects is computed as the shortest distance between the corresponding two nodes in the graph. This distance is used to construct the adjacent matrix and Laplacian matrix used in the Laplacian embedding. The Laplacian embedding in our experiment is different from the one in The classification results are summarized in Although the proposed scheme P1 achieves the best classification performance, the difference between P1relative progression speed of the disease in different ROIs of the same subject, which eliminates the impact of personal variations. On the contrary, the conventional methods study the absolute progression speeds of ROIs among different subjects. Normalizing subjects by the whole brain volume in conventional methods may not completely remove the personal variations.Note that each network feature characterizes the relationship between two ROIs, instead of an individual ROI as in the conventional approaches. Therefore, for the first time, we study the To be an essentially discriminative network feature, the two associated ROIs may satisfy one of the two following conditions:One ROI shows significant difference between the MCI group and the normal control group, while the other ROI is relatively constant with respect to the disease. Therefore the correlation between these two ROIs varies over the two groups in comparison.Both ROIs change with the disease, but their change speeds are different over two different groups.The selected features are different for the twenty randomly partitioned training and test groups used in Section “Comparison of Features”. In our network design, each edge represents the correlation or the “similarity” between a pair of ROI nodes. Pearson correlation is just one of the possible similarity measurements. By viewing Pearson correlation as an inverse distance, it is straightforward to include other commonly used distance metrics, e.g., the Euclidean distance, the Using (4) and (5), we test the performance of the three alternative metrics: the Euclidean distance In this paper, we have presented how hierarchical anatomical brain networks based on T1-weighted MRI can be used to model brain regional correlation. Features extracted from these networks are employed to improve the prediction of MCI from the conventional volumetric measures. The experiments show that, without requiring new sources of information, the improvement brought forth by our proposed approach is statistically significant compared with conventional volumetric measurements. Both the network features and the hierarchical structure contribute to the improvement. Moreover, the selected network features provide us a new perspective of inspecting the discriminative regions of the dementia by revealing the relationship of two ROIs, which is different from the conventional approaches. The flexibility to generalize our proposed method has been demonstrated by different distance metrics tested in our experiment.


The influence of the statistical properties of the network on the knowledge diffusion has been extensively studied. However, the structure evolution and the knowledge generation processes are always integrated simultaneously. By introducing the Cobb-Douglas production function and treating the knowledge growth as a cooperative production of knowledge, in this paper, we present two knowledge-generation dynamic evolving models based on different evolving mechanisms. The first model, named “HDPH model,” adopts the hyperedge growth and the hyperdegree preferential attachment mechanisms. The second model, named “KSPH model,” adopts the hyperedge growth and the knowledge stock preferential attachment mechanisms. We investigate the effect of the parameters  However, in the scientific collaboration network, a new node collaborates with the old nodes to co-author a paper. That the new node joins the network is a process of network construction. Co-authoring a paper is a process of knowledge generation. Therefore, the network construction process and the knowledge generation process can be integrated simultaneously. Furthermore, people tend to create and diffuse knowledge by coauthoring papers in the scientific collaboration systems. In complex network, an edge relates only a pair of nodes. This research technique of scientific collaboration network can not express the information of papers from the viewpoint of complex network, where the nodes represent the authors and the edges indicate the cooperative relationship between them Inspired by the above ideas, we present two knowledge-generation dynamic evolving models among the scientific collaboration hypernetwork by integrating the hypernetwork structure evolution and knowledge generation processes simultaneously. By introducing the Cobb-Douglas production function The remainder of our paper is organized as follows. In Sec. II, the knowledge-generation dynamic evolving models are given. In Sec. III, we investigate the process of knowledge generation, examine the effect of the different parameters Scientific research collaboration is a process of absorbing each other's knowledge and co-creating new knowledge. In economics, the Cobb-Douglas functional form of production functions is widely used to represent the relationship of an output to inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs In the literatures on knowledge transfer models, knowledge has been represented in several ways, e.g., by a stock Let Initial condition: The hypernetwork consists of Determination of the local-world: Select Hyperedge growth: Add a new hyperedge encircling a newly added node and Hyperdegree preferential attachment: Choose Knowledge generation: Suppose that the knowledge stock created by the new hyperedge The HDPH model adopts the hyperedge growth and the hyperdegree preferential attachment mechanisms. The created knowledge stock is equally divided by contributors. The knowledge generation is based on the growth process of the hypernetwork. The HDPH model could be constructed in the following way:After Initial condition: The hypernetwork consists of Determination of the local-world: Select Hyperedge growth: Add a new hyperedge encircling a newly added node and Knowledge stock preferential attachment: Choose Knowledge generation: Suppose that the knowledge stock created by the new hyperedge The KSPH model adopts the hyperedge growth and the knowledge stock preferential attachment mechanisms. The contributor's knowledge increases by an amount proportional to the contributor's owned knowledge stock. The knowledge generation is based on the growth process of the hypernetwork. Meanwhile, the growth process of the hypernetwork depends on the knowledge stock. The KSPH model could be constructed in the following way:After The evolving process of the above two models may be divided into two stages. The first stage generates an initial hypernetwork for local-world evolving process, which contains In order to investigate the effect of the parameters We analyze the knowledge stock distribution of the two models with different parameters For the HDPH model, not all knowledge-stock distributions for For the KSPH model, all knowledge-stock distributions for et.alThe hyperdegree distribution of HDPH model can be theoretically analysed by the mean-field theory. The analytic result indicates that the hyperdegree distribution is independent of the local-world size e ,  see . Zlatić The KSPH model considers that the evolution of the hypernetwork structure will be affected by the knowledge stock. The growth process of the hypernetwork depends on the knowledge stock. Therefore, the hyperdegree distribution of KSPH model is difficult to be theoretically analyzed. We numerically investigate the hyperdegree distribution The numerical simulations of the hyperdegree distribution The knowledge generation and diffusion in the networks often comes with the network structure evolution. By integrating the hypernetwork structure evolution and knowledge generation processes together, we present two knowledge-generation dynamic evolving hypernetwork models (HDPH model and KSPH model). The two models are not based on a static perspective as was the configuration model, but on a dynamical mechanism to construct the hypernetworks. The HDPH model adopts the hyperedge growth and the hyperdegree preferential attachment mechanisms. The created knowledge stock is equally divided by contributors. The KSPH model adopts the hyperedge growth and the knowledge stock preferential attachment mechanisms. The contributor's knowledge increases by an amount proportional to the contributor's owned knowledge stock. Furthermore, the knowledge generation process is simultaneous with the hypernetwork structure evolution.We investigate the effect of the parameters In addition, we also analyze the knowledge stock distribution of the two models with different parameters The hyperdegree distribution of HDPH model can be theoretically analysed by the mean-field theory. The hyperdegree distribution of HDPH model follows a power-law distribution with exponent Firstly, in this work, we introduce the Cobb-Douglas production function in economics to the knowledge generation process. In economics, the Cobb-Douglas production function is applicable to industrial products. We try to use the C–D function to model the knowledge production. Whether it is applicable or not, the Cobb-Douglas form in the knowledge production needs to be tested against statistical evidence in the future work.Secondly, in our models, the knowledge stock's increase of each author is from the overall achievement in a team-based knowledge production process. We propose two knowledge growth mechanisms. One is the created knowledge stock being equally divided by contributors, and the other one is the contributor's knowledge increasing by an amount proportional to the contributor's owned knowledge stock. However, knowledge is different from physical matters. In the real scientific collaboration activities, how to measure the increased knowledge stock of each author is a very complicated problem. Therefore, as another direction of the future work, we need to design a more reasonable knowledge growth mechanism to cater for complicated situation.Thirdly, in this paper, the knowledge has been represented by a stock. At the same time, how to measure the knowledge stock of a paper in the real life is an open question. And when applying the empirical data of the real scientific collaboration hypernetwork to statistically analyse the process of knowledge generation and dissemination, we must address the problem. In the future work, it is a worthwhile problem to make empirical analysis on the knowledge generation and dissemination process in the scientific collaboration hypernetwork.Last but not least, we in this paper have proposed two knowledge-generation dynamic evolving hypernetwork models and studied the knowledge generation process. But the corresponding empirical research about knowledge generation among the scientific collaboration hypernetwork is generally absent. As a complement to this work, we model the real knowledge generation and dissemination cases and statistically analyze the knowledge stock characteristics. Due to the intrinsic intractability of knowledge and knowledge generation, such empirical study is essentially challenging, but this issue is worthy of inquiry in the context of scientific collaboration.File S1(PDF)Click here for additional data file.