The proposed method models the distribution of GM and WM tissues grouping the voxels belonging to each tissue in ROIs associated to a specific neurological disorder. Tissue distribution of normal and abnormal images is modelled by a Self-Organizing map (SOM), generating a set of representative prototypes, and the receptive field (RF) of each SOM prototype defines a ROI. Moreover, the proposed method computes the relative importance of each ROI by means of its discriminative power. The devised method has been assessed using 818 images from the Alzheimer's disease Neuroimaging Initiative (ADNI) which were previously segmented through Statistical Parametric Mapping (SPM). The proposed algorithm was used over these images to parcel ROIs associated to the Alzheimer's Disease (AD). Additionally, this method can be used to extract a reduced set of discriminative features for classification, since it compresses discriminative information contained in the brain. Voxels marked by ROIs which were computed using the proposed method, yield classification results up to 90% of accuracy for  Nowadays, neurodegenerative disorders affect over 30 million people around the world. Due to the increasing life expectancy and ageing of the population in developed nations, they are expected to affect 60 million people worldwide over the next 50 years. A distinctive example of these neurodegenerative disorders is the Alzheimer's Disease (AD). Indeed, the latest estimates argue for global prevalence of AD to be quadrupled by 2050. slow, degenerative disease related to pathological amyloid depositions and hyperphosphorylation of structural proteins in the brain AD can usually be diagnosed by means of neuropsychological tests Other works such as Neurodegeneration relating to AD produces abnormal structural changes in the brain, which eventually result on extreme shrinkage of the hippocampal volume or extreme reduction of its cortical thickness, as well as a severe enlargement of the internal ventricles. However, some structural changes associated to early AD are revealed to be similar to those caused by natural ageing process. Therefore, despite AD diagnosis can be addressed by detecting these structural changes Unlike methods that use intensity voxels for classification Current trend on studies focused on AD/CN and MCI/AD classification consist on using a single imaging modality. As shown above, some methods use functional imaging whereas other use structural MRI, and the analysis of each image modality can reveal different markers associated to the disease. For instance, MRI analysis reports grey matter atrophy that usually results in differences in both, the hippocampus and the entorhinal cortex. Additionally, it has been proved that early changes in the hippocampal volume and entorhinal cortex are related to evidences of early AD, while this is not so obvious in other cerebral structures eigenface approach Previous works such as In our work, structural MRI is used to automatically reveal 3D brain regions associated to AD by means of analyzing the distribution of WM and GM tissues in the brain. The computed ROIs are later used as a mask in order to extract voxels from relevant regions for subsequent analyses. Thus, regions linked to a specific brain disorder are automatically computed by quantizing the space into a number of regions that group similar voxels. This way, it is not necessary to get additional information from any anatomy atlas. Additionally, a measurement of relative importance is calculated for each ROI on the basis of its discriminative capability for AD diagnosis. This is accomplished by computing a number of prototype vectors using the SOM algorithm that quantize the space taking into account differences between CN and AD images. Consequently, the receptive field of each SOM unit represents a ROI on the image and its relative importance can be computed by means of the discriminative power of each voxel. The main contributions of this work can be summarized in the following:A method for automatic ROI delineation is proposed, using SOM to quantize the feature space composed by voxel coordinates and information regarding voxel differences between classes.It automatically reveals brain areas (ROIs) according to patterns learnt to differentiate CN and AD patients (or MCI/AD patients).A relative importance measurement is also computed for each ROI, to indicate its discriminative capability.The method has been assessed through extensive experiments using 818 images from the 1075-T1 ADNI database, yielding 90% (AUC 0.92) and 84% (AUC 0.84) of classification accuracy within CN/AD and MCI/AD, respectively.The rest of this paper is organized as follows. Section materials and methods shows the materials and methods used in this work, including the necessary background to support the next sections and details on the database used to assess the proposed method. Examples of ROI computation are also provided in this section. Experimental results section provides classification results using ROIs computed with the proposed method over the database previously described. Finally, conclusions are drawn in the www.adni-info.org.Data used in the preparation of this article were obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). The ADNI was launched in 2003 by the National Institute on Aging (NIA), the National Institute of Biomedical Imaging and Bioengineering (NIBIB), the Food and Drug Administration (FDA), private pharmaceutical companies and non-profit organizations, as a $60 million, 5-year public-private partnership. The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimers disease (AD). Determination of sensitive and specific markers of very early AD progression is intended to aid researchers and clinicians to develop new treatments and monitor their effectiveness, as well as lessen the time and cost of clinical trials. The Principal Investigator of this initiative is Michael W. Weiner, MD, VA Medical Center and University of California - San Francisco. ADNI is the result of efforts of many co-investigators from a broad range of academic institutions and private corporations, and subjects have been recruited from over 50 sites across the U.S. and Canada. The initial goal of ADNI was to recruit 800 subjects but ADNI has been followed by ADNI-GO and ADNI-2. To date these three protocols have recruited over 1500 adults, ages 55 to 90, to participate in the research, consisting of cognitively normal older individuals, people with early or late MCI, and people with early AD. The follow up duration of each group is specified in the protocols for ADNI-1, ADNI-2 and ADNI-GO. Subjects originally recruited for ADNI-1 and ADNI-GO had the option to be followed in ADNI-2. For up-to-date information, see ADNI1:Screening 1.5T (subjects who have a screening data). This database contains MRI data from 818 subjects and repeated scans in some cases. When multiple scans of the same subject were available, the first one was selected. As a result, 818 images have been used for assessing our approach. Demographic data of patients in the database is summarized in ADNI database Image data pre-processing, segmentation and co-registration of T1-weighted MRI images from the ADNI database have been performed. Initially, images from the ADNI database were nor skull-stripped neither spatially normalized. Thus, all the images had to be pre-processed and co-registered before segmentation. The whole process has been performed using the VBM Pre-processing and co-registration.The whole process was guided by means of tissue probability maps. A nonlinear deformation field that best overlays the tissue probability maps on the individual sujects' image is estimated. The tissue probability maps provided by the International Consortium for Brain Mapping (ICBM) are derived from 452 T1-weighted scans, which were aligned with an atlas space, then corrected for scan inhomogeneities, and finally classified into grey matter, white matter and cerebrospinal fluid. The data were affine registered to the MNI space and down-sampled to 2 mm resolution. Moreover, all images from the database were resized to 121×145×121 voxels.A mutual information affine registration with the tissue probability maps was used to achieve approximate alignment.Spatial normalization was based on a high-dimensional Dartel normalization and used standard Dartel template provided by VBM 8.Segmentation.The number of Gaussians used to represent the intensity distribution for each tissue class was set to 2 for all grey matter, white matter and cerebrospinal fluid. The use of multiple components per tissue allows to reckon partial volume effects and deep GM differing from cortical GM.A very light bias regularization was performed to correct smooth, spatially varying artifacts that modulates the intensity of the images.Gaussian bias-smoothing was not used, though, since according to our experiments, non-smoothed images provided a better classification results.Warping regularization was set to 4 to determine the tradeoff between the two terms of the objective function for registering the tissue probability maps to the image to be processed. One term gives a function of how probable the data is given the parameters. The other is a function of how probable the parameters are, and provides a penalty for unlikely deformations.A spatial adaptive non local means denoising filter is applied to the data in order to remove noise while preserving edges. The smoothing filter size is automatically estimated based on the local variance in the image.A hidden Markov Random Field (MRF) with a weighting of 0.15 was used to encode spatial constraints of neighboring voxels. Neighboring voxels were expected to have the same class labels. The prior probability of the class and the likelihood probability of the observation were combined to estimate the Maximum a posteriori (MAP).Skull stripping was performed by using SPM-VBM tool and VBM templates.As a result, probability maps were obtained for each MRI in the database, which consisted of values in the range Best Matching Unit (BMU) and it is computed as:The Self-Organizing Map (SOM) Moreover, prototypes of neurons belonging to the neighbourhood of the BMU are also updated according toSOM training is accomplished in two phases. The first one provides a rough organization of the map by setting the initial radius to The training process generates the prototype vectors Fisher Discriminant Ratio (FDR) A MRI is composed of a high number of voxels according to a previously-stated image resolution. Images in the ADNI database used in this work contain 121×145×121 voxels after normalization. Since not all the voxels result equally discriminative for classification Similarly, the variance image is defined asFrom 5, aFDR value increases as the variable results in more discriminative values between the two classes. FDR values are further incorporated to the ROI computation stage to calculate the relative importance of each ROI. At this point, it is important to highlight that FDR is considered a part of the training stage. Thus, it is computed by using only images from the training subsets during cross-validation, ensuring that test data is never used for training.Due to the high number of voxels present in a MR image, methods that aim to compress or synthesise the information contained in these voxels in a reduced number of features allow the diminishing of the classification task's computational cost. Regardless of this process, non-relevant features can be taken out. One of the classical tools for dimensionality reduction is the well-known Principal Component Analysis (PCA) whithened dataset PCA generates an orthonormal basis vector indicating the maximum variance directions. Thus, the projection onto this basis maximizes the scatter of all the projected samples. The PCA method can be briefly described as follows. Let The method presented in this paper aims not only to reduce the dimensionality of the input space but also to compute ROIs and then weight them according to their relative importance. The core idea of the method consists on quantize the MRI space by a number of prototypes which model the intensity distribution in different brain areas. Thus, information about intensity is incorporated to the quantization process in order to group the voxels according to their intensity level and being later capable to model the MRI intensity distribution in the SOM space. Therefore, the feature space is composed by vectors which contain the voxel's three-coordinates location in the three first coordinates and the intensity difference between CN and AD images. Such a difference image is computed asThe feature space to be quantized is then formed by vectors The core idea behind the presented method consists on quantizing the space to a number of model vectors, and to categorize them according to their relative importance and the level of intensity in the difference image. Consequently, the number of extracted ROIs corresponds to the number of units in the SOM, and the size of each ROI depends on the size of the receptive field of the corresponding SOM unit.The self-organizing process carried out by SOM provides the models shown in A 3D volume can be reconstructed from the SOM model by means of the vector quantization process as depicted in Similarly, support vector machine.Classification of the feature vectors consisting of the relative importance measure computed as indicated in the ROI modelling section is accomplished by means of Support Vector Machine (SVM). SVMs were introduced in 70's by Vapnik For non-linearly separable data, the optimization process needs to be modified to work in combination with kernel techniques, so that the hyperplane that defines the SVM corresponds to a non-linear decision boundary in the input space. The use of kernels enables to map the data into some other dot product space Database subsection, including CN, MCI and AD patients. Such a procedure aims to objectively evaluate the discriminative power of the computed ROIs. Thus, classification through SVM supervised learning is carried out to group the images according to the value of k-fold, which takes Image Preprocessing section from segmented images, were used as features. Since VAF uses all the information contained in the images without selecting discriminative voxels, it may decrease the classification performance. Our method, which uses voxel selection and feature generation associated to ROIs, outperforms the VAF approach as shown in Statistical significance of voxels section, were performed for comparison. Our proposed method also outperforms the approach which uses PCA for feature extraction as shown in To demonstrate the relevance of the proposed ROI selection method for diagnosis purposes, we applied the devised ROI selection algorithm to the overall database described in the Similarly to the experiments described above for CN/AD patients, experiments that aim to differentiate between MCI and AD patients were carried out. Thus, MCI/AD classification results are shown in At the same time, ROIs extracted from MCI patients have been assessed by means of classification experiments. gold-standard diagnosis in the ADNI database, as only living subjects were analysed. This fact is specially relevant due to the difficulty for diagnosing AD in vivoIt is worth noting that there are several factors that may affect the classification results. One of them is related to the In this work, a method based on unsupervised vector quantization techniques for automatic ROI calculation is presented. Specifically, a three-dimensional Self-Organizing Map is used to model MRI images selecting ROIs related to a particular neurological disorder. Images from controls and AD patients are used to compute tissue differences by means of voxel contrastation. Subsequently, the MRI space is quantized, computing a number of prototype vectors from features extracted taking into account the spatial relationship among voxels, figuring out similar areas within the difference image. Additionally, the relative importance of each cluster is computed by means of the cluster sizes and the statistical significance of the discriminative power of the voxels that make up the ROI. The spatial relationship among clusters is also preserved in the SOM output space due to the SOM's topology preserving properties. The method has been assessed by selecting a set of images from the ADNI


Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics. Neurons of sensory systems encode signals from the environment by sequences of electrical pulses — so-called spikes. This coding of information is fundamentally limited by the presence of intrinsic neural noise. One major noise source is “channel noise” that is generated by the random activity of various types of ion channels in the cell membrane. Slow adaptation currents can also be a source of channel noise. Adaptation currents profoundly shape the signal transmission properties of a neuron by emphasizing fast changes in the stimulus but adapting the spiking frequency to slow stimulus components. Here, we mathematically analyze the effects of both slow adaptation channel noise and fast channel noise on the statistics of spike times in adapting neuron models. Surprisingly, the two noise sources result in qualitatively different distributions and correlations of time intervals between spikes. Our findings add a novel aspect to the function of adaptation currents and can also be used to experimentally distinguish adaptation noise and fast channel noise on the basis of spike sequences. Associated adaptation currents which act on time scales ranging from In previous studies on stochastic models with adaptation, fluctuations were considered to be fast, e.g. Poissonian synaptic spike trains passing through fast synapses or a white Gaussian input current representing a mixture of intrinsic fluctuations and background synaptic input. In particular, the dominating intrinsic source of fluctuations is ion channel noise ents see .In this paper, we analyze a perfect integrate-and-fire (PIF) model in which a population of Our main concern in this paper was the effect of noise associated with the slow dynamics of adaptation on the interspike interval statistics. Specifically, the noise was regarded as the result of the stochastic activity of a finite number of slow “adaptation channels”, e.g. M-type channels . We contopen and a closed state. The transition rates depend on the presence or absence of an action potential. This can be approximated by passing the membrane potential In order to demonstrate the results on two different levels of complexity, we conducted both analytical investigations of a tractable integrate-and-fire model and a simulation study of a biophysically more realistic Hodgkin-Huxley-type neuron model. For the first model we chose the perfect (non-leaky) integrate-and-fire (PIF) model channels . For simThe PIF model, however, describes only the dynamics of the subthreshold voltage. In particular, it does not explicitely yield the suprathreshold time course of the action potential, but only the time instant of its onset (given by the threshold crossings). Nevertheless, the spike-induced activation of adaptation channels can be introduced in the PIF model. To this end, we approximated the activation function therwise , middle.therwise . The timAlthough our model aims at the stationary firing statistics, we would like to stress that it exhibits spike-frequency adaptation in the presence of time-varying stimuli. In particular, spike-frequency adaptation in response to a step stimulus is retained regardless of the considered noise source, channel numbers or approximations made during the theoretical analysis . This isFor the theoretical analysis the channel model describing the dynamics of each individual channel could be considerably simplified by a diffusion approximation. As shown in Put differently, a finite population of slow adaptation channels (instead of an infinite population and hence a deterministic adaption dynamics) entails the presence of an additional noise tion see . In Eq. To study the effect of the two different kinds of noise, we focused on two limit cases: In the limit of infinitely many channels, the adapting PIF model is only driven by white noise. In this case, Eq. (1) readsdeterministic adaptation. A dimensionality analysis shows that the ISI statistics are completely determined by the quantities We call this case ants see . Thus, dIn the opposite limit, we considered only the stochasticity of the adaptation current but not the white noise. Setting stochastic adaptation. As shown in We call this case  The fraction of open channels cted by  . The difThe calculation of the ISI statistics  of the PIF model with noise and spike-frequency adaptation is generally a hard theoretical problem. Here we put forward several novel approximations for the simple limit cases Eq. (2) and Eq. (3). For typical adaptation time constants that are much larger than the mean ISI we found the ISI histogram in the case of pure white noise , analytical expressions for the ISI density and the serial correlation coefficient are known As before, a spike is fired whenever Interestingly, the scaling factor in Eq. (6) has a concrete meaning in terms of spike-frequency adaptation: (64) see . In the (64) see . For a sa priori we cannot expect that this density fits any of the cases we consider here. However, as mentioned above, the ISI density can be captured by an IG for deterministic adaptation  distribution in contrast to cases where fast fluctuations dominate. We recall that the IG distribution yields the ISI histogram for a PIF model driven by white noise without any (deterministic or stochastic) adaptation, so aptation . In factn the IG . With adBy contrast, the ISI histogram in the case of stochastic adaptation as illustrated in This suggests that both cases – deterministic and stochastic adaptation – might be distinguishable from the shape of the ISI histograms even if mean and CV of the ISIs are comparable as for the data in The rescaled kurtosis reveals also differences between the channel and the diffusion model. In In the case of stochastic adaptation, we obtained analytical expressions for oise see . For theThese expressions only depend on the non-dimensional parameter These predictions are confirmed by simulations using different ue of  , , therebyations , . The incrger see  for . ThFor deterministic adaptation In the intermediate range, where the time scale of the adaptation is of the same order as the mean ISI, a pronounced minimum of Another clear distinction between stochastic and deterministic adaptation is revealed by the correlations between ISIs. In several modeling studies it has been found that negative feedback mechanisms like adaptation currents in the presence of white noise give rise to negative correlations between adjacent ISIs Noting that aptation . The sliIn striking contrast, the case of stochastic adaptation yields positive ISI correlations with a slow exponential decay  as prediISI correlations are strongly governed by the time scales in the system. We therefore investigated the role of the time scale separation parameter ent ISIs . For deteory see , in whicFor stochastic adaptation, the positive correlations become strongest for mean ISI , i.e. . channels . The decSo far, we found that the two limit cases of the adapting PIF model can be well distinguished by the values of the shape parameters ith  see .For small channel numbers, i.e. large channel noise, we observed both large values of the rescaled kurtosis We investigated whether our theoretical predictions based on a simple integrate-and-fire model are robust with respect to a more detailed model of the Hodgkin-Huxley type. To this end, we performed simulations of the conductance-based Traub-Miles model with a M-type adaptation current The different ISI statistics for the case of deterministic and stochastic adaptation are analyzed more closely in A clear distinction between both cases appears in the serial correlations of ISIs . Similaraptation  and decaaptation . As in tFinally, we inspected the case in which both white noise and slow adaptation noise is present . As in Fchannels . As for d regime .independent colored noise. The long-range temporal correlations of this noise naturally yield positive ISI correlations and a slow modulation of the instantaneous spiking frequency. The latter typically involves a large kurtosis due to the increased accumulation of both short and long ISIs. A significant amount of colored noise can effect the kurtosis and the ISI correlations so strongly, that details of the spike generation seem to be of minor importance. Thus, it becomes plausible that the spiking statistics of a rather complex neuron model could be explained by a simple integrate-and-fire model including a stochastic adaptation current.The observation that key features of the ISI statistics in the presence of a stochastic adaptation current seem to be conserved across different models suggests a common mechanism underlying these features. As we saw, this mechanism is based upon the fact that a stochastic adaptation current can be effectively described by an In this paper, we have studied how a noisy adaptation current shapes the ISI histogram and the correlations between ISIs. In particular, we have compared the case of pure stochastic adaptation with the case of a deterministic adaptation current and an additional white noise current. Using both a perfect IF model that is amenable to analytical calculations and a more detailed Hodgkin-Huxley type model, we found large differences in the ISI statistics depending on whether noise was mediated by the adaptation current or originated from other noise sources with fast dynamics. As regards the ISI histogram, stochasticity in the adaptation leads to pronounced peaks and a heavy tail compared to the case of deterministic adaptation, for which the ISI density is close to an inverse Gaussian. To quantify the shape of ISI histograms we proposed two measures that allow for a simple comparison with an inverse Gaussian probability density that has the same mean and variance. The first one is a rescaled skewness (involving the third ISI cumulant); the second is a rescaled kurtosis (involving the fourth ISI cumulant). Both quantities possess the property that they assume unity for an inverse Gaussian distribution. If they are larger than unity as in the case of stochastic adaptation the ISI density is more skewed or respectively has a sharper peak and a heavier tail than an inverse Gaussian density with the same variance. If these measures are smaller than one, the ISI histogram tends to be more Gaussian like. Most strikingly, we found that for a stochastic adaptation current the rescaled skewness and kurtosis strongly increase when the time scale separation of adaptation and spiking becomes large  by splitting the deterministic and the noise part of The adaptation currents (26) see  we have  and thus the effects of stochastic adaptation is affected in a controlled way. Another possibility to test our predictions would be to vary the firing rate of the neuron by increasing or decreasing the input current. In this way, the time scale of spiking would change relative to the time scale of adaptation and, thus, the colored noise effect of adaptation noise could be enhanced or attenuated, respectively.Channel noise can crucially influence neural firing especially in the absence of synaptic input Realistic numbers of M-type channels per neuron are difficult to estimate and the numbers used in this paper must be seen as a tuning parameter for the channel noise intensity. Channel densities of the M-type have been estimated to be of the order of one functional channel per The diffusion approximation for the stochastic dynamics of ion channel populations  has been studied by several authors Spike-frequency adaptation has been commonly studied with regard to its mean effect on the firing rate To analyze the slow, voltage-dependent adaptation channels in a simple setup we consider a population of For Here, Therein, In the conductance-based Traub-Miles model, we will use the kinetic scheme with the rate functions given byInserting this relation into Eq. (21), both rate functions show a quasi sigmoidal dependence on the voltage see , such thFor the integrate-and-fire (IF) model we employ a simplified variant that distinguishes only between two values of  to zero . Thus,  This function and the set of spike times In the definition of ents see .Taking the open probability exactly as the fraction of open channels amounts to taking the limit of an infinite population of channels. In the Traub-Miles model or the integrate-and-fire model with deterministic adaptation, this corresponds to adding an adaptation current of the form In this equation, For a finite channel population, the fraction of open channels is given by the stochastic quantity When the channel number is varied, we assume that the maximal conductance per unit membrane area The channel model, Eq. (20), can be approximated by a single Langevin equation for Furthermore, a separation of the adaptation into a deterministic and a stochastic part, Note that Eq. (1), which will be our final diffusion model, also involves the additive-noise approximation presented below.The perfect integrate-and-fire (PIF) model The last term in Eq. (35) represents fast Gaussian input fluctuations of intensity It is a feature of the PIF model that the firing rate is directly proportional to a constant driving current and independent of the noise. However, even for the slowly varying driving current Solving for The noise term in Eq. (31) or (34) is multiplicative, because both arguments of the noise strength For the standard parameter set used in this paper, It is useful to regard a non-dimensional form of Eq. (35). To this end, we measure henceforth voltages in units of The dynamics of the PIF model is completely determined by the four non-dimensional parametersIn the last step, Eqs. (38) and (41) were used. The second term of Again, the adaptation variable In accordance with Eq. (37), the mean adaptation is proportional to the firing rate In the case of deterministic adaptation , the stationary firing rate for stochastic adaptation is again given by Eq. (51).If the stimulus depends on time, i.e. if As an example, let us consider a step of the base current at time This represents exactly the exponential decay of the firing rate in response to a step stimulus, which is typical for spike-frequency adaptation. Eq. (55) has been used in The dynamical response to a step stimulus yields an interesting interpretation of the scaling factor In the following, The second cumulant equals the variance and is related to the coefficient of variation (CV), which is a measure of ISI variability:We further consider the third cumulant, which is related to the skewness Roughly speaking, the kurtosis indicates how much of the variability is due to events that strongly deviate from the mean value. For instance, a unimodal ISI density with a heavier tail compared to another ISI density with the same CV, tends to exhibit a larger kurtosis. This is typically accompanied by a more pronounced peak close to the mean value to balance the heavy tail.In this paper, we want to compare the ISI density with an inverse Gaussian probability density serving as a reference statistic. For an inverse Gaussian ISI distribution (see below) one observes that the skewness is proportional to the CV and the kurtosis scales like the squared CV. This suggests to introduce rescaled versions of the skewness and the kurtosis as follows:By defining the rescaled skewness and kurtosis in this manner, we obtain measures that are identical to unity for an inverse Gaussian ISI density. For larger  values, the ISI density is respectively more (less) skewed and more (less) peaked compared to an inverse Gaussian density. This procedure is somewhat analogous to the definition of the CV, for which the Poisson process serves as a reference for the ISI variability with Furthermore, we consider the correlations among ISIs as quantified by the serial correlation coefficient For the adapting PIF model, the two limit cases that are considered in this paper could be reduced to simplified models, for which analytical results are partly known. Firstly, in the case of deterministic adaptation, i.e. This distribution has a meanFurthermore, by construction we haveThe mean adaptation approximation would wrongly predict that the ISIs are uncorrelated. The reason is that in the PIF model driven by only white Gaussian noise any memory of the ISI history is erased upon reset. A better account of ISI correlations is given below.Secondly, the case of stochastic adaptation can be reduced to a PIF neuron driven by a reduced base current For with Although this formula captures the ISI density at small ISIs, it is of limited use, because the second and higher ISI moments diverge. Throughout the paper we have therefore used the full expression Eq. (69). The mean ISI and the firing rate do not depend on the noise statistics, in fact they are equal to the white noise case, Eq. (65), as shown below (derivation of the ISI cumulants). The squared CV can be obtained to second order in Here we derive an expression for the serial correlation coefficient of a PIF neuron with deterministic adaptation current and white noise driving. We consider the following subthreshold dynamicsIf we set Solving for the limit cycle parameters The serial correlation coefficient for the case of weak noise can be understood by considering small deviations from the limit cycle. Weak noise leads to a distribution of Similarly, noise leads to a distribution of ISIs centered about The last equation allows to express the interval correlations Note, that In order to calculate the correlations Inserting Eq. (83) into Eq.(80) yields a stochastic map for Multiplying Eq. (84) by Mean ISI for a given perturbationLinearizing the exponential We mention, that this expression is consistent with the result in Using Eq. (82) and Eq. (86) in the expression for the serial correlation coefficient Following For the description of the ISI density it is necessary to use the initial condition that corresponds to the distribution of d by see (92)The ISI density is equal to the time-dependent probability flux across the threshold line To carry out a weak-noise expansion of Eq. (91) we change to the variablesIn these variables the Fokker-Planck equation for Furthermore, we consider the characteristic function In the last equation we introduced the functionFrom Eq. (97) and (99) it is clear, that all cumulants can be generated from the function To solve Eq. (100) for weak noise, we expand Inserting into Eq. (100) gives a hierarchy of first-order differential equations for the coefficients The solutions can be obtained order-by-order using the method of characteristics. Here, we report only the first three coefficients Higher-order coefficients can be calculated in the same way, although the expressions become quite lengthy. To obtain the kurtosis including the first noise-dependent term correctly, one has to calculate From the cumulants one finds the rescaled skewness and kurtosis as defined in Eq. (61) and (62):To test the generality of our findings, we simulated the conductance-based Traub Sodium current:Potassium current:Leak current:M-type adaptation current:In this model, the adaptation time constant For the second model with adaptation channel noise, the voltage is described byThe currents As in the PIF model, we assumed the adaptation channels to be two-state ion channels with the transition rates In the model with stochastic adaptation current, the maximal channel conductance


The restoration of complex hand functions by creating a novel bidirectional link between the nervous system and a dexterous hand prosthesis is currently pursued by several research groups. This connection must be fast, intuitive, with a high success rate and quite natural to allow an effective bidirectional flow of information between the user's nervous system and the smart artificial device. This goal can be achieved with several approaches and among them, the use of implantable interfaces connected with the peripheral nervous system, namely intrafascicular electrodes, is considered particularly interesting.Thin-film longitudinal intra-fascicular electrodes were implanted in the median and ulnar nerves of an amputee's stump during a four-week trial. The possibility of decoding motor commands suitable to control a dexterous hand prosthesis was investigated for the first time in this research field by implementing a spike sorting and classification algorithm.The results showed that motor information  could be extracted with classification accuracy around 85% (for three classes plus rest) and that the user could improve his ability to govern motor commands over time as shown by the improved discrimination ability of our classification algorithm.These results open up new and promising possibilities for the development of a neuro-controlled hand prosthesis. The human hand is a versatile organ that is used for grasping heavy or delicate objects and for performing highly complex manipulations on the basis of fine motor control and precise sensory feedback . The resIn case of amputation, it is also possible to use the residual part of amputee muscles and peripheral nerve fibers to control the artificial hand. This approach can be implemented by processing electromyographic (EMG) signals recorded using either non-invasive  or invasThe use of invasive neural interfaces directly connected to the peripheral nervous system (PNS) is potentially appealing because it is able to provide an almost "physiological" condition in which efferent and afferent fibers, previously connected with the natural hand, may return to their role in controlling the prosthetic limb/hand. This is theoretically possible since a significant amount of peripheral nerve fibers, as well as spinal cord and brain connections dedicated to the control of the amputated limb, survive in time and remain available to restore a "physiological" condition also thanks to the plastic abilities of the CNS to reorganize for functional recovery -17.Several invasive PNS interfaces have been developed in the past . AlthougAmong invasive PNS interfaces, longitudinal intra-fascicular electrodes (LIFEs) - namely intrafascicular electrodes inserted longitudinally into the nerve ,27 - areStarting from these encouraging results, the aim of this study was to verify whether "hand-related" actions (such as different grip types or movements of single fingers) can be decoded by processing neural motor-related signals recorded by LIFEs. This result could allow control of a dexterous hand prosthesis using the natural neural "pathway" and increase the usability of actuated artificial hands.ensemble of motor LIFE signals recorded when a motor command is dispatched to the amputated hand/fingers improves movement classification via the interface processor; (iii) whether there is any learning effect during the use of the interface; (iv) whether this kind of approach needs frequent re-calibrations as in the case of invasive cortical neuroprostheses.In particular, the following issues were addressed also as an extension of a recent study on the same case ,25: (i) A more general and clinically-oriented paper on the same subject, concerning the technique of LIFE insertion and LIFE signal analysis, including results on output control, sensory perception, clinical outcome and associated neuroplastic changes has already been published elsewhere .A new version of LIFEs, named thin-film LIFEs (tfLIFE), was used in the experiments . These eP.P., a 26 year old male, suffered amputation of his left arm two years before the implantation due to a car accident. The surgical procedures are detailed elsewhere . BrieflyDuring the first three weeks of experiments P.P. was involved in several experiments addressing different biomedical and neurophysiological issues related to the efficacy of this approach  palmar grasp, (b) pinch grasp, (c) flexion of the little finger. Pictures representing these tasks were randomly presented to him on a computer screen to provide a visual cue. The overall processing scheme is shown in Figure LIFE motor signals were recorded via 4-channel amplifiers .When above a selected threshold, the neural signals recorded were used to teleoperate a dexterous hand prosthesis. The prosthetic hand used was a stand-alone version of the CyberHand prototype, already employed in several research scenarios . This aptranslation-invariant wavelet transform [A wavelet denoising technique was used to improve the signal-to-noise ratio (SNR) in the neural signals recorded. Wavelet denoising is a set of techniques used to remove noise from signals and images. The main idea is to transform the noisy data into an orthogonal time-frequency domain. In that domain, thresholding is applied to the coefficients for noise removal, and the coefficients are finally transformed back into the original domain obtaining the denoised signal . A decomransform  was usedransform . After transform : creatioransform . The charansform .The denoised signals were then used to identify the dispatched motor commands by implementing the following procedure. For each trial, the different recording periods ('epochs') related to the movement classes  were labeled. The three desired movements and the rest were considered as separated classes. The performance metrics considered was the ratios between classes correctly identified out of those presented and the leave one out validation standard method has been used.Each epoch was an example that was used to train the classifier or to test its generalization skills. The feature vector was made of the ratios between the number of spikes matching each spike template and the total number of spikes in the epoch . TherefoF, a classifier based on support vector machines  was uses  but also to the learning ability shown by the user. In fact, Figure In order to understand the importance of using multi-channel electrodes for neural recordings, classification performance was calculated and compared using different recording channels. The results shown in Figure Among the different approaches for restoring the link between the external world and the nervous system, the use of implantable intrafascicular PNS interfaces is of great potential, as confirmed in previous experiments in humans ,7. The eThe aim of our study was to increase the understanding of the basic mechanisms, as well as of the possibilities and limits of this approach, by processing the motor signals recorded the nerve fibers as final output to the target muscles .Two main assumptions were tested: (1) the extraction of spike templates can allow good decoding performance; (2) it is possible to extract more than a simple one degree of freedom control signal (as previously done by other researchers ). In parConcerning the first assumption we moved from previous knowledge  that an The idea of decoding complex high-level information  represents the main novelty of this study. It is a disruptive approach for decoding and potentially quite challenging because of the characteristics of the signals to process. In fact, signals recorded from the peripheral nerves are related to low-level information . Therefore, this "high-level" decoding could be considered similar to understand a global picture (the grip type) with only a few pieces (related to specific muscle commands) of it. This strategy would allow an easier, more efficacious and faster (namely online) control of a dexterous hand prosthesis. In fact, this could increase the number of motor commands which could be dispatched to the hand without a very precise decoding necessary for example for the simultaneous control of the kinematics of several joints.The results of this study, in terms of rate of correct classification of motor tasks, show that the two assumptions were correct, based on good performance achievement and a state control algorithm implementation. This control approach is commonly used in the EMG-based control of hand prostheses  and has Of great interest was that our amputee subject was able to improve his performance during the consecutive trials. This was particularly evident during the experiments by looking at the SNR and was also confirmed by the classification results. However, this was achieved only for two consecutive days and this learning ability has to be confirmed during longer tests.The performance also improved by using several intrafascicular recording channels. This is due to the intrinsic blindness of the implantation procedure: a large number of channels can increase the probability of picking up enough signals to reach good classification levels and to maintain such a rate of appropriate classification stable in time. In fact, an important characteristic of our approach was the robustness of classification during the trials. This kind of interface seems to be quite stable and makes the daily re-calibration of the algorithm - which affects other implantable neuroprostheses - unnecessary. This is very important and could represent a significant advantage during daily activities carried out outside a controlled laboratory environment.Unfortunately, due to the time limitations of our experiments it was not possible to increase the number of grip types that the subject was asked to perform. However, results clearly indicate that multiple movements can be governed, probably more than the three used in the present study. Moreover, it is also possible to combine the state control approach presented in this paper to select different grasping tasks together with a proportional control . ThisIn the near future, the possibility of verifying these findings during chronic experiments with an implanted hand prosthesis for daily activity uses, will be investigated. The analysis of the performance of the LIFE electrodes during long-term implants is very important to understand the potentials and shortcomings of this technology in terms of chronic usability, stability, etc. Moreover, particular attention will be given to characterize long-term changes in the cortical activation and new approaches will be explored for characterizing the long-term usability and for improving the efficacy of intrafascicular electrodes. For example, as previously shown for the central nervous system , actuatiCC hold shares in Prensilia Srl, the company that manufactures robotic hands as the one used in this work, under the license from Scuola Superiore Sant'Anna.SM and PMR contributed to all the stages of this work . JC, LC, SR, and JR developed decoding algorithms for signal processing and classification. MT and GA contributed to the in-vivo experiments and all the clinical training. CC and MCC designed the algorithms for the control of the hand prosthesis. PD, XN, and KY contributed to the design of the protocol. KPH designed tf-LIFEs. All authors read and approved the final manuscript.


Community-based management (CBM) has been implemented in socio-ecological systems (SES) worldwide. CBM has also been the prevailing policy in Sámi pastoral SES in Norway, but the outcomes tend to vary extensively among resource groups (“siidas”). We asked why do some siidas self-organize to manage common pool resources sustainably and others do not? To answer this question we used a mixed methods approach. First, in the statistical analyses we analyzed the relationship between sustainability indicators and structural variables. We found that small winter pastures that are shared by few siidas were managed more sustainably than larger pastures. Seasonal siida stability, i.e., a low turnover of pastoralists working together throughout the year, and equality among herders, also contributed to more sustainable outcomes. Second, interviews were conducted in the five largest pastures to explain the relationships between the structural variables and sustainability. The pastoralists expressed a high level of agreement with respect to sustainable policies, but reported a low level of trust and cooperation among the siidas. The pastoralists requested siida tenures or clear rules and sanctioning mechanisms by an impartial authority rather than flexible organization or more autonomy for the siidas. The lack of nestedness in self-organization for managing pastures on larger scales, combined with the past economic policies, could explain why CBM is less sustainable on the largest winter pastures. We conclude that the scale mis-match between self-organization and the formal governance is a key condition for sustainability. Community-based management (CBM) has been promoted as a sustainable alternative for governing common pool resources, such as pastures, forests, water and fisheries The conventional approach has been to consider the size of the resource system, the group size and the socioeconomic heterogeneity as the key conditions for the sustainable management of SES To self-organize for sustainable resource management, resource users must have a minimum degree of autonomy and secure access to the resource In this study, we focus on the question posed by Elinor Ostrom: “Why do some resource users self-organize to manage common pool resources sustainably and others do not?” We build on a rather unique dataset which allows for comparative quantitative research on the management of reindeer pastures by Sámi pastoralists in Finnmark, Norway. The pastoralists self-organize in groups (siidas) in which the reindeer are herded together To explore how the organization of herders might affect sustainability, we first examined the relationships between indicators of sustainable outcomes and structural variables including: i) the area of the pastures, ii) the inequality of herders with respect to herd size, and iii) seasonal siida stability, i.e., the turnover of pastoralists working together throughout a year. Secondly, the explanatory mechanisms behind these relationships were explored by field studies on the largest winter pastures. The semi-structured interviews focused on the pastoralists’ understanding of the resource situation, trust and institutional arrangements. On the basis of our results, we discuss how the CBM strategies in Norway see  that empData on individual herding units were mostly derived from the ecological statistics compiled annually by the Norwegian reindeer husbandry administration In Finnmark, as much as 39 of the 44 summer pastures are each managed by one siida. The remaining five summer pastures are each shared by two or three siidas. We used the delineation of siida pastures to indicate summer pasture size. In contrast, the five largest winter pastures encompass 11–21 siidas, whereas the five smallest winter pastures are managed by one to six siidas each . We relaWe used the pasture area, inequality among herders and seasonal siida stability as structural predictor variables in the analyses. We expected the pasture size to be an important determinant of sustainability. However, due to difference in the match between the pasture size and the siida organization, we expected the effect of pasture size to differ between summer and winter pastures. Inequality has been hypothesized to influence incentives for collaboration and, therefore, sustainable outcomes lme) using the nlme library in RThe data were analyzed by linear mixed-effect models  to investigate how model simplification affected the relationships revealed by the initial models http://www.ecologyandsociety.org/vol16/iss3/art4/appendix3.html, Accessed 2012 Nov 12, The quantitative analyses showed that unsustainable outcomes were more common in the five largest winter pastures indicating that collective action problems might be more pronounced in these areas. Accordingly, we selected the five largest winter pasture areas for the interview inquiry  and the scale of formal governance (i.e. the need for well-defined boundaries) or, a lack of sufficient autonomy for the pastoralists to make their own decisions. Voluntary programs for establishing customary tenures have been initiated by the administration, but formalizing customary rights through independent courts have also been discussed see . We therOur standards for ethics were approved by the Norwegian Social Science Data Services and included a letter of information about the study before the start of the interview to secure voluntary participation and a perusal of the final transcript of the interview, if requested. We informed about the survey, the purpose and how data would be stored and used. Due to abuse of written statements in the past, Sámi elders are reluctant to provide signatures of any kind. Thus we obtained verbal consent from the participants. This procedure was approved by the Norwegian Social Science Data Services, which check the ethics and is the only institution that issue official licenses to all social science studies in Norway.The size of the winter pasture had, relative to the other structural variables, a strong negative effect on all the sustainable outcome variables . The effThe interviews suggested that the variables used as outcome variables in the statistical analyses were in agreement with the pastoralists’ own views on sustainability Q1, . There wThere was a clear difference in the levels of trust for the summer and winter pastures Q2, . Most suThe lack of conflict resolution mechanisms for the winter pastures was striking Q3.A, . The smaMost of the pastoralists preferred to divide the winter pastures into customary tenures, but they disagreed on the use of voluntary agreements versus formalization through the courts. There were pastoralists who claimed that newly rich pastoralists do not respect the customary tenures, so these respondents only options was to use the court to claim pasture rights. Others argued that the voluntary division of pastures does not work due to overlapping use by different siida groups. Only 12% did not want to divide the winter pastures into smaller tenures related to siida groups. A few warned that such divisions would ruin the traditional culture, solidarity and flexible use of the pastures and move reindeer pastoralism toward ranching.As much as 88% perceived the governance system as a necessary third party for formalized conflict resolution, monitoring and enforcement. The lack of impartial and fair treatment due to kinship or friendship among the co-management boards was the main source of distrust. Recent decisions associated with total allowable reindeer numbers, weighing programs, and the processes behind the division of winter pastures had also caused discontent with the administration. Most pastoralists argued for more impartiality, either by using co-management boards from neighboring regions or by transferring authority to the governor.The pastoralists did not support increased autonomy for the summer siidas. The primary arguments against devolution were the need for regulating the competition between siidas on the winter pasture and the protection against encroachment. Those who partly agreed argued that self-determination could work under the condition that appropriate rules or customary tenures were established on the winter pastures. For some, the transfer of rulemaking authority to the summer siidas was undesirable, as the elites have too much power in the local boards, whereas others maintained that the reindeer are privately owned and they cannot tell their relatives to slaughter their herds. Many pastoralists perceived the 2007 Act that devolved the rulemaking authority to the siidas as a repudiation of liability, as the governing bodies caused the situation. The generous allocation of herding licenses and subsidies allowed too many pastoralists to accumulate herds on shared pastures during the 1980s. Combined with the definition of winter pastures as commons in the 1978 Act, which some pastoralists interpreted as open access, new herds and expansionism have resulted in crowding on the winter pastures.Our results suggest that the match between the scale of self-organization and the scale of formal governance is a key condition for sustainable outcomes in a SES. The CBM was designed to delegate the rulemaking authority to the siidas, but the challenge remains in how the users self-organize at the higher nested levels, i.e. winter pastures. In our case, the collective action problems emerged on the large winter pastures shared by several competing siidas. Our findings were based on the combination of quantitative analyses of data from official databases and interview inquiries, linking structural variables with explanations of sustainable outcomes The effect of pasture size on sustainability differed between seasonal pastures. Large winter pastures had a negative effect on the herders’ livelihood income, the proportion of calf slaughter and the slaughter weights of calves. No such relationships were evident on the summer pastures. Most summer pastures have well-defined boundaries, with usually one siida group having the exclusive rights to the pasture. Accordingly, the size of the summer pasture only had small effects on the sustainability indicators. These differences between seasonal pastures were also evident in the interview inquiry . On the Our assertion that collective action problems are crucial for understanding this pastoral SES, is also corroborated by the fact that a high stability in the social organization of herders and a high degree of equality among herders, in addition to small winter pasture size, had a positive effect on some of the sustainability indicators. Specifically, the quantitative analyses showed that pastoralists belonging to the same siida throughout the year slaughtered a higher proportion of calves compared to herders that changed the siida group seasonally. Calves are generally slaughtered before the herds move into the winter pastures, and calf slaughter will, as explained by the herders in the interviews, spare the winter pastures and reduce the risk of losses of weak animals under unfavorable winter conditions see also . On the As CBM is often based on the subsidiary principle, the nestedness of social organization is easy to ignore when policies are put into practice Critics of CBM have also argued that the strong emphasis on formalized rules, rights and sanctioning mechanisms does not fit the flexible social organization needed in mobile pastoral systems CBM focus on the capabilities of pastoralist groups to establish their own rules, monitoring and sanctioning mechanisms for managing common pastures Text S1The text provides a more detailed description of community-based management of Sámi pastoral ecosystems in Norway.(DOCX)Click here for additional data file.


Recent explosion of biological data brings a great challenge for the traditional clustering algorithms. With increasing scale of data sets, much larger memory and longer runtime are required for the cluster identification problems. The affinity propagation algorithm outperforms many other classical clustering algorithms and is widely applied into the biological researches. However, the time and space complexity become a great bottleneck when handling the large-scale data sets. Moreover, the similarity matrix, whose constructing procedure takes long runtime, is required before running the affinity propagation algorithm, since the algorithm clusters data sets based on the similarities between data pairs.Two types of parallel architectures are proposed in this paper to accelerate the similarity matrix constructing procedure and the affinity propagation algorithm. The memory-shared architecture is used to construct the similarity matrix, and the distributed system is taken for the affinity propagation algorithm, because of its large memory size and great computing capacity. An appropriate way of data partition and reduction is designed in our method, in order to minimize the global communication cost among processes.A speedup of 100 is gained with 128 cores. The runtime is reduced from serval hours to a few seconds, which indicates that parallel algorithm is capable of handling large-scale data sets effectively. The parallel affinity propagation also achieves a good performance when clustering large-scale gene data (microarray) and detecting families in large protein superfamilies. Data clustering is to group a set of objects in such a way that objects in the same group (cluster) have higher similarity with each other than those in the other groups (clusters). It is a common technology for data mining and analysis in many fields, such as pattern recognition, machine learning, bioinformatics and so on. Many novel clustering algorithms have been introduced to handle biological problems, including protein families/superfamilies detecting In the last decade, many clustering algorithms were proposed and widely applied to the biological researches The rapid increment in biological data sets scale poses great challenges for sequential algorithms, and makes the parallel clustering algorithms more attractive http://hpca.shu.edu.cn/mpiap.This paper focuses on the parallel biological clustering for large-scale data sets in the distributed system. A promising algorithm called Affinity Propagation In order to measure the efficiency of the parallel clustering algorithm, the runtime and speedup of the algorithm are recorded. Two parts of runtime are measured. The first one is the runtime of constructing the similarity matrix, and the second is the runtime of the clustering algorithm. Our parallel clustering algorithm runs on the cluster computers environment. The cluster consists of 16 nodes, and in each node, there are 1 quad core Intel Xeon processor and 8 GB memory. All nodes are connected with each other by the gigabit Ethernet.Five data sets (3 gene and 2 protein) were used in the experiments. For gene data, Gene Ontology Overlap Score is used to measure the clustering results. The Gene Ontology (GO) project provides an ontology of defined terms representing gene product properties. The ontology covers three domains: molecular function, biological process and cellular component Jaccard: given two sets, the Jaccard score is defined as the size of the intersection over the size of the union. For clusters PR: The PR score includes two parts, the Precision score and the Recall score. For clusters For each data set, we take an average score over all clusters, weighted by cluster size, to get the For protein data, the protein families are detected by the clustering algorithm. The Recall and Precision Measure Score (F-Measure Score) is used to measure the clustering results. F-measure score considers both recall score and precision score. For a cluster Two protein subsets with family annotations, containing 14927 and 5431 protein sequences, are regarded as the gold-standard and are clustered to measure the algorithm performance in the experiments. The F-measure score varies from 0 to 1, where 0 is the worst and 1 is the best. For each cluster, the maximum value is taken as the F-measure score over all protein families, and the average value over all clusters, weighted by cluster size, is taken as the F-measure score of a data set. The F-measure scores of two protein superfamilies are listed in In order to validate that the parallel affinity propagation algorithm performs well and its results are similar to the non-parallel affinity propagation algorithm, we make the error rates analysis of both algorithms. We get the non-parallel program and a relatively small data set  from the original publication of AP algorithm The parallel affinity propagation clustering algorithm can address the large-scale biological problems such as clustering the microarrays gene data sets and detecting the protein families effectively. The Euclidean distance and BLAST E-value are used in the experiments to describe the similarities of gene data pairs and protein data pairs, respectively. In the similarity matrix construction, the memory-shared architecture minimizes the communication time between data pairs, and the shutter partition of data sets balances the computing loads on cores. Compared with the sequential algorithm, the parallel affinity propagation algorithm reduces the runtime significantly and achieves promising speedups. Also, it handles large-scale biological data sets effectively. From the GO overlap score and F-measure score, the affinity propagation is validated so that it is very feasible in clustering the gene data sets and detecting the protein families. Besides the analysis of microarray gene data and protein families, it is possible and promising to apply the affinity propagation algorithm into some other researches like microbial communities.There are two steps for affinity propagation algorithm to cluster a data set. The first one is constructing the similarity matrix, and the second is exchanging messages (responsibility message and availability message). However, considering the strong correlations between each data points in the procedure of constructing similarity matrix, we implemented parallel similarity matrix construction algorithm in the memory-shared architecture. The parallelism in this kind of parallel architecture is on the thread level, and threads share the memory with each other, so there are nearly no communication cost among threads. For the affinity propagation algorithm, it always requires large memory space to store intermediate information when clustering large-scale data sets. Since the distributed system consisting of many computers, large memory size and great computing capacity are available, it become the best choice for the parallel affinity propagation algorithm.The increase of communication cost leads to a longer algorithm runtime and a lower speedup. In all kinds of communication, the global communication is the most time consuming. The affinity propagation algorithm is parallelized on the process-level, and each core can run one or several processes concurrently. According to two message computing rules, nearly Since affinity propagation algorithm runs based on the similarities between data pairs, the similarity matrix is required to be constructed firstly. There exist many methods to construct the similarities matrix, including the Euclidean distance, Pearson correlation coefficient, E-value(output of BLAST software) and so on. The time complexity of constructing the similarity matrix is about The shutter partition way rather than the sequence way, is used to to alleviate the unbalanced computing load on cores. The sequential partition means that rows of the input matrix are assigned to cores one by one; while the shutter partition means that rows of the input matrix assigned to cores one block by one block, and the length of block equals the number of available cores. For instance, given an input matrix, with In the experiments, the Euclidean distance is taken to describe the similarities between data points. As shown in The affinity propagation algorithm clusters data set based on the similarity matrix, and exchanges two messages between data points. The two messages are responsibility and availability messages. The responsibility When the algorithm runs, three information matrices (one for similarity and two for messages) are required to be stored in the memory. In the information matrices, each row or column represents one data point. For large-scale data sets, it is impossible for the stand-alone computer to run the sequential affinity propagation algorithm because of the nearly endless runtime and the limitation of memory space. Given a data set with more than 50000 data points, it requires nearly 56 GB (double precision) memory space to store three information matrices and the algorithm runtime is more than 30 hours. The parallel affinity propagation in the distributed system can alleviate this kind of limitation significantly.In the distributed system, affinity propagation algorithm runs on the process-level parallelism. Each process is assigned a few rows of the three information matrices, and each core execute one or several processes concurrently. From the The key issue in the parallel affinity propagation algorithm is to parallel exchange messages among data points. According to the message computing rules, the responsibility message is computed by the rows and the availability message is computed by the columns. Since the information matrices are partitioned by the rows, the data chunks of each row are all stored in the local running process when computing the responsibility message. So the responsibility message can be computed independently without communication cost among processes. For the availability message, the summation values of all columns in the information matrices are computed. However, since data chunks of each column are distributed on the different running processes, data chunks required to be gathered from all processes for In order to minimize the global communication times, the local summation of Two kinds of data sets are used here, including the gene data sets and protein data sets. DNA microarrays are extremely powerful tools for such studies in which they allow one to probe virtually the entire transcriptome to give an overall picture of gene expression behavior For protein data sets, protein families are detected in the superfamily by the affinity propagation algorithm. Detecting protein families in large-scale superfamily is a difficult but important biological task. Proteins with the same functions or biological processes should be in the same protein families


As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing  is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior. A self-organized coordination between individual agents is often the hallmark of many natural and man-made complex systems. One of the most prominent examples of such behavior is the phenomenon of synchronization The exact conditions under which large populations of neurons spontaneously synchronize are in general not fully understood, even in the non-delayed coupling case. In the latter case, Mirollo and Strogatz analytically demonstrated that synchrony can be a stable state for a population of globally pulse-coupled oscillators Delay in the interaction among dynamical systems has an ambivanlent effect. In some cases it can stabilize the systems Delay-induced sychronization in complex networks of bursting nodes modeled with Rulkov maps has been recently studied. While an increase of the coupling strength always enhance synchronization, regular or irregular propagating fronts appear intermitently as delays increase It is also reported that diffusive delayed coupling enhance synchrony Our aim is to study the interplay between conduction delays and network topology in an ensemble of delay interconnected neurons. First, we address the ideal situation where all conductance delays are identical and later the situation where the natural frequencies of the neurons are distributed. In order to understand the role played by the pathways in which the neurons interact with other neurons, we consider different interconnection topologies, ranging from regular one-dimensional lattices to scale-free networks. We study two types of neural excitability by mean of two different conductance-based models. In these models, the membrane potential In the Hodgkin and Huxley (HH) model In the Connor-Stevens (CS) model This model includes an additional conductance current, called the A-current, which is responsible of the different excitatory behaviors between both models In both models, the pulsed synaptic transmission between neurons is modeled, following Neurons can also interact with each other through electrical synapses, also known as gap junctions. In the electrical synaptic case, the synaptic current takes the form:We study how both synaptic transmission schemes affect the network synchronization.The synchronization of neurons may depend on the synaptic network in which they are embedded. To study the role played by the different synaptic pathways in the synchronization of our ensemble of neurons, we consider five different topologies such as: regular, small-world, random, scale-free and globally coupled networks. In the regular lattice, neurons are connected with the kth firing of the neuron i. The idea behind this definition is that the phase of a neuron experiments a change of i. Averaging over elements and integrating in time, we obtainTo characterize the synchronization in our network, we define the phase To measure global synchronization we extend the sum in Eq. (10) to all neurons. Then, we quantify the global phase synchronization of neuron Averaging over elements and time we obtain a global order parameter.These order parameters are zero if the phases of the neurons are equal and one if they differ by First we analyze the case of identical neurons. We study the effect that the rewiring probability and the number of connected neighbors have on the synchronization of the system. Then, we consider the situation in which the natural frequencies of the neurons are distributed according to a Gaussian distribution.Finally, we particularize our study to a real network, the macaque cortico-cortical network.Let us consider the situation in which the delays in the connection between neurons are all identical and the neurons operate in a regular spiking regime  model exhibits qualitatively the same synchronization regions. In In order to understand the role played by large-range interconnections, we randomize the regular one-dimensional lattice. eighbors . We obseWith the aim of investigating the mechanism towards the synchronization in our system, we show in 2 and dispersion 2. With these distribution values i.e., change from a spiking oscillatory regime to a stable subthreshold state as the interaction strength increases. As we mentioned before, without interaction The assumption that all neurons in the network are identical and operate in a regular spiking regimen is an ideal situation. For this reason, in what follows we explore the case where the natural frequencies of the neurons differ from each other. In the HH model, the frequency of the spikes of the neurons depends on the injection current tate see . The regtate see . When thAs an example of real anatomical network we investigate the synchronization in the macaque cortico-cortical network We consider each node of the network following the HH neuronal dynamic as described in previous sections. We estimate the degree of synchronization in the network using Eqs. (9) and Eq. (11). It is interesting to notice that  10% see . The sec 10% see  what makWe have performed numerical simulations of delay-coupled neurons described by the HH and CS models. We have initially assumed that the neurons were chemically coupled and embedded in different complex networks. Our results show that, at a local level, all the considered topologies exhibit three different dynamical regimes: in-phase, anti-phase and out-of-phase. At a global level, however, only networks with certain degree of randomness in the connectivity  allow for a coherent response. These results were also observed when considering electrical coupling, highlighting the generality of the network synchronizing mechanisms. Besides the network architecture, axonal conduction delays also play an important role in the generation of coherent dynamics. We found that such communication latencies do not simply add to the phase difference obtained in the non-delayed case but can determine whether the interconnected cells can set in a coherent firing at all. We expect that our results provide insights in more complex situations, for instance in the presence of distributed delays.When neurons are not identical, but their natural frequencies are distributed, the region of phase synchronization decreases. Moreover, we found that the number of active neurons decreases for low coupling strengths due to the different frequencies. This emphasizes the importance of having small diversity in the system to obtain a coherent response. Besides the mechanisms studied here, other aspects could be considered as well. Inhibitory neurons and heterogeneous delays might play a significant role and will be considered in detail in future studies.Text S1The parameter for both models are shown in (TEX)Click here for additional data file.Table S1Parameters of the Hodgkin-Huxley model.(PDF)Click here for additional data file.Table S2Parameters of the Connor-Stevens model.(PDF)Click here for additional data file.


At a solid/liquid interface, physico-chemical phenomena occur that lead to the separation of electrical charges, establishing a zone called electrical double layer. The convection of one part of these charges by the liquid flow is the cause of the flow electrification phenomenon which is suspected of being responsible of incidents in the industry. The P' Institute of Poitiers University and CNRS has developed an original sensor called “capacitive sensor” that allows the characterization of the mechanisms involved in the generation, accumulation and transfer of charges. As an example, this sensor included in the design of high power transformers, could easily show the evolution of electrostatic charge generation developed during the operating time of the transformer and, therefore, point out the operations leading to electrostatic hazards and, then, monitor the transformer to prevent such risks. Electrically charged species of one sign appear on the solid surface while species of the opposite sign are distributed within the liquid. These areas are responsible for electrokinetic phenomena including the phenomenon of flow electrification. Often associated with a major risk in the industrial world this phenomenon still attracts a lot of attention. In fact, the flow electrification phenomenon could induce charge accumulation in a duct or in a tank, enough to produce catastrophic electrostatic discharges. For hydrocarbon liquids such as oils and gasoline, many accidents caused by this phenomenon have been identified –5.For the last thirty years, flow electrification events have been suspected to be responsible for power transformer failures. Damage surveys revealed evidence of electrical discharges  on inner pressboards –10.In transformers, the electrical current circulating in the windings generates heat. The dielectric liquid ensures the electrical insulation of coils and the cooling of the transformer through its forced circulation. The oil impregnated papers and pressboards are used to insulate and to support the copper windings. The oil flow at the pressboard surface leads, on the one hand, to a space charge in the oil which can relax in contact with grounded metallic walls, and, on the other hand, to a space charge in the pressboard which accumulates. In real transformers, the phenomenon is even more complex because the pressboard is porous and not homogenous but it is a combination of several components that may induce various physico-chemical reactions with the oil impurities. More, the aging of power transformer components , due to temperature and moisture, influences the flow electrification phenomena. Indeed, it seems that flow electrification might generate a surface charge, which would induce electrical discharges at the pressboard-oil interface enhancing the phenomenon. The results showed that the space charge density was multiplied by three or four when the pressboard had been degraded by electrical discharges. This conclusion was alarming because it seemed that a chain reaction might happen inside the power transformer, until its failure .Nowadays, the Electrostatic Charging Tendency (ECT) measurement in the Westinghouse protocol –15 and, An experimental sensor called the capacitive sensor has been developed for ten years in the P' Institute of Poitiers University (previously known as the LEA Laboratory) with the collaboration of EDF. This sensor is based on the accident analyses in high power transformers in which electric discharges were observed on pressboard surfaces in very well insulated parts of transformers.2.etc. are, in the current state of knowledge, hypothetical mechanisms that may explain the creation of charges. In hydrocarbon mixtures as insulating oils, chemical impurities (at a few ppm concentration) from the liquid would cause the phenomena. In any case, the physico-chemical reactions at the interface leads to a separation of electric charges, forming two oppositely charged areas: one in the solid and the other in the liquid, the electroneutrality of the solid/liquid couple is always preserved.The origin of the charge separation at the solid/liquid interface is still not well understood. Specific adsorption, desorption, corrosion Different models can be used to describe the electrical double layer. By likening it to a charged capacitor, one plate being associated with the solid and the other plate in the liquid, Perrin and Helmholtz ,18 propoIn high power transformers, the forced oil flow leads to a charge accumulation on the pressboard surface that increases the local electrical potential. The capacitive sensor was developed for estimating the accumulated charges  on a pressboard, or any other solid dielectric materials, for a given geometry and experimental protocol routinely applied. Moreover it allows one to analyze all the charge exchanges and movements, and the electric equilibrium.3.The capacitive sensor has been tested in a flow loop facility developed in the laboratory .3.1.A stainless steel loop  was buil® in order to avoid any chemical reaction and oil pollution. Flow electrification phenomenon is quite sensitive to any pollution.The loop is made exclusively of materials inert to mineral oils such as stainless steel, glass and vitonThe dimensioning of the pipes and the heat exchanger allows limiting the velocity of the oil. It is negligible compared to the oil flow velocity in the sensor. Thus, the oil entering the sensor can be considered completely electrically uncharged.The heat exchanger works thanks to a hot water circulation so without electrical perturbation (such as heat resistors) in the setup.3.2.2 cross section, and 300 mm in length) made of 3 mm thickness pressboard sheets stuck together and inserted in a PTFE frame. Two stainless steel electrodes (240 × 50 mm) are placed facing the largest external surfaces of the pressboard duct embedded in the PTFE frame. 2 mm thickness of PTFE insulates the pressboard from the electrodes. Connected to a picometer (Keithley 610C), these electrodes allow measuring a capacitive current called the accumulation current (7) correlated to the charge trapped on the pressboard surface and to the local potential increase. This configuration intends to simulate the pressboard parts inside power transformers which have high leakage impedance having regard to the imposed potential (windings and tank). The increase of the electric potential favors the migration of trapped charges on the solid surface to the ground. The electrical leakages occur upstream and downstream of the PTFE frame towards the two stainless steel tubes. Insulated from the rest of the loop by PTFE flanges coupling, and connected to two ammeters, these tubes allow measuring two currents called respectively upstream and downstream leakage currents (8–9). Moreover, the liquid charges are carried by the flow into the relaxation vessel  for 24 hours. The filling of the equipment is then done also under vacuum by direct transfer from commercial oil tanks. Finally oil flows in the loop for about 2 hours with a bulk pressure of 2,000 Pa to impregnate the pressboard duct. In addition, a 24 hours relaxation period is always applied before starting the experiment campaign.The measurement sessions are planned on two or three consecutive days. They include an oil temperature cycle (20–10–20–40–60–80–20 °C) representative of different operating conditions of the transformer: start-up, operation, over-heating. More, this temperature cycle allows observing evolution of parameters after heating and cooling. For each temperature, three laminar oil flow rates , leading respectively to mean velocities of 40, 68 and 95 cm/s in the pressboard duct are tested.3.4.Over 100 oil/pressboard pairs have been assessed on the sensor with different objectives:Qualification of new products (“standard pair”): oils  proposed by the oil industries are constantly changing their chemical composition for economic and technical reasons. Some oils are disappearing as new products are marketed. All these developments require determining the physical properties of these oils, such as electrostatic behavior, before use in power transformers.Monitoring the aging and maintenance of operating transformers (“standard pair”): the evolution over time of dielectric materials may require technical operations such as oil reconditioning or regeneration, topping up the oil level in the transformer or more simply to change the oil. The oil testing into the loop can then assess the impact of these operations on its electrostatic behavior.Screening of transformers under suspicion (“suspect pair”): specific patterns of dissolved gases in oil, electric discharge activities (detected by acoustic sensors) are all factors suggesting an electrostatic hazard in a transformer. Some pressboards and oils coming from these transformers have been studied for contribution to their supervision. In what follows, an oil/pressboard couple will be qualified as “suspect pair” if at least one of the two dielectrics is coming from a suspect transformer.Tools for studies of electrostatic behavior (“research pair”): the chemistry of pressboards and oils plays an important role in the electrostatic risk. In order to study it, pressboards whose chemistry is perfectly controlled and specially designed, and oils containing additives such as inhibitors and BTA, have been studied in the loop for the understanding of electrostatic mechanisms.4.4.1.versus time. The sign of the currents is representative of the majority of the different mineral oil/pressboard pairs studied. With the exception of a few pairs, including silicone oils for example, currents related to pressboard charges  are negative, the current associated with the oil (streaming current) is positive.As soon as the oil starts to flow, a charge is generated at the interface. Positive charges in the oil are carried away by the flow and induce the streaming current which passes by a maximum value before reaching a steady state. In the same time, opposite charges are trapped inside the solid pressboard. The magnitude of the accumulation current increases and comes back more or less rapidly to zero. The surface potential increases, until reaching a steady state leakage current toward the grounded outlet and inlet ducts through paths along the interface. The dynamic of the transient state, the magnitude of the streaming current and the maximum value of the accumulation current depend on the oil/pressboard pair. When the oil flow is stopped, the continuous charge separation process stops at the interface and all solid charges leak to the ground. Accumulation current is then positive with negative leakage currents. It can be checked that the sum of the leakage (inlet and outlet), accumulation and streaming currents is equal to zero at all time.Characteristic parameters considered as relevant with regard to flow electrification have been measured for several combinations of (new and used) oil/pressboard pairs. They depend on the studied pair, oil temperature and flow velocity. The principal studied parameters are:versus infinite time of the accumulation current with oil flow.Charge accumulation “Q”, obtained from integration Steady state streaming current.4.2.The electrical equivalent circuit allows representing this measurement system  24,25].,25.24,25Considering this circuit, the solid potential directly proportional to the solid accumulation charges depends on the generating current magnitude and the electrical properties of the solid/liquid couple.5.After 10 years of tests and over hundred pairs of oil/pressboard expertise, the sensor has never allowed the production of electrostatic discharges and to reproduce the electrostatic hazards. The dimension of the sensor relative to power transformers is probably at the origin.The potential on the surface pressboard (charge accumulation) is probably limited by the electrical insulation of the sensor, which is much lower than that encountered in practice. Anyway, the device allows comparing different oil/pressboard couples  and 6 inversus flow rate, as well as temperature for different new oils and the same pressboard, respectively. Current generation behaviors are quite classical. They increase with flow rate and temperature. The current varies globally between 10 and 1,000 pA with some exceptional lower or higher values. For charge accumulation, the behavior is more complex. In fact, if the charge accumulation increases with the flow rate for all the different oil/pressboard studied versus temperature it is not foreseeable. It could increase, decrease or pass by a maximum or minimum. In fact, the charge accumulation is link to antagonist effects. The temperature raising favored the charge generation process at the interface but, at the same time, it increases the oil electrical conductivity and the charge leakage. Thus, the magnitude of the charge accumulation fluctuates over three decades of 0.1 nC to 100 nC.In the past reducing the oil flow rate has been one answer to the electrostatic hazard in high power transformers. However, its efficiency is not so evident considering the behavior of charge accumulation due to the increasing of oil temperature which inevitably occurs with flow rate reduction. And moreover, it does not also consider the premature aging of the cellulose and other materials due to higher temperature resulting of lower cooling.versus oil resistivity for one flow rate and one temperature are presented in Charge accumulation measurements for standard pairs and suspect pairs 6.Thanks to this capacitive sensor, the measurement of the accumulated charge allows assessment of power transformer behaviour towards flow electrification and electrostatic hazard. Such a sensor could be easily re-designed to be implemented on the oil circuit of a real high power transformer in order to monitor online the flow electrification hazards in the transformer.