This paper introduces an approach for parameters identification of astatistical predicting model with the use of the available individual data.Unknown parameters are separated into two groups: the ones specifyingthe average trend over large set of individuals and the ones describing thedetails of a concrete person. In order to calculate the vector of unknownparameters, a multidimensional constrained optimization problem is solvedminimizing the discrepancy between real data and the model prediction overthe set of feasible solutions. Both the individual retrospective data and factorsinfluencing the individual dynamics are taken into account. The application ofthe method for predicting the movement of a patient with congenital motility disorders is considered. Multidimensional statistics methods, including predicting and dependencies analysis, are required to research complex systems with many random factors –4. In orModeling of biomedical systems provides actual application of mathematical methods and algorithms. This paper studies the problem of locomotor development prediction for people with congenital motility abnormalities. The authors propose an approach to identify the parameters of a statistical predictive model taking into account the available set of individual data.Mathematical methods and information technologies are important tools in modern biomedical research. Together with physicomechanical modeling of physiological systems –7, the sOne of the disadvantages of statistical predictive models is that they are only applicable to an average individual. In order to get a more accurate prediction it is necessary to identify statistical predictive model parameters using data for a concrete person. Using this approach which is known as “individual prediction” method , 17 in mY quantifies the level of locomotor development. In order to calculate Y an expert evaluates 12 different groups of locomotor skills. The expert estimations are then arranged according to the five-point scale and the index Y is defined as the sum of the estimations. Due to the construction algorithm the index Y is defined within the interval . The best locomotor development corresponds to the top boundary of parameter Y and the worst locomotor development corresponds to the lowest value.The motility index Y(t), where t is the patient's age. The process yJ)((t) corresponds to each patient J in the group.The motility index dependence on age for a group of patients is considered to be a random process t and t′, Dy(t) and Dy(t′) are dispersions of Y(t) at the moments t and t′, and M is the expectation operator.To analyze the stochastic process structure the following correlation function is used as follows:The available statistics database contains 157 observations of cerebral palsy patients. The research sample was based on occasional patient visits to a rehabilitation centre during their first nine years of life. Experts determined each patient's motility index during their visits. Detailed information was collected on each patient: medical status of parents and close relatives prior to the individual's conception and characteristics of prenatal and perinatal periods .N = 5) and the complete initial sample of 157 observations was used for calculating the average parameters.Despite the presence of relatively large number of observations, it was only possible to focus on 5 people who were constantly observed during the entire research period. Given the data limitation the study of locomotor skills development was conducted on a group of 5 people (Y(t) is shown in t is the age (in months). t = 15 (months).A scatter diagram of random process When the correlation function is close to one, the process is characterized by a strong dependence between the time slices. This indicates that the process realizations are similar. The similarity is the necessary condition for the application of the proposed method.Individual prediction of motility index is based on the following algorithm. The first step determines the age dependence of the average motility. The consecutive selection method of the exponential terms  is used The individual motility index trend is constructed as bounded from above monotonically increasing function:This paper studies the locomotor skills accumulation process only. The loss of such skills is not taken into account therefore the monotonically increasing assumption could be used. The motility index boundaries are defined by their calculation method (from 0 to 60).Pr is the risk factors during pregnancy and birth that have the highest influence on the motility index, and δr is the correlation between Pr and the motility index.The generalized factor of prenatal and intranatal conditions is introduced as follows:Pr factors being responsible for development delay and, as such, affecting the absolute term value A0J)( is used.The assumption of A0J) identification, Θ0 is the number of real motility index values in the interval of the initial individual observation τ0, yγJ) is calculated using linear approximation of the real motility index dependence at the initial time on the generalized prenatal and intranatal factors for a group of patients. The calculated coefficient μ is used for A0J)( = A0J)(|Φ=0 + μΦJ) and prediction period (next five years). The first period data is used to develop the motility index prediction model while the second period data serve as a test for prediction results .The initial locomotor development dynamics of the observed patient (|Φ=0 = −3.00.Solving the system  gives thμ obtained by the least-squares method [A0J*)( = A0J*)(|Φ=0 + μΦJ*)( = −14.17. The remaining coefficients are A1J*)( = 17.04.The coefficient s method  for the FJ*)((t) = −14.17 + 60.52(1 − et−0.01) + 17.04(1 − et−0.09) is shown in R2 = 0.92.The identified individual motility index trend The proposed method of parameters identification for a statistical predictive model based on data set of patient information can be successfully applied conditioned on the correlation function being close to one. This method is based on multidimensional statistical analyses –4 and inThe application of the method to statistical modeling of medical and social systems resulted in an algorithm which does not require modeling of physical and mechanical processes. The obtained algorithm is based on statistical analysis only. The application of the algorithm significantly improves the prediction accuracy compared to the predictions based on average statistics. The improvement has been successfully demonstrated in an example of individual locomotor development prediction for a patient with congenital motility disorders.The results show the advantages of the proposed method when the predicted index has a significant variation within the group with the prediction interval being larger than the base period.


The simulation results for electromagnetic energy harvesters (EMEHs) under broad band stationary Gaussian random excitations indicate the importance of both a high transformation factor and a high mechanical quality factor to achieve favourable mean power, mean square load voltage, and output spectral density. The optimum load is different for random vibrations and for sinusoidal vibration. Reducing the total damping ratio under band-limited random excitation yields a higher mean square load voltage. Reduced bandwidth resulting from decreased mechanical damping can be compensated by increasing the electrical damping (transformation factor) leading to a higher mean square load voltage and power. Nonlinear EMEHs with a Duffing spring and with linear plus cubic damping are modeled using the method of statistical linearization. These nonlinear EMEHs exhibit approximately linear behaviour under low levels of broadband stationary Gaussian random vibration; however, at higher levels of such excitation the central (resonant) frequency of the spectral density of the output voltage shifts due to the increased nonlinear stiffness and the bandwidth broadens slightly. Nonlinear EMEHs exhibit lower maximum output voltage and central frequency of the spectral density with nonlinear damping compared to linear damping. Stronger nonlinear damping yields broader bandwidths at stable resonant frequency. The growing demand for autonomous and self-powered sensors  has resuMost of the developed linear and nonlinear resonant energy harvesters have been tested and characterized under harmonic excitations; however, real environmental vibrations do not contain one steady single frequency but the vibration is rather distributed over a broad band of frequencies and is random in nature. The power spectral density (PSD) of the acceleration along the tangential direction of a car tire at a speed of 50 km/h, for example, has a rich energy content in a broad band from 5 Hz to 1 kHz . The vib−5 and 5 × 10−4 g2/Hz , of the errorωeq; that is, the equationFor a stationary Gaussian random excitation with zero mean, the response of the harvester will also be stationary Gaussian with zero mean. The solution of  can be oσz of the relative displacement z(t). Using the method described in  is to be minimized with respect to square of the equivalent frequency ωeq and equivalent damping coefficient term μeq; that is, equationsμeq and the equivalent frequency ωeq.To obtain an approximate solution for the response of the nonlinear harvester, the errore=2ζTωn(zquations∂∂ωeq2E = σz2, and σz of the relative displacement z(t). The assumption of z(t) and μT = 2ζTωn of the linear EMEH where α = 0 and the equivalent frequencyωn of the linear case with η = 0.For the relative displacement ˙2]=σz˙2 –39 in  = S0, the SD of the load voltageFor a Gaussian white noise base excitation μeq = 2ζTeqωeq and μT = 2ζTωn in  the shift in resonant frequency is minimal even if the difference in α is large. This indicates that at the excitation level equal to or less than 0.0001 g2/rad/s, contributions from the nonlinear effects are negligible. The EMEH will be operating in the linear regime with approximately constant resonant  frequency of the SD of the response.For a nonlinear EMEH with combined nonlinear stiffness and damping, the equivalent resonant frequency for a stiffness damping factor of 2/rad/s. With increase in the transformation factor, the peak value of the mean power increases and the optimum load changes.The mean power as a function of load resistance for several values of the transformation factor is shown in Analytical models for linear and nonlinear electromagnetic energy harvesters (EMEHs) for random vibrations have been developed and simulations were performed to predict the behaviour of these harvesters under broad band random excitations. In contrast to harmonic excitation, the simulation results have shown different output responses when linear and nonlinear EMEHs are subjected to broad band random excitation.For linear EMEHs under broad band stationary Gaussian random excitation, the simulation results of the mean power, mean square load voltage, spectral density of the device output, and the harvester bandwidth show the significance of both the transformation and the mechanical quality factors. For larger values of the product of merit the mean power becomes less dependent on the optimum load and the device can be operated off its optimum load condition. The increase of the transformation factor for EMEHs with a small mechanical quality factor required the device to be operated at the optimum load for better performance. Moreover, the optimum load condition under random vibration is quite different from that of harmonic excitations. Higher values of the transformation factor have shown to broaden the bandwidth of the harvester and the bandwidth is dependent on the load resistance in such a case; however, at lower transformation factor, the bandwidth solely depends on the mechanical quality factor and is independent of the load resistance.For linear EMEHs the SD of the load voltage under band-limited random excitation is nonzero only over the input frequency band and is maximum in the vicinity of the natural frequency similar to that of broad band excitation. The mean square load voltage depends on the frequency band of the excitation and the total damping ratio of the harvester. Higher values of the mean square of the load voltage require small values of the total damping ratio. The electrical damping ratio (transformation factor) should be as high as possible for high power generation, therefore for smaller values of the total damping ratio the mechanical quality factor must be increased. The associated reduction in the bandwidth of the harvester must then be compensated by increasing the transformation factor.For nonlinear EMEHs the statistical linearization method was used for modeling under broad band random vibration. The response of nonlinear EMEHs not only depends on the spectral density of the base acceleration but also on the standard deviations of the relative velocity and the relative displacement. Under low levels of random excitation, the contribution from the nonlinear terms is negligible, the linear stiffness and linear damping are dominant, harvesters operate in the linear regime, and the response of a nonlinear device is just similar to a linear EMEH. When these nonlinear harvesters are subjected to higher levels of random excitations to invoke the nonlinear effects, the simulation results have shown that not only the maximum value of the load voltage is increased but also the central (resonant) frequency of the spectral density has been shifted towards higher frequencies. The shift in the central frequency is attributed to the increased stiffness. However, this shift becomes less significant in case of EMEHs with nonlinear damping, since the nonlinear damping term contributes inversely to the resonance frequency. Moreover, slightly broader bandwidths are obtained in the nonlinear regime in comparison to operating in the linear regime. The presence of high levels of nonlinear damping not only increases the bandwidth of the harvester at the expense of decreased peak value of the load voltage spectral density, but it also leads to a stable resonant frequency even at relatively high levels of random excitation.


PeptideProphet is a post-processing algorithm designed to evaluate the confidence in identifications of MS/MS spectra returned by a database search. In this manuscript we describe the "what and how" of PeptideProphet in a manner aimed at statisticians and life scientists who would like to gain a more in-depth understanding of the underlying statistical modeling. The theory and rationale behind the mixture-modeling approach taken by PeptideProphet is discussed from a statistical model-building perspective followed by a description of how a model can be used to express confidence in the identification of individual peptides or sets of peptides. We also demonstrate how to evaluate the quality of model fit and select an appropriate model from several available alternatives. We illustrate the use of PeptideProphet in association with the Trans-Proteomic Pipeline, a free suite of software used for protein identification. N). MS/MS spectra are individually matched to peptides by searching through a database of peptides predicted from the genome of the organism. The way the searches are performed can be constrained using different search parameters, such as the number of tryptic termini (NTT), number of missed cleavages (NMC) or the mass difference of the observed precursor ion mass and the weight of the theoretical peptide (ΔM).In mass-spectrometry shotgun proteomics, the first phase of analysis is the identification of peptides in complex biological mixtures digested by enzymes such as trypsin. Dependent on the peptides in the biological mixture, an experiment will produce a certain number of spectra  and ΔDot. PeptideProphet can be used with any database search algorithm that returns a quantitative score.We will discuss PeptideProphet in the context of two database search algorithms: SEQUEST  and TandN spectra that have been matched to a peptide and we will refer to these spectra as identified spectra.Given a database search algorithm, every spectrum that is observed will be scored against the peptides in the database. For each spectrum, the highest scoring peptide (depending on the scoring criterion) is typically chosen as the best match. The best match is the potential peptide sequence that generated its corresponding observed spectrum. Thus, we have XCorr > 2.5) does not reflect the quality of the identification. Such a rule may accept too many incorrectly identified spectra. Thus, statistical inference is needed to model the presence of noise.The necessity of PeptideProphet arises because the spectra are subject to noise making it difficult to determine if the peptide that it is matched to is correct. The spectrum itself is generated from a peptide sequence and peaks can be missing or reduced in intensity. Because the spectrum that is being generated is subject to noise the database-based criterion will vary when comparing theoretical spectra to observed spectra. Additionally, when searching the database, the correct peptide sequence may be absent. Because of this noise, how do we determine confidence in an identified spectrum? Traditional standards  Evaluation of confidence in individual identified spectra using the posterior probability.(b) Evaluation of confidence in sets of identified spectra: produce a cutoff on the scores to determine a set of correctly identified spectra while controlling the False-Discovery Rate, defined as the expected proportion of false positives.We will first discuss the basic version of PeptideProphet and then discuss the three extensions.This dataset uses the first LC-MS/MS replicate file from the Western Consortium of the National Cancer Institute's Mouse Models of Human Cancer . The datThis dataset uses spectra generated from a linear ion trap Fourier transform instrument that was published in . In partEvery statistical approach requires the definition of the following components in the problem:experimental unit where we have N observed spectra with N being generally large (in the thousands or more). Since the number of spectra N is typically very large, the identified spectra can be viewed as the underlying population.1. PeptideProphet works with the observed spectra as the S is called a test statistic because it is the function of the observed experimental unit that is being used to answer our hypotheses.2. An observed score is interpreted as a test statistic. In statistics the summarized score 3. PeptideProphet assumes that the test statistic comes from a mixture of two distributions: one from the distribution of correct identifications, and the other from the distribution of the incorrect identifications. The distributions may be characterized by a few parameters (parametric) or many parameters (semi or non-parametric).hypotheses for each identified spectrum. Let i Tbe the true status of identified spectrum i where i T= 0 indicates that the identified spectrum was incorrectly identified and where i T= 1 indicates that the identified spectrum was correctly identified. We then wish to compare:4. The goal of PeptideProphet is to test two competing 5. Inference: confidence is determined for individual spectra or sets of spectra.• If the researcher is interested in a set of spectrum identifications, the False Discovery Rate should be controlled.δ, is the expected proportion of all scores i S>δ that are truly incorrect . This situation is synonymous to performing N multiple hypothesis tests where P (R > 0) is assumed to be 1 when we perform many tests (N is large). The False Discovery Rate is the expected proportion of incorrectly rejected null hypotheses out of the total rejected hypotheses. For a given cutoff if we were to repeat the experiment an infinite number of times and use the same cutoff each time the expected False Discovery Rate is the average proportion of incorrectly identified and accepted spectra out of the total number of incorrectly identified spectra.We determine the confidence in a set of spectra by controlling the False Discovery Rate. The False Discovery Rate, given a cutoff δ is the expected proportion of all truly incorrectly identified spectra that are considered to be correctly identified. From the terms in Table An alternative confidence rate that is rarely used is the False Positive Rate (FPR). The False Positive Rate, given a cutoff i sto be considered significant. It is represented by i sat a single point but examines the False Discovery Rate of all possible scores. Unlike the False Discovery Rate, the q-value is a monotonic quantity with respect to the score cutoff.Many users prefer the q-value which is the minimum False Discovery Rate required for a score f scores . This co• If the researcher is interested in specific spectrum identifications the posterior error probability is most commonly used as it quantifies the confidence of a single identified spectrum.PEP. In other words using a probability model for iS, we can find the probability of an identified spectrum being incorrect given its test statistic. Note that we can also calculate The posterior error probability represents (locfdr) ,11.i sis the ith observed score then the p-value represents i sassuming that the ith identified spectrum was incorrectly identified. The p-value is similar to the FPR in that the p-value is the probability of observing a score equal to or greater than i sassuming that it is one of the N0 truly null hypotheses.Alternatively the p-value can be used. If XCorr, ΔCn, logDot, Δdot, etc.), PeptideProphet rescores the identified peptide with a discriminant function, using the database-based criterion as the covariates for fitting the discriminant function. The goal is to fit a function that separates correct scores from incorrect scores. If i Sis the summarized score for the ith identified spectrum from a SEQUEST search result, a discriminant function produces a linear function f:First each spectrum  is observed and potentially identified using a database-based criterion .In the basic version of PeptideProphet the i Sto parameters via a sampling distribution of the test statistic under Hi 0and aiH. All scores iS's are independent and identically distributed (iid). The sampling distribution of i Sis assumed to follow a Normal distribution if the identified spectrum is correct (i T= 1) and Gamma distribution if the identified spectrum is incorrect (T = 0). Notationally we have that π0 is used to represent the overall proportion of incorrect identifications of identified spectra in the population. This formulation results in a 2-group mixture model similar to what is established by Efron [PeptideProphet relates scores by Efron  where weThe last equality is due to the fact that all scores are independent and identically distributed (iid). Due to different discriminant functions being used for each charge, a different sampling distribution and set of parameters are produced for each precursor ion charge (we will refer to this simply as the charge).M (delta mass) that can be used to improve the estimation of the sampling distribution of the identified spectra [There may be additional information available, such as the NTT (number of tryptic termini), NMC (number of missed cleavages), and Δ spectra ,12,13. F spectra . This isTf=0, NTT, TfNMC=0, , Tf=0, MΔ, TfNTT=1, , Tf=1, NMC, and Tf=1, M Δare discrete. It is assumed, conditional on the identified spectrum being incorrect or correct, that the members of  are independent, as shown above.Note that the density functions of 0, μ, σ, α, β, and γ) and second to estimate the confidence in the correctness of an identified spectrum. The EM-algorithm iterates between two steps, called the E-step and the M-step in order to estimate the value of model parameters. With a large enough set of identified spectra (say 100), the EM-algorithm will always converge [0, μ, σ, α, β, and γ.PeptideProphet is considered an Empirical Bayesian approach because it uses each identified spectrum twice: once to estimate via the Expectation-Maximimzation  algorithconverge . The algi sand its correctness status iT, usage of Bayes Theorem yields π0 over the sum of the Gamma and Normal densities scaled by π0 and 1 - π0 at score is.In the E-step, given the estimated values of the model parameters, the probability of each score being correct (or incorrect) is calculated. Given a single observed score is, the model parameters are re-estimated by finding the values with the maximum likelihood. The estimate of π0 is μ and σ2 are:In the M-step, given estimated membership probabilities γ is simply the minimum of the scores is, i = 1, ..., N. In order to estimate α and β let α and β areFor the Gamma distribution, the estimate of ε where ε is a small number, such as 0.0001. The algorithm then outputs estimated parameters of α, β, δ, μ and σ, as well as the estimate of π0 (denoted with hats when estimates). The algorithm is detailed in Figure Due to the speed of the algorithm in working with only two mixture components, the process of the E and M-step can be iterated repeatedly until the model parameters do not change by a specified Deviations of the assumptions, or a low number of identified spectra can lead to an inadequate or unstable model fit and incorrect conclusions. This can be diagnosed by visual inspection, and also by the bootstrap. We recommend using visual inspection over goodness of fit tests as tests do not explore the specific fitting issues that may influence subsequent inference of the identified spectra. In fact goodness of fit tests simply attempt to summarize the goodness of fit into one summary statistic whereas we are typically interested in the fit at certain locations of the mixture distribution. There are several visual attributes of the mixture distribution that researchers should be aware of and some remedies for them.Do the empirical scores follow the fitted curves well? Particular attention needs to be paid to the tails of the distributions, especially the right tail of the distribution of scores of incorrect identifications (red) and the left tail of the distribution of scores of correct identifications (blue). This is often of most interest to researchers as the identified spectra in these regions are considered to be borderline correct or incorrect. In the case of Figure Do the curves highly overlap? Although high overlap does not necessarily indicate a poor fit it will lead to smaller sets of confidently identified spectra. Overlaps that occur in situations of highly constrained searches can be remedied with techniques in later sections. Overlap in the case of a small number of spectra  where each is of size N from the original dataset. At least 100 to 500 bootstrapped samples are recommended. For each bootstrapped sample b, we can refit the PeptideProphet model to receive bootstrapped estimates of μ, the bootstrap bias estimate is B increases the bias does not move towards 0. The bootstrap variance estimate is defined as Bootstrapping can be performed by sampling with replacement π0, μ, and σ are shown in Figure μ and σ showing how unstable the estimates for the Charge 2 distribution given the small number of identified spectra.Three hundred bootstrapped samples for the Human Plasma data for charges 2 and 3 were performed and the bootstrapped estimates for B bootstrapped samples to the original estimates. The experimenter may also view the deviations that occur between the original sample and a single bootstrapped sample. Although a histogram of both samples would suffice, a quantile-to-quantile plot is an easy-to-read plot that exemplifies the deviations between the two plots. The quantile-to-quantile plot plots the quantiles of one distribution versus the matched quantiles of the other. For example if there are 10 values in two datasets the quantile-to-quantile plot would display the 10, 20, 30,..., and 100th percentiles of one distribution matched with the respective 10, 20, 30, ..., and 100th percentiles of the second distribution. Distributions that are alike should result in a quantile-to-quantile plot that is linear. Deviations from linearity at different quantiles in the plot imply differences between the two distributions at those associated quantiles. Although no quantile-to-quantile plot will be perfectly linear the plot should not deviate much at the center and right portions of the plot as the accuracy of the estimated confidence of identified spectra relies heavily upon a good fit at these locations. The quantile-to-quantile plot for Charge 2 in Figure The mean squared error summarizes the overall deviation of parameter estimates from δ is concluded to be correct. In many experiments we are interested in the statistical properties of the list of spectrum identifications with scores above δ.In order to determine the correctness of the spectrum identifications, a decision rule is defined where any spectrum identification with a score above t is the average of the estimated local false discovery rates of identified spectra with scores greater than In order to estimate the False Discovery Rate given a decision rule cutoff two approaches may be used. Because all scores are assumed to follow the same fitted distribution the False Discovery Rate can be estimated with (S>t|T=1). This ca(S>t|T=1),11. The t can also be estimated using the area under the fitted frequency curve of the distribution of scores for incorrect identifications as seen in Figure The False Positive Rate for a cutoff ρ requires the estimation of the False Discovery Rate at every point i sfrom i = 1, 2, ..., N. The q-value for a point ρ is the minimum False Discovery Rate among all points i ssuch that i s≤ ρ. The estimated False Discovery Rate can be found using the model-based estimates or by interpreting each posterior error probability as a local false discovery rate. The q-value is often useful if a monotonically increasing error rate is desired for decreasing cutoff values. For example, in the case of Figure The estimation of the q-value at a specific point We now discuss the estimation of the posterior error probability and the p-value. These measures are properties of a single spectrum and are synonymous to performing a single hypothesis test. In Figure i T= 0 (our hypotheses of interest) given its test statistic is According to Bayes Theorem the posterior probability of is.The p-value is estimated as PEP). The advantage of the p-value is that it only requires the use of the distribution of scores for incorrect identifications as it ignores the distribution of scores for correct identifications. Notice that in Figure The posterior error probability may be preferred over the p-value because it also yields an estimate for the probability of an identified spectrum to being correct  decoy peptide sequence. Hits where the best incorrect decoy peptide sequence is found to be the match are used to estimate the FDR.In the separate Target-Decoy strategy each spectrum is searched once in the forward database and searched again independently in the decoy database. The distribution of scores from the peptides identified via the decoy database is used to estimate the form of the distribution of incorrectly identified spectra. This approach ignores competition between forward and decoy sequences.same database. The decoy scores are forced to only contribute to the estimation of α, β, and γ of the Gamma distribution. PeptideProphet accomplishes this by assuming any decoy match has a posterior error probability of 1. In the EM-algorithm as described earlier, i pfor any decoy is assumed to be 1 at every iteration. The semisupervised version of PeptideProphet helps estimate the parameters of the Gamma distribution better and thus indirectly improves the estimation of π0, μ, and σ as well. As seen in Figure The semisupervised version of PeptideProphet utilizes the concatenated Target-Decoy strategy by simply combining the target and decoy sequences into the The quality of fit of the Gamma and Normal distributions may rely on how the database is searched (constrained versus unconstrained search) or the search algorithm that is used . As is th, the distribution of scores for incorrect identifications is estimated using n0 is the number of decoys, K is the Normal density function, and i Sis the score of decoy i. The greater the h the smoother the function while the smaller the h the more rough the function. The parameter h can be specified using any method such as using the mean integrated square error. Cross-validation can be used as well. The distribution of scores for correct identifications is estimated in the same fashion as well but using only forward scores. Pseudocode of the semiparametric approach can be seen in Figure One approach is to estimate the distributional forms using a kernel density (semi-parametric) approach  as opposAn example of this approach can be seen in Figure To avoid overfitting, this approach should only be used in the cases of strong deviations between the fitted distributions and the observed scores, such as the parametric fit (dashed-lines) in Figure Overlap in the distributions of scores of correct and incorrect identifications can be due to a suboptimal scoring function, which does not discriminate well between the properties of correct and incorrect identifications. This often occurs in cases of constrained searches where the database that is searched is much smaller than the unconstrained search space that was used to find the coefficients in the fixed discriminant function. For additional information on constrained versus unconstrained searches, see . A solutβ's from Equations 1 or 2 by extracting identified spectra with high posterior error probabilities and identified spectra with low posterior error probabilities. When retraining the β's the algorithm will randomly sample identified spectra with low posterior error probabilities I times and produce I different estimates. The average of these I β's is the updated β. This entire step is repeated by re-estimating posterior error probabilities and updating β until the β do not change by a small ε.Pseudocode of the adaptive version of PeptideProphet can be seen in Figure The improvement of the adaptive discriminant function over the fixed discriminant function for the Controlled Mixture dataset in a constrained search space is displayed in Figure best peptide sequence match, use the new discriminant function to also rescore peptide sequence matches that ranked close to the best peptide sequence match). Every time a new discriminant function is estimated .The Trans-Proteomic Pipieline (TPP) is an open source program developed at the Institute for Systems Biology designed for complete proteomic analysis starting from spectrum identification to protein identification and quantification and can be downloaded from /sashimi/. In thisWe present an example using the Human Plasma dataset where the spectra are searched through Tandem with the k-score plugin with TPP version 4.4. PeptideProphet automatically models all precursor ion charges and outputs the probability of correct identification. A mixture model using the Normal for the distribution of correct scores and a Gumbel distribution for the distribution of incorrect scores.PEP), so numbers close to 1 here are desirable. The remaining columns list, in order, the spectrum label, Tandem expect score, the fraction of ions matched, the peptide sequence match, the protein match, and the calculated neutral peptide mass. In this example any protein label with a "rev" is a decoy. Each hyperlink will lead to additional information. For example, clicking on a peptide sequence will lead to a BLAST search or clicking on the fraction of ions matched will display the observed spectrum.In Figure Clicking on 0.7664, or the ninth entry "2b_plasma_0mM_C1.00024.00024.1" on the identified spectra list, results in information of the model fit by PeptideProphet in Figure We will now discuss how to use the information in Figures PEP values under the "Min Prob" column. In other words, "Min Prob" represents the minimum posterior probability of being correct in order to conclude that an identified spectrum is correct. For example, a "Min Prob" of 0.95 implies that only identified spectra with PEP's lesser than 0.05 are considered correct or that (1 - PEP) must be greater than 0.95 to be considered correct.1. False Discovery Rate: estimates of the False Discovery Rate can be obtained three ways. In the upper-right hand corner of Figure 0) is 0.04 which yields an estimate of π0 as 0.96. The Normal's (Gaussian) estimated mean μ is 2.6 with an estimated standard deviation σ of 1.90. The Gumbel's estimated G μparameter is -1.16 with an estimated β parameter as 0.76. Alternatively, the expected value (mean) of the Gumbel is -1.16 with a standard deviation of 0.98. If the experimenter is not interested in NTT, NMC, and ΔM, for a cutoff score t, the estimated FDR can then be estimated by P(S >t|T = 0) is found using the Normal distribution and P(S >t|T = 1) is found using the Gumbel distribution. Suppose the experimenter wanted to restrict the FDR calculation to identified spectra with only 0 missed cleavages. According to the output in the distribution of correct scores, a randomly selected correctly identified spectra has a 0.926 probability of having 0 missed cleavages and a 0.074 probability of having 1 to 2 missed cleavages. For the distribution of incorrect scores, probabilities are 0.404 and 0.596 for 0 and 1 missed cleavages respectively. The estimated FDR would then beA second approach is to use the estimated model parameters in Figure The calculation takes into account that among the correctly identified spectra, it is estimated that a majority of the identified spectra have 0 missed cleavages.t and then to calculate A third approach of estimating the False Discovery Rate is to download all posterior probabilities, convert them to posterior error probabilities  by taking the complement, define a cutoff point 2. False Positive Rate or p-value: using the Gumbel's estimated parameters, the false positive rate can be found by looking at the tail area.δ can be calculated by estimating the False Discovery Rate at the score value of every identified spectra and then by finding the minimum False Discovery Rate among all scores 3. q-value: the q-value at a specific point NTT, NMC, and ΔM. If the experimenter was interested in the posterior error probability of a score independent of NTT, NMC, and ΔM, this can still be calculated using the estimated model parameters.4. Posterior Error Probability and Local False Discovery Rate: these are most easily found by finding the complement of the values in the first column of Figure All inference for semisupervised and semiparametric PeptideProphet cases are identical. Inference would be identical for the adaptive version of PeptideProphet but it is not implemented in TPP at this time but is available from the authors upon request.i is indexed from 1 to the number of peptides linked to the protein in question.Following the execution of PeptideProphet the next step in analysis is often the identification of proteins present in the sample. In this different analysis, the experimental unit changes from being a spectrum to a peptide. TPP can be used to run ProteinProphet, a computational algorithm that can utilize PeptideProphet's estimated probabilities to determine the probability for the presence of proteins in two steps . In the PeptideProphet is available for use on the Trans-Proteomic Pipeline with many other database search tools . The statistical approach of PeptideProphet is generalizable to any database search algorithm that returns a quantitative score for each identified spectrum.μ and β is another common distribution used for the distribution of scores of incorrect identifications. A generalization of the Gumbel distribution is the Extreme Value Distribution. Additional information, such as the NTT, may be incorporated into the summarized score by using a different machine learning approach instead of a discriminant function. Quantities like the NTT were left out of the summarized discriminant score due to its discrete nature. For example, the logistic regression function would allow discrete and continuous covariates to be transformed into a single summarized score while separating identified spectra with T = 0 from identified spectra with T = 1.Although we used the Gamma and Normal distributions to model the components of the PeptideProphet model, there are no limitation to the choice of parametric distribution for describing the distributions of scores for incorrect and correct identifications in PeptideProphet. The Gumbel distribution, with parameters The Target-Decoy approach used in this manuscript is an approach that pioneered the use of decoys for the estimation of the False Discovery Rate and its results are often compared to other techniques . For thek0 normal distributions (that may have different means and variances) and the incorrect distribution is represented by a separate mixture distribution of k1 normal distributions. Parameters k0 and k1 are unknown. Each score i sis a member of either the overall correct or incorrect distributions, but are then further assigned as a member to one of the sub-components of the mixture representing the correct or incorrect distribution. Gibbs sampling is used to estimate the forms of the sub-components . Although the variable component and kernel methods perform similarly there are minor computational and modeling issues to consider [only for estimating the negative distribution. The advantages of the kernel approach are that: (1) The variable component method is much more computationally intensive and more complicated (and thus the Kernel Estimation is less intensive), (2) The variable component method requires the specification of priors, and (3) Kernel estimation is very well known and commonly used.An alternative approach which relaxes the parametric assumptions is the variable component approach which uses an unknown mixture of Gaussians to represent the incorrect and correct distributions of scores . The corconsider . The advThe authors declare that they have no competing interests.K.M. implemented the statistical analysis framework, analyzed the datasets and wrote the manuscript. O.V. supervised the statistical aspects of the work, and wrote the manuscript. A.N. supervised the statistical and the mass spectrometry-based aspects of the work.


Humans frequently engage in arbitrary, conventional behavior whose primary purpose is to identify with cultural in-groups. The propensity for doing so is established early in human ontogeny as children become progressively enmeshed in their own cultural milieu. This is exemplified by their habitual replication of causally redundant actions shown to them by adults. Yet children seemingly ignore such actions shown to them by peers. How then does culture get transmitted intra-generationally? Here we suggest the answer might be ‘in play’.Using a diffusion chain design preschoolers first watched an adult retrieve a toy from a novel apparatus using a series of actions, some of which were obviously redundant. These children could then show another child how to open the apparatus, who in turn could show a third child. When the adult modeled the actions in a playful manner they were retained down to the third child at higher rates than when the adult seeded them in a functionally oriented way.Our results draw attention to the possibility that play might serve a critical function in the transmission of human culture by providing a mechanism for arbitrary ideas to spread between children. When learning novel skills from adults children will replicate all of the actions demonstrated to them, including those having no apparent purpose or causal function McGuigan and Graham The strong propensity for children to absorb and repeat the behaviors of adults is argued to be fundamental to the proliferation of cultural practices and traditions To test this we adapted the diffusion chain technique employed by McGuigan and Graham Further, psychology as a discipline has been criticized for focusing data collection on an overly limited sample of the world's population As predicted, preliminary analyses revealed that there were no significant differences in the responses of the Brisbane and Colombo children across any of the dependent variables. All subsequent analyses were thus conducted collapsed across communities. Further, regardless of chain position, for each condition there were no significant differences in children's production of the disconnected and connected actions or in their success opening the boxes. Thus, in order to increase statistical power data was collapsed to form one overall measure where a score of 7 indicates perfect replication of the adults initial demonstration (3 disconnected actions+3 connected actions+successful box opening).F  = 177.99, p<.001, partial η2 = .93 (see p<.001 for both), with children in the Playful condition also producing significantly more actions than those in the Functional condition (p = .046).The first step in the primary analysis was to establish whether or not social learning of the actions from the modeling adult occurred. Demonstrating that it had, a one-way ANOVA with condition  as the between-groups factor and overall score as the dependent variable was significant,  .93 see . AlthougF  = 35.22, p<.001, partial η2 = .74, and F  = 36.81, p<.001, partial η2 = .60 respectively. Critically, indicating different rates of retention, the Condition X Chain Position interaction was also significant, F  = 10.64, p<.001, partial η2 = .46.Having established that children first in the Functional and Playful chains had socially learned the actions the next step was to evaluate whether the actions were transmitted at different rates through the chains. In order to do this, a repeated-measures ANOVA was run with Condition  as a between-subjects factor and Chain Position  as a within-subjects factor. The main effects for Condition and Chain Position were significant, First Child in Chain analysis reported above revealed condition-based differences in children's responses to the adult model. To further clarify the Condition X Chain Position interaction a series of post-hoc independent-samples t-tests were conducted comparing the responses of children in each condition at the second and third positions of each chain. At the second position in the chain children in the No Demonstration Control condition produced significantly fewer actions  than children in the Functional condition , and children in the Playful condition . The difference between children in the Functional and Playful conditions approached significance, t(18) = 1.87, p = .077.The t(18) = 3.30, p = .004], or children in the No Demonstration Control condition . There was no difference between children in the Functional and No Demonstration Control conditions, t(16) = 1.20, p = .249. Thus, in contrast to those in the Playful condition, by the third generation, children in the Functional condition were no longer producing the target actions at rates distinct from those who were not exposed to them in the beginning.For children at the third position, those in the Playful condition produced significantly more actions  than children in either the Functional condition [M = 1.50, SD = 1.43, Children have been consistently shown to copy all of the actions used by an adult when solving a novel task, even when the acts clearly have no causal relevance to the demonstrated outcome and even when they may actually compromise success. And they have been demonstrated to do so from early in ontogeny, in atypically developing populations and from wide-ranging cultural groups  We reasoned that the previously demonstrated lack of children's over-imitation of other children might be attributable to the nature of the initial adult demonstration. That is, when an adult seeds the target action in the first child it is typically done in a serious, pedagogical manner. This might facilitate adult-child transmission Although there was some deterioration in the exhibition of the irrelevant target actions from the first to the third child in both experimental conditions, the loss was greater for children in the Functional condition. Indeed, by the third child in each Playful chain, 8 of 10 children still exhibited at least one of the disconnected actions and 7 children exhibited at least one of the connected actions. In stark contrast only 2 children in the Functional condition produced a disconnected action and only 2 produced a connected action . Framing the initial demonstration as ‘playful’ thus appears to facilitate the retention and transmission of redundant actions. A limitation of this work is that we did not directly code children's behavior when interacting with each other, and hence we cannot unequivocally claim that a playful attitude facilitated transmission of the irrelevant actions. Future research is thus needed to definitively establish what aspects of child-child interaction lead to irrelevant actions being passed on and adopted.According to the contact principle mechanical interactions cannot occur at a distance, something that even very young infants are sensitive to. Because they are less likely to be misinterpreted as having a casual connection to the target outcome, Lyons et al. It is also notable that in order to emphasize their non-serious nature and to circumvent the need for narrative to be transmitted as well as actions, children in the Playful condition were given toy objects whereas those in the Functional condition were not. It is thus possible that the results we report are attributable to the different objects used. However, this seems unlikely. Half of the children in the no demonstration control condition were given one of the playful objects to use; yet not one of these children spontaneously produced any of the irrelevant actions. Nonetheless, by virtue of their very nature, the car and cow have pre-established affordances as play objects and this could have primed children's reactions. Future research is thus needed to determine if children will respond in the same way as those in the current study if they are modeled playful actions on unfamiliar, ambiguous objects.It has been argued that children acquire new skills and behaviors by copying adults and older peers who are perceived as being more knowledgeable The notion that play serves to place irrelevant actions in a social frame has wider implications for existing views on over-imitation. It has been argued that this phenomenon stems from a motivation to be like and be liked by others Children often incorporate elements of the lives of the adults around them when they play: That is, they bring part of their culture in The participants' parents provided written informed consent and the Behavioural & Social Science Ethical Review Committee of the University of Queensland specifically approved this study (Application #2009001642).M = 53.5 months; SD = 3.4 months; Range = 48 months to 59 months) from Brisbane, Australia participated in this study. All children tested were White and lived in metropolitan suburbs surrounding a large university. An additional two children were tested but excluded from the data set as a result of experimenter error. Both were first in No Demonstration control condition chains. Other children who subsequently served as the first child in the relevant chains replaced these children. Forty-two (21 boys) similarly aged children  from Colombo, Sri Lanka also participated. Almost all the Sri Lankan children were Sri Lankan, an island that classifies as part of the South Asian subcontinent. Three children were of Indian origin, and one child was half White but had lived in Sri Lanka for most of her life.Forty-two children (24 boys) aged between 4 and 5 years , and two for the Playful condition – a toy cow and a toy car. It was necessary to use different objects across conditions in order to emphasize the playful nature of the latter while avoiding the need for verbal descriptions to be passed from child to child of what the objects were or how they were to be employed. The objects were used evenly across children and boxes in their respective conditions.Two similar opaque wooden boxes (19.5 cm×12.5 cm×6.5 cm) were used see . Each coAll children were tested in a quiet area of their childcare center away from any activities or other children. Children were randomly allocated to one of three conditions. Across all conditions the adult acted in a warm and friendly way, engaging the children with appropriate levels of eye contact.‘watch me and then you can have a go’. She then slowly and deliberately performed one of two distinct sequences  of irrelevant disconnected actions and irrelevant connected actions . This was followed by the action that disengaged the hidden mechanism and opened the box. When the adult performed the actions she included verbalizations that were either descriptive or were intended to echo the sounds being made by the object . Her actions were modeled in a way that was intended to engage the child via ostensive communicative cues ‘now it's your turn’. If necessary the child was given generic prompts . This phase was terminated when the child either opened the box or after 10 minutes had expired.Child A (the first child in the diffusion chain) was asked to sit to the side of the adult demonstrator so that both were facing one of the boxes. The demonstrator took the object associated with the box and said ‘now it's your turn’ as per Child A. This procedure continued through to the third and final child.After Child A had opened the box, regardless of the means used, Child B was brought into the test area and told to wait while the first child had a second attempt at opening the box. No explicit instructions were given to either child about teaching or imitating, and the experimenter ensured that each child had a clear view of the box, the object, and the actions being performed. After Child A had finished demonstrating, he/she left the test area and Child B was given the box and object and told This general procedure for this condition was identical to the Functional Condition. However, the action sequences shown to Child A were performed by the adult using one of the two play objects. The actions themselves were also modeled emphasizing their playful manner, incorporating knowing looks and smiles ‘lots of boys and girls have had a go, and now it's your turn’. Children were then allowed to manipulate the box as they wished until they either opened the box or after 10 minutes expired. When Child B was brought in Child A was asked to demonstrate ‘what you can do with it’.Child A was shown the box and associated object, and was told, There were three dependent variables for each box: (1) the frequency with which each child produced the disconnected irrelevant actions; (2) the frequency with which each child produced the connected irrelevant actions; and (3) whether or not the box was opened. For the Brisbane children, responses were coded from video recorded during each session. A second observer, blind to the aims and hypotheses of the study and to the child's condition, independently coded a chain from each condition . There was 100% agreement across raters for all dependent measures. We were unable to obtain ethical approval to video the children in Colombo. Coding was therefore conducted in real time by two observers (the third author and a volunteer research assistant). Inter-observer agreement was high for each dependent measure: for disconnected irrelevant actions Cohen's κ = .81; for connected irrelevant actions κ = .80; and for box opening Cohen's κ = .95. As the more experienced of the two coders, data was subsequently based on that taken by the third author.


This paper presents a complete implementation of the Principal Component Analysis (PCA) algorithm in Field Programmable Gate Array (FPGA) devices applied to high rate background segmentation of images. The classical sequential execution of different parts of the PCA algorithm has been parallelized. This parallelization has led to the specific development and implementation in hardware of the different stages of PCA, such as computation of the correlation matrix, matrix diagonalization using the Jacobi method and subspace projections of images. On the application side, the paper presents a motion detection algorithm, also entirely implemented on the FPGA, and based on the developed PCA core. This consists of dynamically thresholding the differences between the input image and the one obtained by expressing the input image using the PCA linear subspace previously obtained as a background model. The proposal achieves a high ratio of processed images (up to 120 frames per second) and high quality segmentation results, with a completely embedded and reliable hardware architecture based on commercial CMOS sensors and FPGA devices. The gad-hoc low-cost platform. In fact the FPGA used to validate the proposal could be considered as a FPGA with medium/low features (Xilinx V2P7).It is usual for the platforms chosen to carry out these algorithms based on sequential programs, in which the only improvements currently available consist in applying multi-threading programming techniques so the power of the new multicore processors may be used. However, from a performance point of view these processing architectures are not so efficient in many applications like the digital processing of images, which normally requires a high number of operations to be handled at the bit level as quickly as possible, by processing in parallel a small number of input samples. Due to the sequential architecture of conventional computers, a notorious amount of operations cannot be performed concurrently. Another issue is the amount of data processed in each instruction, which is limited by the type and width of used communication bus and the image capture board. For this reason, when a large amount of data must be handled, the system performs slowly. This has given rise to solutions that make use of coprocessor systems that handle low level preprocessing tasks, where the amount of data to be processed is high but the operations to be carried out are simple . Our proetc.The detection of both static and moving objects within a captured area is one of the more common tasks undertaken by many computer vision applications. Movement analysis is involved, among other things, in real time applications such as navigation and tracking and obtaining information about static and moving objects within a scene . MovemenWithin the field of image processing previous works have partially developed the processing algorithm of PCA using programmable devices. In  for examad-hoc HW/SW partition of the system is made, without adequately exploring the design space (HW/SW co-design methods).These situations make difficult to segment/divide the hardware processing of the different parts of PCA. For this reason, executing PCA is normally divided between an FPGA and a PC or microprocessor , so thatOne of the main contributions of this work is the FPGA implementation of the complete PCA algorithm on reconfigurable hardware; indeed it is the first work in the literature to do so. Classic sequential execution of different parts of the PCA algorithm has been parallelized. This parallelization has led to the development and implementation of seldom used alternatives for the different stages of PCA. One example is the calculation of eigenvalues and eigenvectors, matrix multiplication in hardware or calculation of a dynamic threshold for detecting moving objects. This latter issue is another major contribution of the paper because the information generated by PCA is used to detect moving objects. In this work, PCA is implemented on an FPGA to detect moving objects within a scene, based on the PCA algorithm. To achieve this, a specifically designed intelligent camera has been implemented based on a CMOS sensor and an FPGA . Thanks The other sections of this paper are as follows: Section 2 sets out the mathematical foundations of the PCA algorithm applied to image processing; Section 3 describes the platform design; Section 4 presents the implementation in VHDL of the PCA algorithm on an FPGA; and finally, Sections 5 and 6 set out the results and present the conclusions respectively.2.Principal Component Analysis (PCA) is a method that is used in different fields, such as statistics, power electronics or artificial vision. The main feature of PCA is the reduction of redundant information, retaining only information that is fundamental .Artificial vision is a good example of a field where the PCA technique can be applied directly, as an image contains a large number of highly correlated variables (pixels). Therefore, applying the PCA technique to image processing allows us to reduce the redundant information of the initial variables and determine the degree of similarity between two or more images by analyzing only the basic features within the transformed space. This last feature is of interest as far as the detection of new objects within the scene is concerned.2.1.Capturing M images to construct a reference model of the scene. We identify each of M references image by Ii ∈ ℜN×N, with i = 1,...M and where it is assumed that the spatial resolution of the images is N × N.N 2 × 1Each image is represented as a column vector of the dimensions Ψ ∈ ℜN2×1 given for:Ii,j is the j  element of Ii image.Calculating the mean image from the M reference images : A ∈ ℜ2×MN (3) whose columns are the vectors Φj = Ij − Ψ (2):Form a matrix Obtaining the covariance matrix, C ∈ ℜ2×N2N from the matrix A (4):Obtaining the associated eigenvalues and eigenvectors of the matrix C. Given that matrix A is of the size 2N × M and generally 2N >> M, to reduce the number of operations that must be performed, the eigenvalues and eigenvectors of (AT · A) are calculated (5):V ∈ ℜ M × M is the matrix of the eigenvectors of AT · A. The eigenvalues of C match up with those of AT · A while the eigenvectors of C are obtained from (6):Obtaining the principal eigenvalues. From the eigenvalues obtained in point 6 the most significant eigenvalues t are selected, using for example, the criteria the normalized root mean square error (RMSE)  are the eigenvectors associated to the eigenvalues 1λ > 2λ > ….> tλ:The transformation matrix The PCA algorithm can be applied to images using the following steps ,10:CaptM, which is the number of captured reference images used to build the background. Theoretically, it is a good idea to employ a high M value that allows different lighting conditions of the same scene to be considered. However the use of a high M number implies a significant increase in computational load and memory storage. The features of external memory in which background images will be loaded, will determinate the size of M. Due to this fact, the bus width of used external memory (128 bits) and according to the results shown in [M = 8 associated to the same scene without moving obstacles and under soft natural lighting variations. Thanks to this size and CMOS features, it is possible to read from the sensor 8 pixels in each clock period.An important issue is the quantification of the value l memory 8 bits anM = 8 has been chosen. Once the transformation matrix Ut has been obtained, the next step is to determine whether in a newly captured image of the scene new objects have appeared. To do this the following steps must be performed:Projection onto the transformed space. The first step is the projection onto the transformed space using (9):Ω ∈ ℜt×1 is characterized by a vector of dimension t , where each component iω represents the contribution of each eigenvector in the representation of Ij.Recovering the projected image. Once the image has been projected onto the transformed space using (9), then Φ̂ ∈ ℜN2×1 is recovered using (10):Determining the existence of new objects in the scene. Finally, the captured image is compared with the recovered image, thus obtaining what is termed the error recovery. If the result of the comparison is above a determined threshold (MDTh) it implies the presence of new objects in the scene (11):MDTh is a dynamically obtained value that is adjusted according to the conditions of the scene.Spatial localization of the detected object. To detect the presence of new objects it is only necessary to apply expression (11). However, if we want to know in which part of the scene the new object has appeared a localization method must be found.. With the aim of reducing the effect of noise, the value of each pixel of the captured image and that of the recovered image is averaged with that of the adjacent pixels by means of a mask of q × q elements. As a result a matrix known as an average distance map is obtained (MDV ∈ ℜN2×2N), where every one of its elements  corresponds to the Euclidean distance between the corresponding average pixels of the original and recovered image (12).According to the results shown in  in our cMDV has been obtained, the next step is to threshold the map so that the new objects can be found easily. To do this, a new binary image is built (BW) where each element is the result of a comparison between each MDV pixel and a MDTh threshold (13):Once the 3.CMOS sensor controller: This block is responsible for implementing image demands to the CMOS sensor such as parameterizing its internal registers according to the desired configuration .Image capture controller: the purpose of this block is to allow the user to select an area of interest within the image from the CMOS sensor.External memory controller: the system is equipped with a 128 MB, SDRAM memory bank that is external to the FPGA. Images from the CMOS sensor are stored in this bank.Communications Controller with the PC: this block controls the communication between the FPGA and the PC. This is used to transmit commands and results.Head Controller: This block is responsible for synchronizing the entire system so that everything works correctly and at maximum speed.PCA algorithm: This block implements the PCA algorithm and its implementation is the most important contribution of this work.The system proposed is based on a high speed CMOS sensor  and an 4.The mathematical complexity of the operations of the PCA algorithm presented in Section 2  makes it impractical to implement them directly on reconfigurable hardware. The proposal and selection of different hardware structures and computing alternatives in order to obtain an efficient solution to resolve these operations on FPGAs is essential for the PCA implementation and, thus, constitutes one of the major contributions of this paper. This section presents the hardware solution found which permits the PCA algorithm to be implemented on an FPGA. 4.1.Ut. This first phase includes five stages:M images (Ψ ∈ ℜN2×1) and the matrix A ∈ ℜN2×M (3).Calculating the mean of the CT ∈ ℜM×M (5).Obtaining the covariance matrix V ∈ ℜM×M and the posterior matrix of the reduced eigenvectors Vt ∈ ℜM×t.Calculating the eigenvectors of the matrix Ut ∈ ℜN2×t from Vt ∈ ℜM×M where t < M.Obtaining the eigenvectors of the matrix Calculating the norms of matrix eigenvectors.The first phase of the PCA algorithm is the generation of the eigenvectors of the reduced transformation matrix 4.1.1.M images in an SDRAM external memory. The block shown in M = 8 images are stored in different memory components (B1). Once the eight pixels have been extracted, one for each image, the mean calculation process is initiated using a set of cascade adders (see B2 6).The hardware architecture that has been developed for this module stores the captured s see B2 . As this4.1.2.CT from matrix A, means the product of two matrices AT · A, must be produced on an FPGA, which entails a complex process. In the case of the PCA the aim is to multiplex the matrix multiplication module using it to: generate the covariance matrix, generate the eigenvector matrix (Ut), project an image onto the transformed space and recover the projected image. Different approaches to the matrix multiplication have been analyzed and developed by the authors [ad-hoc matrix multiplier system based on a semi-systolic array proposed by the authors in [Generating  authors . After tthors in  has been4.1.3.The computation of eigenvalues and eigenvectors represents the greatest computational burden on the PCA algorithm. Different techniques have been proposed for obtaining the eigenvalues of a matrix using specific hardware, all of them based on recurrent methods that look to diagonalize the matrix ,16. Once4.1.4.t eigenvectors is to arrange the eigenvalues and their associated eigenvectors in either ascending or descending order. This step is necessary as the Jacobi method does not generate the eigenvalues in order. To determine t, the largest t eigenvalues are found and then their associated eigenvectors are selected depending on how much bigger than the eigenvalues that have been obtained the user wants them to be (7). In this work, bubble sort has been used as the sorting algorithm [The first step in determining the most significant lgorithm .4.1.5.Ut, according to (6), the matrix A must be multiplied by Vt. To do this, once again the semi-systolic array presented in [To obtain the matrix ented in  is used.4.1.6.Utn according to (15):The eigenvectors obtained in the previous stage do not possess a unit module so they must be normalized (14) Φ̂j it is only necessary to express this matrix in accordance with the squared norm, as shown in (16):To implement in hardware the arithmetical operations shown in expressions (14) and (15) is extremely complex as a consequence of the square root, and it also uses a large amount of resources. To avoid calculating the square root when calculating 4.2.on-line stage. For this to be done, the new captured image is projected onto the transformed space so that it can be recovered later and studied to determine whether or not there is a new object in the scene. To do this the following steps are followed:Subtraction of the mean of the present image: If Ij is the captured image, Φj is obtained.Projecting Φj onto the transformed space and obtaining Φ̂j: With the aim of reaching the maximum concurrence possible when executing (16), first the Determining the recovery error: In this final stage, the degree of similarity between Φj and Φ̂jis evaluated.If there is a new object in the captured image, with respect to the reference scene, it is determined during the on-line stage. With respect to the internal workings of the system shown in Ij is captured and later stored in the external memory so that the system has an initial latency of one image. As explained earlier, once Φj has been obtained the next step is to produce the t). In accordance with the percentage of significant eigenvalues (see (7)), a value of t equals 6 has been decided upon. This reduction introduces a recovery error (ε) (17), after analyzing 1,000 images it could be seen that the induced error is approximately 1%: is used . It is i2norms. As each component of Once the first results from the To perform the division operation on an FPGA, there are basically two possibilities: either design a division unit specifically for that purpose, or use a coordinate rotation digital computer (CORDIC) algorithm . In thisΦ̂j. Once again, to perform this fourth matrix multiplication, the semi-systolic array described in [When the first component of the division has been obtained, the next step to be performed in (16) is to obtain ribed in  is used.4.3.ε) system in reconfigurable hardware (17). It proposes the building of an error recovery map or Map of Distances (MD) that will permit the new objects to be located spatially. The size of this map of distances will coincide with the size of the image, where each of its positions is the pixel to pixel Euclidean distance between Φ̂j and Φj. A new Map of Distances (MDV) will be built in order to reduce the noise effect. The final detection of moving obstacles will be obtained using the dynamic threshold MDTh (11). Calculating MDTh presents difficulties as it must be adaptable and its value depends on both the features of the scene under analysis and the lighting conditions. For this reason, in this section we present a new method for dynamically calculating the threshold that minimizes the false detection of new objects within the scene of interest. Φ̂j and Φj (green blocks). Next the hardware solution implemented in each block of This section presents the solution developed for implementing an identification of new objects from the error recovery (4.3.1.MD is obtained from (18), ε′j being the square of the Euclidean distance between each component Φji ∈ Φj and Φ̂ji ∈ Φ̂j i = 1,....N2 (for images of the size N × N):The Map of Distances MD only requires one subtraction and one multiplication operation, so that with an adder/subtraction block and a multiplier connected in cascade the segmented execution of (18) can be performed.Working with the square of the Euclidean distance rather than the Euclidean distance (17), facilitates the design of hardware associated with this function, as it avoids the need to perform the square root operation. As such, to obtain MD have been generated, the generating of the map of average distances (MDV) can be started. The use of a mask of q × q components is proposed that averages the pixels adjacent to MD, applying a 2D low-pass filter. The components that make up the map MDV are ε′i,wv; i, w = 1,....,N.Once the initial components of q, different sizes applied to different maps MD have been simulated; all of them are fixed point encoded. The size chosen for q is 3, given that it provides the algorithm with a certain degree of robustness and reliability, and few hardware resources are required.To provide a compromise value to the size of mask q × q (3 × 3) on the adjacent pixels the corresponding convolution function is implemented [To implement the averaging function with masks of lemented . To selelemented , evaluatε′i,wv component of the MDV it is necessary to perform a nine component sum backlog and one multiplication for the equivalent factor in fixed point:To perform the convolution between a matrix and a generic mask, nine multiplication operations and eight accumulation operations must be performed for each resulting component. However, when all the coefficients of the mask have been identified, as happens in our case, another way of performing the convolution is according to (19), whereby one that reduces the number of multiplications to one. In this way, to obtain each 4.3.2.MDV) has been obtained, the next step is to analyze the map to evaluate whether or not there are new objects in the scene of interest. To do so, a threshold MDTh is obtained, which, when applied to MDV makes it possible to perform the segmentation and as a consequence detect the presence of new objects. The value of MDTh must be dynamic as its value must adapt, amongst other factors, to changes in light within the scene. In order to obtain this dynamic MDTh different alternatives have been proposed, [f intervals) of the maximum Euclidean distances of each column of the MDV  until it considers that the threshold is situated in the extreme interval and then classifies all the pixels in the image as belonging to the background. The number of histogram intervals (f) has been empirically set at 10, as with this value the developed proposal works correctly.To find a valley, a hardware block has been designed to check the memory of 5.This section sets out the results obtained in detecting new objects with a FPGA running PCA algorithm. All the images presented in this work have been captured by an “intelligent camera” described in .PCA_TOTAL) from the moment the first M images are captured, the total time consumed is given by (20), with From a quantitative point of view, in calculating the execution time of the entire proposal presented in this work , an internal data width of 18 bits (n = 8) and 23 iterations for the Jacobi algorithm the value obtained in clock cycles is:CLK_CAMERA is the signal period of the CMOS sensor’s clock and TCLK the FPGA’s master clock. Clock Camera is generated by the FPGA using a DCM  block. Thanks to this element and a bank register managed for a FSM (finite state machine), both clocks working rightly. To obtain a ratio of the number of images the system processes, if the CMOS sensor’s clock (TCLK_CAMERA) is 66 MHz and the FPGA’s master clock is 100 MHz (frequency reached once the entire system has been implemented) a minimum of 121 images of 256 × 256 pixels have been processed per second. This ratio increases notably if any of the following situations occur:Number of significant eigenvectors (t) under four. In this case the number of matrix multiplication operations (6), (9) and (10) are notably reduced. In this way the new TPCA_TOTAL value would reach an equivalent image per second ratio of 189.Selective actualization. Cadence is another very important factor that conditions the number of images processed per second when updating the eigenvectors of the matrix (background model). If the eigenvalues of the matrix are not continuously updated, but between one update and another b images pass, the new ratio of images per second obtained is shown in b = 100 onwards, independent of the number of significant eigenvectors, the system reaches its maximum value at around 250 images per second for t ≤ 3 and around 190 for t ≥ 4. This is because the system segmentation is at its most efficient at this number of images. In slices point of view, it has been possible to implement the entire system on a medium to low range FPGA like the Xilinx XC2VP7.As may be seen from this figure, from When it comes to calculating the number of complete clock cycles employed by Tained in . AdjustiWith respect to the frequency of the FPGA clock, according to the reports generated by the implementation tool, a maximum value of 1,124 MHz for the entire FPGA is assured. However, the master frequency chosen for our design is 100 MHz as from this value all the other necessary frequencies can be generated .binning process on the FPGA. This sequence was captured in the grounds of the University of Alcala where the distance between the objects to be detected, in this case people and the camera, is 25 meters.As for the real results obtained, 6.etc.) responds to the requirements of many applications, where the goal is the detection of new objects in the scene, even in those cases where, for a variety of reasons, (changes in lighting for example) a continuous update of the background model is required. The proposed solution is a significant improvement on other hybrid solutions based on the use of a PC and an FPGA [This work presents a new image capture and processing system implemented on FPGAs for detecting new objects in a scene, starting from a reference model of the scene. To achieve this, the Principle Component Analysis (PCA) technique has been used. The main objective is to parallelize it in order to achieve a concurrent execution which will enable processing speeds of around 120 images per second to be reached. This processing speed, including all stages included in the PCA technique (calculating eigenvalues and eigenvectors, projection and recovery of images to/from the transformed space, obtaining map of distances,  an FPGA . The com


The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks  and to have a critical influence on epidemics' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion . This allows us to derive analytical estimates for the epidemic threshold and the rate of spread of the disease. It also allows us to readily incorporate survey data, as illustrated in this study with data from the National Survey of Sexual Attitudes and Lifestyles (NATSAL) carried out in the UK. Contact structure between hosts is known to have a key influence on disease spread ith line and jth column can take the value 0 or 1 to indicate respectively the absence or the presence of a contact between individuals i and j. Contact networks are widely used because they possess several convenient properties, one of which being that the dominant eigenvalue of the adjacency matrix is an indicator of the initial propagation speed of an infectious disease spreading on this network One way to capture contact structure is to use a network k. This result holds both for static networks . For instance, the number of secondary infections generated by a typical infected host in a fully susceptible population, i.e. the basic reproductive number β and recover from the infection at a rate γ. On both static and dynamic heterogeneous networks with a large or even diverging variance in the distribution of the number of contacts, epidemics die out only for very small or even vanishing transmission rates β.One of the typical key assumptions epidemiological models on networks make to obtain such elegant expressions for An increasing number of studies in epidemiology point to the importance of considering weighted networks. Some examples include the spread of sexually-transmitted infections k contacts among which (s)he randomly distributes l interaction events. We validate our analytical results using numerical simulations on networks.Here, we present an original framework, which builds on configuration type network epidemic approaches Importantly, since this framework relies on summary statistics of the network and does not require knowledge of the exact shape of the network, it can be parametrized using large scale survey data. The network information we lose by using these summary statistics requires that we make the assumption that there is no assortativity between individuals in our framework. However, we show that even with these assumption we can approximate epidemic dynamics better than with non weighted networks.k contacts and l interaction events per time interval, which are distributed among their k contacts  and number of interaction events (l). Such a joint probability distribution l given that the individual has k contacts. If l = k and 0 otherwise, we are then back to a ‘classical’ network case, with an exact linear dependency between the number of contacts and the number of interaction events . Our framework can capture more general situations by explicitly choosing The model is broadly applicable as it can be parameterised through any joint probability distribution of the number of partners , the transmission probability per interaction event of the pathogen (β) and the probability for each of his/her contacts to points to an infected individual –(3), we need expressions for the temporal dynamics of the Equations for the epidemic model on weighted networks).The set of differential equations describing the epidemic process is derived by careful bookkeeping of the links along which an infectious agent spreads  and l interaction events per time interval drawn from the distribution k contacts. Networks were generated by assigning each host a number per se due to its node-centric view  was done at random but by respecting their assigned number of interaction events per contact. The problem is that not all probability distribution If the number of interaction events per time and per contact is large (i.e. if Weight assortativity arises in networks that have a (nearly) constant number of contacts k per individual and where the number of interaction events l is distributed in a heterogeneous way, thus leading to an early expansion among the most highly active individuals. This can accelerate the initial expansion of an epidemic but, at the same time, it also constrains disease spread compared to what one could expect from the analytical approach. Alternatively, the network can also segregate with respect to the number of contacts an individual holds (i.e. contact or degree assortativity). An extreme case can be observed when a (nearly) constant number of interaction events has to be distributed among a heterogeneous number of contacts. This leads to a (near) isolation of individuals with single contacts from the epidemic process  and l interaction events as drawn from the probability distribution l interaction events a node has are then distributed multinomially among its k stubs. Stubs are randomly matched together, with matches being rejected if the weights of the stubs differ by more than one interaction event. In addition matches are rejected if they differ by more than 10% of the smaller weight involved to avoid biases in nodes with few links. If stubs with non-identical weights are matched, the contact is assigned the mean weight randomly rounded to the next integer. This results in the empirical distribution Networks for simulation are obtained by first generating 10,000 nodes with i, transmission occurs at rate β is the probability of transmission per sex act, W is the weighted adjacency matrix listing the number of interaction events per time unit between all pairs of nodes, and I is the set of infected nodes connected to node i. Infected nodes recover at rate γ. For each case analyzed, 20 nodes were initially infected uniformly at random in a population of 10,000 and 100 replicate simulations were carried out over each of 20 replicate networks.We use the Gillespie direct algorithm The derivation of the early exponential growth rate I) and the average number of contacts per individual found originally in the total population . This means that the contact the infection has spread from is discounted and that all ‘new’ contacts are assumed to still be susceptible in the early phase of an epidemic. In order to correctly estimate As there is no explicit expression for Altogether we have,We also have If we assume that l) to have k excess contacts. This probability is The basic reproductive ratioThe basic reproductive ratio l an individual has does not necessarily increase linearly with his/her number of partners k. To create these networks, we used combinations of Poisson and power law distributions for the number of contacts k and interaction events per time l. This allowed us to introduce arbitrary combinations of homogeneous or heterogeneous behaviour in the way contacts are made and in the number of interaction events established, that may be either independent or dependent (as in the linear case).In order to test our analytical model, we consider epidemiological dynamics taking place on artificial networks on which we release the constraints found in ‘classical’/unweighted networks by assuming that the number of interaction events I) from repeated simulation runs with the results derived from the analytical approach using the probability generating functions corresponding to Agreement between approximations and simulations) and To validate the model, we compared the epidemic prevalence (k follows a power law) and a homogeneous distribution of interaction events (l is Poisson distributed). This is because the strongest constraints on network topology are expected to occur with these distributions . This is particularly true in networks where the average weight per contact is inversely proportional to the number of contacts an individual has. In our simulations, this effect is the clearest when There are different ways to assess the initial propagation of an infectious agent in an otherwise fully susceptible population. One possibility is to estimate the initial exponential growth rate in the number of infected individuals  is more appropriate to capture the next stages of early epidemic expansion because it accounts for the fact that spatial structure has been sensed or set by the epidemic process. We thus use it for the derivation of The basic reproductive ratioThe expressions for β) are weighted by the number of interaction events per contact. This makes sense because this corresponds to a transmission rate. Note that there is a slight difference between In the expression for k) and the interaction events (l) an individual maintains equally affect epidemic spread. At the same time the correlation between these quantities is relevant to model rapid epidemic spread: for epidemic control, targeting individuals with most contacts or interaction events can prove to be much less efficient than targeting those who maximise both. The formulae in k is interpreted as the number of interaction events More interestingly, the expressions for k) and sex acts  a person has within certain time frames.The knowledge of transmission networks along which an infectious agent can spread within a host population is of great importance to public health. These networks might be hard to assess for air-borne infections because they are very dynamic k) and sex acts  an individual has are heterogeneously distributed. However, their joint distribution l does not scale linearly with the number of partners k an individual has. This is also supported by Pearson's correlation coefficient which is 0.15, i.e. positive but not indicating a strong linear relationship between k and l  or heterogeneous (power law). This is also reflected more quantitatively in the expression for k) correlates with their number of sex acts (l) the faster the early epidemic expansion.In our ‘Validation’ section we have shown that, regarding the number of interaction events, a deviation from the linear behaviour decreases epidemic expansion and peak prevalence, especially for transmission networks that are characterized by a heterogeneous distribution in the number of contacts per individual β = 0.01 per sex act in two scenarios. We chose to model SI dynamics by setting γ = 0 in order to simulate HIV spreading on a short time scale, but the model could be evaluated with analogous results for SIR dynamics . t = 10 years) the probability of being infected grows with the number of contacts k an individual has, and even more so with the number of sex acts l (s)he has.The framework can also be used to follow the dynamics in the epidemic subgroups and to identify risk groups along the course of the epidemics , which can enforce correlations among nodes in certain networks. Also clustering is observed in many contact networks Most analytical and numerical models predict disease spread on network using only one summary statistics, the distribution of the number of partners. We show that additional insights can be gained, while maintaining some analytical results, by including another summary statistics, such as the distribution of the number of sex acts knowing the number of partners. These data are easier to collect than full information of the contact network , which makes our framework widely applicable. We demonstrate this applicability here using data from the NATSAL study conducted in the UK. We note that for some artificial distributions, our results begin to diverge from simulations on real networks. However, the framework has proven to be applicable for empirical distributions and analysis of more empirical data will allows us to further test the robustness of the method using more realistic assumptions.Figure S1β = 0.01 but recovery can occur at a rate γ = 0.004 per 4 weeks, i.e. parameters corresponding to Epidemic SIR dynamics on the network as presented in (PNG)Click here for additional data file.Figure S2Epidemic incidence or rate of infection  cf.  for SI d(PNG)Click here for additional data file.Figure S3vs. the self-reported number of sexual partners over the last 4 years. In Panel B, we plot the self-reported number of sex acts over the last 4 weeks vs. the self-reported number of sexual partners over the last 3 months. In Panel C, we plot the self-reported number of sex acts over the last 7 days vs. the self-reported number of sexual partners over the last 3 months. In all three cases, the data do not support a linear relationship (the number of sex acts per partner decreases with the number of partners/contacts).Relationship between a person's total number of sex acts and number of partners derived from the NATSAL data. In Panel A, we plot the self-reported number of sex acts over the last 4 weeks (PNG)Click here for additional data file.Table S1Model notations.(PDF)Click here for additional data file.Table S2Agreement between approximations and simulations.(PDF)Click here for additional data file.Text S1Supporting Information.(PDF)Click here for additional data file.