Stereoscopic vision delivers a sense of depth based on binocular information but additionally acts as a mechanism for achieving correspondence between patterns arriving at the left and right eyes. We analyse quantitatively the cortical architecture for stereoscopic vision in two areas of macaque visual cortex. For primary visual cortex V1, the result is consistent with a module that is isotropic in cortical space with a diameter of at least 3 mm in surface extent. This implies that the module for stereo is larger than the repeat distance between ocular dominance columns in V1. By contrast, in the extrastriate cortical area V5/MT, which has a specialized architecture for stereo depth, the module for representation of stereo is about 1 mm in surface extent, so the representation of stereo in V5/MT is more compressed than V1 in terms of neural wiring of the neocortex. The surface extent estimated for stereo in V5/MT is consistent with measurements of its specialized domains for binocular disparity. Within V1, we suggest that long-range horizontal, anatomical connections form functional modules that serve both binocular and monocular pattern recognition: this common function may explain the distortion and disruption of monocular pattern vision observed in amblyopia.This article is part of the themed issue ‘Vision in our three-dimensional world’. These differences are created by the horizontal separation of the eyes in the head. Julesz  recogniza,b, these two processes in stereoscopic vision are illustrated. Triangulation from the eyes (figure 1a) can be used to recover the depth of objects in the scene. Figure 1b shows the requirement for pattern matching between the left and right eyes’ neural signals. In a crowded set of features with multiple similar features, the brain must find the correct matches between pairs of features (shown by the linking arrow between the left and right eye images in figure 1b), otherwise depth cannot be recovered accurately. Julesz highlighted this ‘correspondence problem’, as it became subsequently known [Figure 1c shows such a stereogram suitable for viewing with red–green stereo glasses.In figure 1ly known , with hiThe relationship that defines the presence of correspondence in stereoscopic vision is essentially structural and mathematical. The formal requirement is to establish the mapping from one field of pattern elements to another. Unless the neural mechanisms can establish this local matching, the brain will be unable to detect any higher-order structural relationships, which in the case of stereo vision reveal the size and shape of the figure defined by the differences in binocular disparity, as well as the figure's depth profile.Considering the relationship as a mathematical abstraction is useful because it highlights the problem in the form in which it is presented to a network of neurons in the visual cortex. These neurons receive signals from various sources, rearrange the signals according to the connectivity within the network and pass these rearranged signals onward to further neurons. If the connectivity of the network has been set by learning rules or processes of developmental plasticity that are local to the neurons in the network, then, in many ways, the source of the input signals does not really matter. Locally, the neurons just receive signals from multiple sources, respond to the consistent, common components of those signals and then pass the result onward to other neurons. Regarded in this way, there is nothing special or unique about the sources of the signals being processed. Whether or not the common components happen to derive from stereoscopic correspondence is incidental.Julesz understood the logic behind this point: in his 1960 paper ,6. This 2.For isolated visual features, the question of how the nervous system matches features in the left and right eye's images is potentially explicable at the neuronal level, as a result of the discovery of neurons in the primary visual cortex with specific binocular properties ,8. TheseWhile isolated contours are certainly encountered from time to time in our everyday visual environment, our stereo system must also operate in a different kind of visual scene, which is rich in many overlapping contours and features. Helmholtz noted the ability of stereoscopic vision to contribute to the analysis of these complex binocular scenes, referring to the vividness with which cracks, cavities and surfaces could be resolved in stereoscopic photographs of glacial ice . Julesz b), they consist of a pair of micropatterns with locally corresponding features across the grid of dots. In the construction of these patterns, whether a particular dot is black or white is the outcome of sampling a random process, but once it is determined that a dot in the left eye's image is black, then the corresponding dot in the right eye's image must be black also. Hence, the relationship of the dots when comparing the eyes’ images with each other is fixed rather than random. The pair of arrows linked together in figure 1b shows the correct correspondence between a pair of white dots, one from each eye. Julesz pointed out that this pairing must be established in the presence of multiple alternative possible pairings, which in figure 1b are available by pairing with one of the other two nearby white dots.If we look in detail at a pair of image regions  arising from one of Julesz's random-dot figures b, they c3.Neurophysiological studies in visual areas of the macaque monkey have shown the presence of neurons tuned selectively for binocular disparity , the initial locations in which the thalamic axons lie are strongly segregated, with some locations being dominated by the left eye and others by the right eye . The segHubel and Wiesel first identified these structures, which are especially prominent in layer 4 of V1. They conceived that within a single OD column there might be a small but steady progressive change in the retinotopic location of the neuronal receptive fields across the width of one column. At the column boundary, the neural signals switch to being dominated by the other eye and at the same time the preferred position shifts back, against the previous progression, by about half the spatial distance traversed in the neighbouring column devoted to the other eye . With thThe above description was very much derived from work with Old World monkeys, chiefly macaque. Different forms of visual cortical mapping are found in other species , with evThis highly local wiring to form binocular neurons mandates a maximum offset between left and right eye signals, which is the size of an OD column projected back out into the spatial world. If the spatial separation of inputs that is required to serve stereoscopic vision proved to be greater than the size of a single OD column, then this suggests that the relevant anatomical connections must be established by lateral neural connections that pass horizontally across the cortex.The idea under discussion here is that stereoscopic disparity might be processed by neural connectivity structured by the neighbourhood relationships of OD columns . A distiEvidence that lateral connections passing horizontally across the cortex may be important for binocular vision is available from the observations with injections of the anterograde tracer biocytin, either targeted into the centre of an OD column or avoiding the centres of these columns . Injecti5.Most of the above discussion has concentrated around the cortical organization for disparity selectivity in V1. Signalling of disparity by V1 neurons is simply an initial stage in the generation of neuronal responses that can potentially explain the behavioural and perceptual responses to stereoscopic depth ,34–36. WThis comparison is potentially revealing as V5/MT neurons possess a range of properties which indicate that this stage of processing is closer to the requirements to explain perceptual behaviour –20,37–39(a)a, the receptive field is drawn in angular coordinates, whereas in the bottom panel, figure 3c, the receptive field is drawn in spatial coordinates with respect to the position of the monkey's interocular baseline. The latter gives us a scale version of how disparity selective neurons signal the presence of features in the three-dimensional scene before the observer.For cortical area V1, we need to establish the relevant range over which binocular disparities are computed, which may be derived from earlier work from our laboratory ,42. Figufigure 3b introduces a schematic for the interpretation of the quantitative measurements of selectivity for binocular disparity (shown as D-max in figure 3b) and the spatial extent over which these disparity-specific responses are pooled (shown as the binocular integration zone). Based upon the analysis of responses in single neurons, we then form a population response for a group of neurons that have been recorded from a distinct subregion of V1. We consider the population response in conjunction with the cortical magnification factor to estimate what these population responses must mean in terms of lateral neural connections across the neocortical surface.To build the picture of how the receptive fields of single neurons relate to cortical architecture, we need to consider how these neurons pool signals for horizontal disparity across their receptive fields. Figure 3(b)b gives this schematically. Neural activity from points in the left and the right eyes  arrive within the binocular receptive field of the neuron . The horizontal separation of the green and red dots represents binocular disparity and is indicated by the length of the black horizontal arrows. The largest disparity that the neuron can encode is here termed D-max, by analogy with the measure used in human perceptual studies [The range of disparities encoded by a neuron's receptive field gives us the range of sensitivity to binocular depth, projected back onto the retinotopic coordinate frame of the eyes and the visual cortex. Figure 3 studies ,44.b. Although this zone extends both horizontally and vertically, it is specifically the integration zone for horizontal binocular disparity. Unlike Cumming [figure 3b, a vertical disparity would be equivalent to a vertical, rather than a horizontal, offset in the positions of green and red dots representing the inputs from the eyes. It is already established that the binocular integration zone cannot be estimated directly from the receptive field size measured with simple luminance stimuli, such as bars, spots and gratings [Disparity-sensitive neurons do not simply respond to binocular disparity at a single point in the retinotopic coordinate system. Rather they pool or integrate visual signals over a lateral extent in the same frame of retinotopic coordinates . This isfigure 3 Cumming , there igratings –48. We na). A roughly sinusoidal modulation of firing rate results, which declines in amplitude as the spatial frequency of the waveform is increased (figure 4b). Quantification of the point at which the modulation falls to two-third of its peak is both a measure of the acuity of the neuron for detecting spatial modulation of disparity (figure 4c) and a measure of the size of the integration zone over which the neuron gathers information about horizontal disparity [The size of the binocular integration zone for pooling of horizontal disparity can be measured quantitatively by testing the cortical neurons with a field of random dots whose disparity varies with a sinusoidal waveform as a function of spatial position . This spfigure 4isparity ,48.Figud) were interpreted using a single Gaussian weighting function (as in c) to describe the size and shape of the binocular integration zone. Use of a single Gaussian is acceptable, given that almost all measurements of the response of neurons to disparity modulation give low-pass, rather than band-pass, tuning curves as a function of disparity modulation frequency (similar to those shown in figure 4c). The average high-frequency cut-off for the disparity modulation was 0.5 cycles per degree (figure 4d), much lower than the high-frequency cut-off for detection of sinusoidal modulations of luminance in the same neurons [The estimates of receptive field integration size for a set of 55 V1 neurons d were inon as in c to desc neurons .(c)et al. [figure 5a as a function of eccentricities near the fovea. There is not a great deal of variation as a function of eccentricity over this range, so the population response can be approximated by a single Gaussian curve with a spread (σ) of 0.5°. For the dimension of depth away from the head, a Gaussian function with this spread is plotted in figure 5c, after being transformed into coordinates of spatial distance relative to the interocular baseline.In order to gain a measure of the capacity of the population to signal stereo disparity, signals from individual neurons are pooled to gain an estimate of the responses of the population to stereo disparities. The range of the population response for stereoscopic disparity, as estimated by Prince et al. , is showd. In terms of a Gaussian weighting, this is equivalent to a standard deviation (σ) of 0.32°. The schematic of the V1 population response for eccentricities in the range 1–4° is shown in spatial coordinates in figure 5c. In total, this is the product of two Gaussian functions, one describing the range of disparities encoded by V1 neurons (from figure 5a) and the other describing the binocular integration zone (from disparity modulation measures in figure 4d).This can be combined with the population estimate of the binocular integration zone for stereoscopic disparity. This is derived from the average high-frequency cut-off for disparity modulation in V1 neurons as shown in figure 4(d)In order to estimate the cortical distance that is implied by interactions on this scale in visual field coordinates, it is necessary to make use of measurements of the cortical magnification factor: in linear terms, this is the distance in mm across the cortical surface that is devoted to the analysis of 1° of visual angle within the visual field. The magnification factor of macaques and humans varies substantially across the visual field, reflecting the dominance of foveal central vision in the primate visual system. Numerically, magnification factor is large in central foveal vision and declines away from the fovea.Macaca fascicularis), an early estimate [−1 at an eccentricity of 2.5°, the closest position with respect to the fovea at which estimates were reliable. This work was based on electrophysiological recording of cells sequentially with a microelectrode and subsequent reconstruction of electrode tracks from histological material.Gaining a quantitative estimate of the cortical magnification factor is not straightforward. Measurements within the foveal region are hard to achieve and published data provide some divergence of estimates. For juvenile monkeys . This implies lateral connections in the cortex of 1.5 mm, reasonably consistent with estimates for V1 derived from anterograde tracing with biocytin  and wellA second observation ,58 is tha shows the extent of population sensitivity for stereoscopic vision as laid out on the cortical surface of V1. The contour plot is transformed by the size of the cortical magnification factor from the sensitivity profile in angular coordinates (as shown for a single neuron's receptive field in figure 3a). The dimensions in the vertical (y-axis) for disparity are derived from the population profiles for disparity range in figure 5a. The dimensions in the horizontal (x-axis) are the estimated size of the binocular integration zone, summarized schematically in figure 3b and measured quantitatively in figure 4d.Figure 6a.— First, the disparity range and binocular integration zone are reasonably matched to each other size and are therefore consistent with a roughly isotropic set of horizontal cortical connections running laterally across the surface of V1 .et al. [— Second, contrary to Prince et al. , the disBoth these conclusions can be sustained under the conservative assumption that the V1 magnification factor is 3 mm degree−1 for the region of the visual field from which the neurons were recorded. If the true magnification factor were larger, then the second conclusion would be more strongly upheld. Note that these conclusions apply to the way in which the cortex processes horizontal disparities: neurons in V1 show a strong degree of specialization for horizontal, rather than vertical, disparity [There are two important conclusions that can be drawn from figure 6isparity .b) encoded within the neuronal population. To deal with the largest horizontal disparities encoded in V1, these connections need to stretch over about 3–4 mm of cortex. Connections running over a similar distance are also responsible for integrating laterally (shown as the binocular integration zone in figure 3b), thereby pooling signals about horizontal disparity from nearby horizontal and vertical points in the visual field.In summary, the data suggest that a single wiring principle may underlie cortical connectivity for two aspects of stereoscopic vision in V1. There are neural connections that run across visual cortex to build sensitivity to the range of horizontal binocular disparities 2 in extent. However, the three papers quoted all use diverse techniques , and there is some divergence in the estimated size of V5/MT, even taking account of differences in body weight and species. It has also been asserted that the mapping of the visual field onto V5/MT may be non-uniform, with an expanded representation of the inferior quadrant in each hemisphere [The relationship between the scale of visual receptive field properties and visual eccentricity is much shallower in cortical area V5/MT compared with V1. In the macaque, area V5/MT is smaller than V1 by a factor of 10–20× measured in area ,60,61, smisphere . For theThe detailed arrangements for recording from V5/MT used in our laboratory have been previously reported ,20. The Each neuronal recording site was accessed using an oblique approach to area V5/MT, using a guide tube that was directed towards V5/MT approaching the target from the posterior side. The guide tubes were inserted through a rectangular grid of locations, organized around a reference point defined by the recording chamber that was chronically implanted by surgery at a fixed location on the skull. The verification of the V5/MT recording site was made on the basis of the sequence of grey matter and white matter boundaries encountered during the advance of the electrode, the high proportion of neurons selective for the direction of visual movement, the consistent organization of receptive fields from different recording sites in forming a map and, at the end of the procedure, histological verification.a. This shows the location of V5/MT in one macaque monkey on the posterior bank of the superior temporal sulcus [figure 7a or in planes parallel to it.An example of histology is shown in figure 7l sulcus . The angThe spacing of these electrode tracks with respect to location across the surface of V5/MT is given by the relative angle between the grid and the cortical surface and the spacing of the insertion points across the grid. There will also be some inevitable variation in the exact trajectory of the electrode, even if it is inserted into precisely the same grid location, because the electrodes themselves may flex or bend a little as they move through the cortical tissue. For these reasons, the analysis of receptive field locations with respect to the cortical surface is based on the averaged value of many estimates of receptive field location from sequential electrode penetrations at the same grid points.−1 over most of the area of V5/MT from which recordings were made, with only a few outliers. For the present purposes, we adopt a median estimate of 0.5 mm degree−1.Paired estimates of receptive field locations from different grid positions were referenced to the corresponding pairs of cortical locations in area V5/MT. Each pair of differences contributes one estimate to the calculation of cortical magnification factor . The raw data are shown in electronic supplementary material, figure S1, where they are plotted in cortical coordinates  and eccentricity in the visual field. The left–right and dorsal–ventral plots confirm the expected topography on the cortical map with higher values of magnification factor towards the fovea being represented as lateral and ventral on the cortical surface. The eccentricity plot shows that cortical magnification factor decreases as eccentricity increases. There is considerable scatter in these data, so a surface smoothing procedure was used to extract the estimates of cortical magnification factor. The resulting values are within the range 0.3–0.7 mm degreeb and in coordinates of three-dimensional space in figure 5d. The data for V5/MT show a slight over-representation of near disparities, as reported previously [figure 5d. It must be acknowledged that there is less certainty about the estimation of the other dimension considered for V1, which is the lateral extent of pooling for horizontal disparity in V5/MT. There are no quantitative estimates based on corrugation sensitivity for V5/MT neurons, as there are for V1 neurons. The V5/MT population response along the axis of horizontal distance as plotted in figure 5d is based on the differences in classical receptive field size measurements between V5/MT and V1 [This value of cortical magnification factor was applied to V5/MT measurements in the same way as earlier for V1. First, we took the range of horizontal disparities encoded in V5/MT as plotted in angular coordinates in figure 5eviously ,64, so tT and V1 , under tc,d, the representation of disparity in V5/MT is somewhat broader than that in the primary visual cortex V1. Figure 6b shows the transformation of the population response of figure 5d into estimates of cortical distances across V5/MT using the magnification factor derived earlier. Although there is a moderate broadening of the angular size of the population receptive fields between V1 and V5/MT, the representation in cortical distance in figure 6b shows that there is actually an anatomical convergence. Thus, based on this analysis, a wide area of V1 anatomically converges to a smaller area of V5/MT .In spatial terms, comparing figure 5The size of the disparity-processing domain is such that the entire range of disparities can be accommodated within an average distance of 1 mm across the cortical surface of V5/MT. The variation in our estimate of magnification factor might raise this to 1.4 mm or lower it to 0.6 mm at different locations within V5/MT. De Angelis & Newsome  conducteIn comparison with the organization of OD columns in V1, there is of course no exactly equivalent structure for V5/MT, as V5/MT does not possess OD columns. However, anatomical tracing of intrinsic connections in V5/MT does suggest connectivity extending over many millimetres of cortex with repeat patch-like connectivity at approximately 2 mm distances . The fun6.It is important to understand whether the measures of interaction distance developed here are applicable to the explanation of perceptual phenomena. With sparse, isolated features, human observers are able to perform a near–far discrimination over wider ranges than maximum range of interaction distance measured here with random-dot patterns. Therefore, the most direct comparison is with perceptual thresholds that are measured with random element stimuli, specifically designed to probe the fine ‘pattern matching’ aspect of stereoscopic vision .For two of the animals from which the V1 recordings were obtained, behavioural tests of their perception are available. Using the dynamic random-dot stereoscopic stimuli employed in the recording experiments, one animal could discriminate between near and far disparities of ±0.6°, whereas the other's range was slightly more limited . This di7.On the basis of the measurements of sensitivity to horizontal disparity in cortical area V1, we suggest that V1 is organized for stereoscopic processing into a functional module about 3–4 mm across. This is several times larger than the size of an OD column. The same calculations for V5/MT suggest a domain that is about 1 mm across, in agreement with the estimates for mapping disparity-specific regions of this cortical area . Anatomiet al. [There are further differences in the arrangements for encoding of stereoscopic disparity in these two cortical regions. Within V1, there is a wide range of selectivity for disparity, even locally at the same neurophysiological recording site. When recording with a single electrode, it is possible to extract the activity of single, isolated neurons for comparison with the activity of a cluster of more poorly isolated neurons simultaneously recorded at the same site. In V1, the tuning of single neuron activity for disparity is only weakly related to the tuning of the neighbouring neurons, assessed either in terms of selectivity for disparity or in terms of the preferred disparity of the neuron . This coet al.  for a siet al. [figure 3c that denotes the functional connectivity of the binocular integration zone.For the case of V1, the data analysed in this paper indicate that the cortical organization for processing of binocular disparity is isotropic, which is a novel aspect that has not been previously identified. We have analysed the disparity range encoded by the population of V1 neurons and the integration zone over which these horizontal binocular disparities are pooled. When these ranges are expressed in terms of cortical representation , these ranges are matched to one another in cortical distance. We suggest that this reflects a more fundamental feature of the underlying cortical anatomy, which is that the functional module for disparity processing in V1 is defined anatomically by local horizontal connectivity of 3–6 mm in cortical extent . Connectet al.  may set Earlier in the paper, we referred to Julesz’ conception that there might be a binocular pattern recognition system ‘identical to’ the monocular pattern recognition system. We consider further here the idea that this identity between binocular and monocular pattern recognition systems might be fulfilled in part by this highly specialized network of V1 neurons serving foveal vision. Recall that in humans the central 3° of visual field are served by something close to 30% of the primary visual cortex . We exam(a)Amblyopia is characterized by weaker or disrupted pattern vision, which persists in the absence of obvious pathology in the eye or central nervous system . AmblyopAn eye that exhibits unilateral amblyopia is often referred to colloquially as a weaker or lazy eye. In animal studies that model amblyopia by imposing a period of unilateral deprivation of input to one eye, the synaptic connections from that eye to cortex are reduced. Orthoptic therapy is often targeted at improving the weaker eye by requiring the child to wear a patch over the stronger eye to give the weaker eye a chance to increase the strength of its connections with the visual brain.However, the concept of the weaker eye is not the whole story. It has been recognized for a long time that the visual symptoms of amblyopia are not simply described by a veil of reduced visibility over one eye . Even whThe contribution of typical binocular development to the establishment of accurate monocular pattern vision is highlighted in a large-scale screening of visual function in a group of more than 400 adults who either had measurable amblyopia or exhibited risk factors for its development . This st(b)Julesz's pioneering work ,72 reveaThe disruption of stereo with spatially dense random-dot stereo figures by inversion of the contrast relationship between the dots in the left and right eyes was noted by Julesz . The reaAbsence of stereopsis with anti-correlated random-dot figures is most complete when a region with disparities programmed into the anti-correlated random dots is embedded within a surround region that is also anti-correlated . ObserveIf we are looking for an explanation of these results in the responses of neurons tuned to binocular disparity recorded from the visual cortex, then there is a striking discrepancy between the perceptual reports and the responses of neurons in primary visual cortex. In awake, behaving monkeys, Cumming & Parker  found thCortical area V5/MT of the macaque has been more strongly associated with the perception of stereoscopic depth. Nonetheless, the neurons of this area show substantial modulations to the disparity content of anti-correlated figures . Moreove8.This analysis and review has focused on the important role of stereoscopic vision as a detector of patterns that correspond between the left and right eyes. This capacity is crucial for animals or humans to exploit stereo for the breaking of camouflage. The same capacity seems to be lost in a targeted way in some forms of amblyopia and, in a way that is not fully understood, this binocular loss also leads to loss of performance in monocular pattern sensitivity in the amblyopic eye. Stereo and monocular pattern detection appear to share resources even though they are apparently different aspects of pattern vision. What is striking about these various types of visual cognitive capability is that the perception of the spatial relationships is immediate and effortless. While the neural mechanisms underlying these capabilities are initially established in the fine-grain spatial map of the primary visual cortex, it is the relationship between this fine-grain map in V1 and neural architectures of the numerous extrastriate visual areas that is responsible for the full performance of this pattern detecting system.


Magnetic resonance (MR) techniques used to detect lesions of the ligament complex for articulation of the ankle lack the desired accuracy for the study of the calcaneofibular ligament (CFL). The lack of sensitivity of the conventional techniques is due to variations in the dimensions of the CFL. The best results are obtained when the image plane is oriented parallel to the ligament. This study aims to develop a model that addresses the width, length and angle parameters of the CFL and the orientation of the MR image plane, and thus determine a technique in the oblique transversal plane with the foot in anatomical flexion, that is adequate for the majority of patients.To determine this orientation and adapt it to the majority of people, images of the articulation of the ankle in the 3D isotropic, volumetric, sagittal plane of 100 volunteers were taken using the MR technique. None of the volunteers had a clinical history of ligament lesions, serious pathologies, or surgeries. A measurement of the length, width, and angle of the CFL relative to the sole of the foot was performed using the MR tools. A virtual model was developed that simulated the visualization of the CFL in the oblique transversal image plane from 35° to 45° using the CFL dimensions of 100 volunteers. The comparison of the simulations with the reconstructed images validated the model and permitted the calculation of the agreement and sensitivity of each technique in the detection of the complete CFL.Using the simulator, it was possible to obtain the limit angle for complete CFL visualization as a function of its dimensions for any angle of the oblique transversal image plane of the MR.The results suggest that a single image acquisition technique in the oblique transversal plane at 38° with the foot in anatomical flexion would serve the majority of patients. The ligament complex of the ankle is composed of anatomical structures of various ligaments that are difficult to analyze. Among these structures, the calcaneofibular ligament (CFL) is frequently injured in young adults, especially individuals involved in sports such as basketball and football. This ligament is also the most vulnerable during inversion of the ankle. AccordiMagnetic Resonance (MR), a non-invasive and well accepted imaging technique, has beeThe lack of sensitivity of these techniques can be explained by variations in the dimensions of the CFL. In fact, Mayerhofer et al. proved tThus, in this investigation, to consider the influence of the width, length, and angle of the CFL, a model that addresses these parameters and the orientation of the MR image plane was developed. A technique was thereby determined, using the oblique transversal plane with the foot in an anatomical flexion that evidenced the whole CFL for the majority of healthy subjects.Male and female adult volunteers with ages between 21 and 50 years were selected by the doctors of the Department of Radiology of the Lumen Diagnostics Centre.The inclusion criteria were volunteers without a history of ankle sprains and without CFL lesions, without fractures, congenital diseases, or orthopedic surgeries involving the ankle and foot. Cases where fracture of the CFL was detected in the volumetric acquisition of the images were excluded from the sample. The acquisition of volumetric isotropic images of the volunteers in the sagittal plane was performed. The images of these volunteers were reported and sent to the researchers (CAE 03556912.0.0000.5497).The volumetric isotropic MR images of the 100 volunteers were first used to determine the dimensions of the CFL using the tools of the supervisory system of the Achieva Magnetic Resonance device. The measurements were performed 3 times by two technicians specializing in the musculoskeletal system.Next, a computational model was developed that represents the CFL relative to the image plane and determines whether there is complete visualization of this ligament. The model can consider all of the dimensions of the ligament with the foot in the anatomical position and simulates the visualization of any orientation of the oblique transversal image plane.To validate the computerized model, the CFL and its visualization were initially simulated considering the oblique transversal image plane at 35°. This technique was chosen because 35° is the CFL angle with the highest prevalence in the studied population. The CFL morphometric data from the volunteers were used for the simulation.As follow, the images were acquired in oblique plane at 35° and the isotropies images from the 100 volunteers were reconstructed in the same image plane. The accuracy of image detection was obtained directly in the oblique plane at 35° and compared with the reconstructed images accuracy. This comparison was also accomplished with the simulated images using the C contingency test.After validating the model, simulations were performed considering the oblique image plane at 36°, 37°, 38°, 39°, 40°, 41°, 42°, and 45°. The accuracy of detection was calculated to determine the best technique.To test the method, reconstructions of the 100 volumetric isotropic images were performed in the oblique transversal plane at 38°, which was considered to be the most efficient by the simulator, and at the 45° angle used by many clinics. These images, without technical information, were evaluated at work stations by 2 Radiology Technicians specialized in Magnetic Resonance of the musculoskeletal system. The examiners analyzed the images and, in consensus, evaluated which images visualized the entire length of the CFL.An analysis of agreement of the accuracy obtained across the various techniques was performed, both of the reconstructed images and of the simulations using the C contingency test. The reports from the doctors of the Lumen Diagnostic Centre were considered to be the gold standard.3; matrix 300 × 250; number of excitations 2; and acquisition time 3 minutes and 10 seconds)  weighted turbo spin echo (PDW-TSE) sequence without fat saturation in the sagittal plane The volunteers were positioned in the supine position with the arms extended along the body, and the sequences were performed with free breathing. During the exams, the position of the foot relative to the ankle was maintained at an angle of 90°, using immobilizers and special foams to maintain an anatomical position.The 3D sagittal volumetric images of the 100 volunteers permitted multiplanar reconstructions. For these reconstructions, the multiplanar reconstruction (MPR) commands were used, followed by the orientation of the oblique transversal plane and then the line setting function to select an angle of 35°, 38° and 45° Figure .Figure 2Before to start this research with the specific, this research project was approved by the Ethics Committee advice in Research involving humans at the University of Mogi das Cruzes .All participants were informed about the aims, and methodology of the study, as well as about the privacy of research subjects and confidentiality of their personal information, and institutional affiliations of the researcher.Images were used in the volumetric sagittal plane to measure the average angle, length, and width of the CFL of each volunteer.To measure the angle, using the “Line Setting” tool with angle option, a straight line was traced in each image in the sagittal plane, parallel to the horizontal flat surface, and another line was traced parallel to the plane of the ligament investigated Figure . After tThe programming and graphic development module of MatLab® was used to simulate the limits of complete visualization of the calcaneofibular ligament (CFL) as a function of the angle of the image plane.The variable dimensions  are input into the model by the user. The application considers the CFL as a rectangle represented by continuous red lines. Initially, the central axis of the rectangle is aligned with the image plane, represented by a dotted blue line Figure . The recF = 50 , with YF depending on the angular coefficient of the line  until it achieves the biometric position provided by the user. The matrix of rotation M is given by equation The rectangle is rotated around the central point , using equation The “Processing” menu allows the user to choose the direction (clockwise or counter clockwise) of rotation of the CFL as a function of the image plane. The application calculates the new coordinates as a function of the ordinate axis  of the representation of the CFL can be found. The expressions used in this phase are equations From YAs a result, the simulator shows the representation of the CFL (width and length), the angle of the image plane (α), the angle of the CFL (γ), the maximum angular variation as a function of the image plane (β), and whether complete visualization of this ligament occurred, as shown in Figure Another characteristic of the developed tool is the possibility of exporting the input and output data to a MS Excel® spreadsheet. This application also permits the printing of the graphical controls in conjunction with the data panels.The averages of the measurements of the width (W), length (L), and angle of the CFL (γ) were calculated, thus the prevalence of these values Figures  and11.FThe average angle of the CFL from the sample varied from 29° to 50°, with the highest prevalence being at 35° and with 80% of the sample between 35° and 41°. The width of the CFL varied from 1 to 10 mm with the highest prevalence between 4 and 7 mm. The length varied from 18 to 30 mm, and the most frequent measurements were 20 mm (17 cases) and 24 mm (25 cases).The reconstructed images and the simulations, both with the technique at 35°, where the complete CFL was not visualized, are in Table The accuracy of the images reconstructed at 35° was 96%, and the simulation accuracy at 35° was 95%. The 1% difference between the accuracy of the simulation and the accuracy of the reconstructed images shows that the model is valid for predicting the efficiency of the technique in the detection of the complete CFL.The position of the CFL that was not visualized in the simulation using the oblique transversal technique at 35°, shown in Figures Using the simulator, it was possible to obtain the maximum angular variation that allows the complete CFL visualization as a function of its dimensions for any angle of the oblique transversal image plane of the MR. Table Figure Table The C contingency test was applied to relate 2 variables: the GS with the multiplanar reconstruction (MPR) and later the GS with the simulated data (Sim) for the 35°, 38°, and 45° angles. Both, considering a degree of freedom of 99 and p = 1, showing that the technique at 38° provides the closest result to the report from the doctors of the lumen clinic Table .Table 6Additionally, the C contingency test was applied to relate 3 variables: the GS with the MPR and the Sim images for the 35°, 38°, and 45° angles, considering one degree of freedom = 198 and p = 1. Table The average values obtained for the length, width, and angle of the CFL in this study are similar to the values obtained in the studies with cadaver samples performed by Golanó et al., Taser eA study evaluateWhen a ligament is not completely visualized in the image, a lesion is diagnosed. However, the reliability of this discovery does not depend only on the lesion but also on the technical aspects of the magnetic resonance exam and the anatomical variations of the ligament. The use of an inappropriate image plane can provide images that lead to an incorrect diagnosis. Other pVarious researchers have sought to improve the complete detection of the CFL. Initially, the studies investigated the best image plane and foot position to avoid false positive. Beltran et al. used theA study performed by Boonthathip et al. showed tThis study did not address the cases of false negatives in patients with suspicions of lesion of the CFL or cases of CFL partially torn.This MR technique is proposed to improve the diagnosis for the majority of patients with suspicions of CFL ankle lesions, minimizing the possibility of false positives. This technique determine the most appropriate image plane. The choice of MR as a tool to measure CFL is due to the lack of protocols for CFL ankle lesions. In addition, this approach provided better sensitivity to investigate correlates impairment such as degenerative, traumatic, and ligament diseases of the ankle.In future studies we will analyze the oblique transversal technique of the ankle at the angle of 38° for patients with CFL lesions.


We present the development and application of a generic analysis scheme for the measurement of neutrino spectra with the IceCube detector. This scheme is based on regularized unfolding, preceded by an event selection which uses a Minimum Redundancy Maximum Relevance algorithm to select the relevant variables and a random forest for the classification of events. The analysis has been developed using IceCube data from the 59-string configuration of the detector. 27,771 neutrino candidates were detected in 346 days of livetime. A rejection of 99.9999 % of the atmospheric muon background is achieved. The energy spectrum of the atmospheric neutrino flux is obtained using the TRUEE unfolding program. The unfolded spectrum of atmospheric muon neutrinos covers an energy range from 100 GeV to 1 PeV. Compared to the previous measurement using the detector in the 40-string configuration, the analysis presented here, extends the upper end of the atmospheric neutrino spectrum by more than a factor of two, reaching an energy region that has not been previously accessed by spectral measurements. Measuring the energy spectrum of atmospheric muon neutrinos is particularly challenging due to its steeply falling behavior. As neutrinos cannot be detected directly, their flux is measured through the detection of neutrino-induced muons. However, atmospheric muons produced in extended air showers when a cosmic ray interacts with a nucleus in the Earth’s atmosphere constitute a natural background to atmospheric neutrino searches. In a detector like IceCube , the majFurthermore, the energy of the neutrino cannot be accessed directly, but needs to be inferred from energy dependent observables. These challenges demand a sophisticated data analysis chain, considering both the separation of signal and background events and the reconstruction of the spectrum by using unfolding techniques.This paper describes a novel analysis approach aimed at measuring the atmospheric muon-neutrino spectrum. We use experimental data taken with IceCube in the 59-string configuration. The analysis consists of an event selection based on a data pre-processing using quality cuts on a few selected variables, followed by a machine learning algorithm for final event selection.In a machine learning algorithm events are classified according to their properties. Rules for this classification are automatically derived from a set of events for which the class is known, e.g. simulated events. The induction of classification rules is generally referred to as training.All analysis steps were carefully validated and are based on well established methods from Computer Science and Statistics. This approach was found to outperform previous measurements  with resThe paper is organized as follows: In Sect. IceCube is a cubic-kilometer neutrino detector located at the geographic South Pole. Neutrinos are detected through the Cherenkov light emitted by secondary particles produced in neutrino-nucleon interactions in or around the detector. The detector consists of an array of digital optical modules (DOMs) mounted on 86 cables (or strings). The strings are arranged in an hexagon with typical horizontal spacing of 125 m, and hold 60 DOMs each. The vertical separation between DOMs is 17 m and they are deployed at depths between 1450 m and 2450 m. Eight strings at the center of the array were deployed with a distance of about 70 m and vertical DOM distance of 7 m. This denser configuration is part of the DeepCore detector [IceTop stations are located on the top of the strings, forming an air-shower array with a nominal grid spacing matching the 125 m of the in-ice part of the detector. Each station consists of two tanks equipped with downward facing DOMs with their lower hemisphere embedded in the ice. Two DOMs are deployed per tank for redundancy and flexibility [The Cherenkov light emitted by muons produced in neutrino interactions can be used to reconstruct the muon trajectory. Since at high energies (TeV or above) the direction of the muon deviates only marginally from the direction of the neutrino, the direction of the incoming neutrino can be reconstructed as well. The pointing resolution of IceCube was found to be 0.7track-like events originating from charged current (CC) cascade-like events produced in CC interactions of There are two primary detection channels in IceCube, the first one being Data for this analysis were taken between May 2009 and May 2010, when the detector consisted of 59 strings. This configuration is referred to as IceCube-59. The analysis is based on a preselection of events which is provided to the analyzers by the IceCube Collaboration.Although primarily designed for the detection of high-energy neutrinos from astrophysical sources, IceCube can also be used for investigating the atmospheric neutrino spectrum over several orders of magnitude in energy. Despite the fact that the atmospheric g Frejus , AMANDA g Frejus , ANTARESentclass1pt{minimag Frejus .The flux of atmospheric muon neutrinos is dominated by neutrinos originating from the decay of pions and kaons, produced in extended air showers, up to energies of ν≈500TeV   Algorithm [The quality of an automated, machine learning-based, event selection largely depends on the set of variables used . In this analysis the variables considered as input for the learner were the reconstructed properties of the events and different measures of the quality of the reconstruction. As not all variables are equally well suited for the event selection, and since using all available variables would result in an unreasonably large consumption of computing resources, a representation in fewer dimensions needs to be found. In general, a manual selection based on knowledge about the detector and the classification problem at hand will result in a good set of variables for training the classification algorithm. It will, however, not necessarily result in the lgorithm  for the Within MRMR the relevance of a set of variables is computed from an equation :3\docume to Ref. .As variable selections are in general carried out on a limited number of events, their performance might be influenced by statistical fluctuations within those subsets. The average performance given by the cross validation is a valid output. However, one might want to additionally inspect the stability of the variable selection. The stability expresses the variance over different cross validation splits. Two stability measures, Jaccard index and Kuncheva’s index  were useA similar stability measure is Kuncheva’s index, defined as:The stability of the variable selection was tested with respect to the number of variables selected. To perform this test the number of variables was increased stepwise by one variable in the range between one and 50 variables. For each number of variables the MRMR variable selection was restarted and repeated 10 times on 10 disjoint subsets of events. The overall stability lections :6\documeThe stability measures presented in Eqs. Twenty-five variables were selected as this number represents a reasonable trade-off between variable selection stability and the anticipated resource consumption of the learner. Moreover, the separation power of the remaining variables was found to be close to zero.direct when their arrival time at the DOM agrees with that expected for unscattered cherenkov photons [Attributes found to yield large separation power in this analysis are zenith angles, the length of the track obtained from direct photons and the number of direct photons detected in various time windows. Photons are referred to as  photons .signal (atmospheric neutrinos) and background (atmospheric muons).In general, the evaluation of the performance of a classification algorithm consists of the two important steps of training and testing the algorithm. From the machine learning point of view the event selection can be formalized in terms of a classification task with the classes A random forest , which uWithin the cross validation 70,000 simulated neutrino events and 750,000 simulated background events were used. In a cross validation events are split into to model  using COto model .The 25 variables selected by the MRMR algorithm were used for the training of the forest. In order to improve the overall performance of the event selection three additional parameters were created and added according to the findings in .Within the forest, every event is labeled as signal or background according to its attributes by every tree. The final output score is then computed by averaging over the classifications of the individual trees in the forest.The ratio of signal and background events used for training the forest was varied systematically. These tests yielded that the signal-to-background ratio available for training did not result in an optimal performance of the learner. Within the tests it was found that very good results in terms of signal efficiency and background rejection can be obtained using 27,000 simulated signal- and 27,000 simulated background events for the training of the forest. Furthermore, a reasonable trade-off between signal efficiency and background rejection could be achieved using this setting. In order to provide the learner with this number of events a simple sampling operation was carried out inside the cross validation. Within this sampling 27,000 simulated neutrino events and 27,000 simulated background events were drawn at random. Helping the learning algorithm by using balanced training and test sets does not imply that the application of the learned function works only on balanced class distributions. Empirically, we have observed that the decision function obtained from balanced samples can be successfully applied to extremely biased samples. As the sampling only concerned the training of the random forest, the number of events available for testing remained unchanged.memorized as neutrino-like by the forest, events with similar patterns will always be labelled as signal, independent of the underlying energy distribution. Furthermore, the result achieved using a decision tree depends only weakly on the underlying distribution used for training. After classification every event was re-weighted according to an atmospheric flux in order to obtain a prediction of the neutrino rate.The neutrino events used in the training process were simulated according to an In general, the performance of a random forest is found to increase with the number of trees. However, the larger the number of trees, the larger the computational cost for training and testing (CPU time and memory). It was found that 500 trees provided a reasonable tradeoff between the performance of the classification algorithm and the computational cost. Therefore, the forest was trained and validated using 500 trees.The output scores of the random forest for simulated events and experimental data are shown in Figs. Unfolding the energy distribution of the neutrino sample requires an extremely strict rejection of atmospheric muons. This is due to the fact that only a small number of events is found to populate the highest energy bins. Therefore, a single high energy muon might cause a flattening of the unfolded spectrum at high energies and thus mimic a prompt or astrophysical flux of neutrinos. We chose a very strict cut of statistical uncertainty of the event selection, which is introduced due to statistical fluctuations in the training and test sets, was estimated from the cross validation results. The statistical uncertainty can be calculated from the signal efficiency and background rejection of the individual iterations. A statistical uncertainty of 1.6 % was estimated for the expected number of neutrino candidates, which indicates a stable and reliable performance of the forest.The systematic uncertainty of the event selection was estimated by applying the forest to simulated events produced with different DOM efficiencies and a different modeling of the ice. For this purpose the efficiencies of all DOMs were either increased or decreased by 10 % from their nominal values. The modeling of the ice was taken into account by using the SPICE Mie ice model [The ce model  instead After verifying the performance of the random forest the final model was trained using 27,000 simulated neutrino events and 27,000 simulated background events. The events for each class were drawn at random from the total sample of available simulated events.The application of the entire event selection chain on the full set of IceCube-59 data yielded 27,771 neutrino candidates in 346 days of detector live-time  were used as input for the unfolding. Direct hits have not suffered scattering in the ice from their emission point to the DOM and therefore keep precise timing information, which is essential for an accurate track reconstruction. For the unfolding only direct hits from a time window ranging from The energy dependence of the three input variables for simulated events is depicted in Figs. Truee [The verification of the unfolding result consists of two different tests. The first test is based on multiple unfoldings of a specified number of simulated events, which are drawn at random. This kind of test can be accessed via Truee . The secThe result of the first test is shown in Fig. The individual populations observed in the figure correspond to the individual energy bins of the final unfolding result. The line-like structures observed for small event numbers are due to the fact that only integers are possible as event number for the true MC distributions, whereas real numbers can be returned as the unfolding result for the individual bins.Truee fail to account for the difference between the predicted bin content and the number of injected events, large deviations are observed. This further implies that an overestimation is obtained in case no events are present in the last bin on experimental data. As soon as one event is present in this bin, an underestimation is observed.The rather large deviation between the unfolding result and the number of injected events obtained for the highest energy bins is a result of the steeply falling spectrum of atmospheric neutrinos and the applied bootstrapping procedure. Due to the small number of expected events in the last bin, either 0 or 1 events are drawn randomly from the true distribution. Two or more events are only drawn in rather rare cases. Based on the response matrix, which accounts for the limited statistics in the highest energy bins by using ten times more events compared to experimental data, only a fraction of an event is reconstructed for the highest energy bin. As the statistical uncertainties derived in Truee the statistical uncertainties are computed as the square root of the diagonal elements of the covariance matrix. This test can therefore be used to validate the statistical uncertainties returned by the algorithm. The unfolding result is compared to the underlying distribution of events. If the difference between the unfolding result and the true value is covered by the statistical uncertainty returned by Truee, the statistical uncertainties are estimated correctly. For cases where the statistical uncertainty fails to cover this difference the statistical uncertainty is scaled up. For the analysis presented here an underestimation of the number of injected events is observed for the 9th and 10th bin, respectively. This underestimation is not covered by the statistical uncertainty, which is thus scaled up by a factor of 1.9 for the 9th, and a factor of 6.3 for the 10th bin.Within In a second test, simulated events are re-weighted according to the unfolding result see Fig. . For a sThe outcome of the re-weighting is depicted in Figs. As the unfolding result is obtained by using a response matrix determined from Monte Carlo simulation, the properties of the simulation will affect the unfolding result. In order to determine the effect of different simulation settings on the spectrum of atmospheric neutrinos, additional unfoldings were carried out using different sets of simulated events for the determination of the response matrix. For each simulation set used for the estimation of systematic uncertainties one property was changed with respect to the default simulation set.The setting for the efficiency of the DOMs was varied by cited in  and is tFurther systematic tests were carried out by using simulated events generated with a cited in . The modcited in  instead Truee. No indications for instabilities were observed for any of the systematic tests.The response matrices obtained for the individual systematic sets of data were then applied to real data in order to estimate the size of the systematic uncertainties. Prior to the application on real data, however, every setting was checked using the multiple unfoldings in Thus, five additional unfolding results were obtained on real data. The difference between the unfolding result obtained using the standard Monte Carlo sets and the systematic Monte Carlo sets were computed bin-wise and for every setting. The final uncertainties were calculated by adding the obtained differences in quadrature. This procedure further offers the advantage that all systematic uncertainties are derived on experimental data.For energies up to 1 TeV the total systematic uncertainty is dominated by the uncertainty arising from the modeling of the ice. For energies above 1 TeV the uncertainties due to the DOM efficiencies and the modeling of the ice were found to be of approximately the same size. A more precise modeling of the ice and a better understanding of the DOM efficiency, are therfore likely to reduce the systematic uncertainties of future measurements.Truee is depicted in Fig. The number of unfolded events as returned by Figure Compared to the IceCube-40 result the systematic uncertainties of the spectrum were reduced, especially at low and intermediate energies. The decreased error bars are due to a better understanding of systematic effects in IceCube. Due to the relatively large systematic uncertainties at high energies, no statement can be made about a possible contribution of neutrinos from the decay of charmed mesons. Furthermore, no statement about a possible contribution of neutrinos from astrophysical sources can be made in this analysis.In general, a good agreement between the unfolded flux and the models is observed. Deviations of The acceptance-corrected flux of atmospheric neutrinos as well as the relative uncertainties are summarized in Table In order to study the dependence of the atmospheric neutrino flux on the zenith angle, additional unfoldings were carried out dividing the data into two separate sets according to the reconstructed zenith angle. The first zenith band contains events with a reconstructed zenith angle between The result of unfolding the two different angular regions is depicted in Fig. In general, a good agreement between the unfolded distribution and the theoretical model is observed. The unfolding results for the two angular bins are summarized in Tables Figure elescope . The meaIn this paper we presented the measurement of the atmospheric This increase in the accessible energy was achieved by using a dedicated event selection procedure, which utilized state of the art algorithms from the field of machine learning and data mining. Using a random forest preceded by an Minimum Redundancy Maximum Relevance variable selection we were able to reject 99.9999 % of the incoming background events. At this background rejection 27,771 atmospheric neutrino candidates were detected in 346 days of IceCube-59. This corresponds to 80.3 neutrino events per day, which is a significant improvement over the 49.3 neutrino events per day reported in [Truee. The unfolding result was validated using a bootstrapping procedure implemented in Truee. A test using multiple unfoldings of simulated neutrino events selected at random yielded a very good agreement between the unfolding result and the true distribution of events, thus validating the overall stability of the unfolding process. Comparing the unfolding results to theoretical models, one finds that no statement on a possible contribution of a prompt and/or astrophysical component to the overall flux of atmospheric neutrinos can be made, due to the relatively large uncertainties at high energies.An energy spectrum of the atmospheric Additional years of measurements with IceCube in the 79-string and in the 86-string configurations are likely to confirm the results from  in spectIn summary we find that the data analysis chain presented in this paper yields highly stable results for both event selection and the reconstruction of the spectrum. The entire analysis procedure can therefore be applied to all other sets of IceCube data with only minor changes. The analysis chain is especially well suited for measurements of the atmospheric neutrino flux, where future analyzers only have to account for the different detector geometry.


A new wavelet-based method is presented in this work for estimating and tracking the pitch period. The main idea of the proposed new approach consists in extracting the cepstrum excitation signal and applying on it a wavelet transform whose resulting approximation coefficients are smoothed, for a better pitch determination. Although the principle of the algorithms proposed has already been considered previously, the novelty of our methods relies in the use of powerful wavelet transforms well adapted to pitch determination. The wavelet transforms considered in this article are the discrete wavelet transform and the dual tree complex wavelet transform. This article, by all the provided experimental results, corroborates the idea of decomposing the cepstrum excitation by using wavelet transforms for improving pitch detection. Another interesting point of this article relies in using a simple but efficient voicing decision  which on one hand respects the real-time process with low latency and on the other hand allows obtaining low classifications errors. The accuracy of the proposed pitch tracking algorithms has been evaluated using the international Bagshaw and the Keele databases which include male and female speakers. Our various experimental results demonstrate that the proposed methods provide important performance improvements when compared with previously published pitch determination algorithms. The extraction of the cepstrum excitation signal and the wavelet decomposition of this signal into 3 levels in order to obtain the approximation signals we enhance using a VisuShrink method   and a modulus operators are applied then to this windowed signal in order to obtain an amplitude spectrum;A log operator is then applied;Finally an IFFT (Inverse Fast Fourier Transform) is applied to this log amplitude spectrum in order to obtain the cepstrum signal.The cepstrum signal is composed of two parts:As explained below below, Fig. The four major differences between our approach and the ACEP method , from the excitation cepstrum located in the high quefrencies. Then we apply to the excitation part of the cepstrum signal a wavelet transform in order to obtain the approximation coefficients we enhance.Step 2: From the enhanced approximations, we estimate the pitch period;Step 3: Simple but efficient voiced/unvoiced decisions are carried out in order to track the pitch period.The block diagram shown in Fig. Oc first vocal tract coefficients. In our study we fix Oc to 20. That means that for a sampling frequency of 20 kHz, the maximum pitch frequency which can be determined is 1000 Hz (20 kHz/Oc). The cepstrum excitation signal is useful in speech processing domain and especially in pitch determination algorithms, because the low-frequency periodic excitation can be extracted from it. Human pitch detectors assume that pitch frequency is between 50 and 600 Hz generally. Trying to detect higher pitch frequency may introduce errors in the extraction. The fact that our algorithms can determine  pitch frequency up to 1000 Hz, with low classification errors, is another proof of the high precision of our pitch detectors.The cepstrum signal can be used to separate the excitation signal (which contains the pitch) from the transfer function . From the log-cepstrum, we set to zero the first coefficients representing the vocal tract information. In our experiments, Oc is the number of vocal tract cepstral coefficients. Figure The wavelet transform is applied to the log-cepstrum excitation signal in order to minimize the classification errors using a number of levels, which we experimentally fixed to 3 see Fig. . In the The main idea of our approach consists in smoothing these coefficients, in order to better estimate the pitch period given by the local maximum peak index at each decomposition level ; k is an index of a particular coefficient of cA[i] ; and T1 , is the universal threshold given by Formula The literature proposes several methods for signal denoising such as VisuShrink  or random ones (unvoiced regions). The role of the pitch tracking algorithm is to detect correctly the voiced/unvoiced speech components.S using an experimentally-determined threshold T2 .L is the number of preceding considered frames (for our experiment E(j) of a particular frame j is defined as the log sum of the squared values of the signal samples. For a particular frame whose speech signal (windowed by a Hamming window) is below an experimentally determined threshold T3, we classify it as an unvoiced frame, otherwise it is considered as possibly voiced. Consequently our voiced/unvoiced decision is given by Formula T2 in our experiments is 10 and T3 is 76 dB. These thresholds have been determined experimentally.In this section, we present the voicing decision method used for estimating the pitch. We can solve this issue by using a threshold in order to decide if the current frame is voiced or unvoiced (Rabiner and Sambur Starting with isolated peaks: the pitch peak is eliminated if its duration is bellow 13.5 ms (which corresponds to 9 frames). The shift used between two consecutive frames, in our study, is 1.5 ms (30 samples).Concerning valleys: we rebuilt the pitch contour linearly if the duration of the valley is also below 13.5 ms. We propose to regularize the pitch tracking in respecting the real time process. So emphasis is placed on the very low latency obtained which is 13.5  ms.In pitch tracking, the results obtained can detect false estimations of the F0 by the presence of parasitic peaks or valleys. When thresholding criteria failed, we correct the pitch contour from parasitic peaks and valleys by using the following technique:The test of the proposed approach and the voicing decision used were evaluated over the Bagshaw  and authored by Paul Bagshaw. The speech and laryngograph signals of this database were sampled at 20 kHz. It contains 0.12 h of speech, 50 English sentences each pronounced by one male and one female speaker. The fundamental frequency was computed by estimating the location of the glottal pulses in the laryngograph data and taking the inverse of the distance between each pair of consecutive pulses. Each fundamental frequency estimate is associated to the time instant in the middle of the pair of pulses used to derive the estimate.The Keele database The Keele Pitch Database was recorded at Keele University. Data were collected for five male and five female English speakers, each of them read a phonetically balanced text: the “north-wind story”. The speech and laryngograph signals were sampled at 20 kHz. The fundamental frequency was estimated by applying an autocorrelation on windows of 25.6 ms shifted by intervals of 10 ms.Figures Classification Error (CE) is the percentage of unvoiced frames classified as voiced plus the percentage of voiced frames classified as unvoiced : percentage of voiced frames with an estimated F0 value that deviates from the reference value more than 20 %. When the error is less than −20 %, it is counted as a gross error low; errors exceeding +20 % are counted as gross error high.Mean is the mean of the absolute differences between the reference and the estimated fundamental frequency values.Standard Deviation (SD) is the standard deviation of the absolute differences between the estimated and reference pitch values.Tables CEP is the cepstrum-based pitch reference estimation algorithm Noll  for extrMCEP is the Modified CEP  implies the evaluation of the classification error (CE)   metric , which must be compared with the latency obtained by the eCATE++ algorithm (20.25 ms), and low classification errors for both the Bagshaw and Keele databases.


The aim of the work was to assess among pregnant women from small towns and villages in Poland: the prevalence of smoking, credibility of smoking, and influence of socioeconomic factors on smoking status.The data came from 4512 interviews with women in different trimesters of pregnancy. The interviews were collected in 2007 and 2008 year in towns up to 8000 citizens in 12 voivodeships.Prevalence of smoking in the beginning of pregnancy was confirmed by 34.6 % of women. During the pregnancy 14.7 % of women declared quitting smoking and 19.9 % continued smoking. Cigarette smoking was most frequent in those with a primary education, unemployed, very low incomes in household, and having both smoking parents. In multifactorial analysis, risk of smoking was highest (95 % CI 1.74–6.06) for women that were divorced or not living with a partner compared with married.Rates of active smoking among a population of pregnant women living in small towns in Poland are very high. Since the correlates of smoking during pregnancy are a low education level and a low economic status of the pregnant woman, these socioeconomic groups should be first priority targets. Tobacco smoking represents a huge health hazard for both a pregnant woman and her fetus and it also represents the most important modifiable risk factor for fetal and neonatal morbidity and mortality  that went through a political and economic transformation in early 1990s. Health indicators in these countries were at that time much worse than the corresponding figures reported for the 15 ‘old’ members of the European Union. Despite an improvement in these indicators over the past two decades, the rate of changes has not been satisfactory . Midwives are usually considered by pregnant women as the group of healthcare professionals with whom a better emotional rapport can be established. They usually have more time for the patient and, being women themselves, show more empathy for another woman’s concerns regarding the course of pregnancy. These factors lead to a greater trust being placed in them, which was a factor is contributing to truthful reporting of facts in a survey where the respondent was not completely anonymous at the time of data collection. This lack of anonymity resulted from the fact that the questionnaire was administered during a routine visit at a gynecology and prenatal care clinic. Anonymization of data was carried out only after the visit.Prior to the research roll-out, the midwives had been specifically trained in interviewing methods and the use of carbon monoxide meters as described below. The interview was conducted once with all pregnant women who reported for their first or subsequent consultation with a midwife, regardless of the stage of pregnancy, within the 3 months of program implementation in each province.The questionnaire, developed specifically for the purposes of this study, consisted of 34 questions, of which 24 were about active and passive tobacco smoking, and 10 were about socioeconomic factors. Following the approach used by Mullen et al., a question concerning regular daily smoking before and during pregnancy was used for initial screening  Fig. . With thTo deliver a comprehensive assessment of the exposure of pregnant women to tobacco smoke, the percentages of those who continue smoking and of non-smokers who are exposed to passive smoking have also been considered together Fig. . Taking Among 664 the women who declared being ex-smokers and who spontaneously quit at the onset of pregnancy, the 15.5 % misreported their non-smoking status and 3.5 % refused to be tested.The relationship between smoking in pregnancy and selected socioeconomic factors is shown in Table With regard to active smoking, the most significant variables were ‘divorced or not living with a partner’  and ‘both parents were smokers’ . Other statistically significant factors in the multifactorial analysis included: lower education status of the pregnant woman, lower education status education of the spouse/partner, social status of the pregnant woman (unemployed), and the age of the pregnant woman. In unifactorial analysis, the same variables were found to be significant predictors (OR) of smoking in pregnancy.We provided novel data on smoking prevalence among pregnant women in small towns in Poland. Early population-based studies included the entire group of women of childbearing age which, consequently, makes the interpretation of results at a very detailed level of small town population rather difficult. Our data showed that at the time when the survey was taken, over one in three women were smoking tobacco cigarettes at the beginning of their pregnancy. This number is higher than 24.4 % national overall/average smoking prevalence among women reported in 2009 in the GATS study  reported by pregnant women in Lodz, one of the poorest cities in Poland (Fronczak et al. When the rates of smokers in pregnancy in our survey are compared with studies carried out in other countries, we can see a quite wide range of results. In Western and Northern Europe, the rates are: Finland—14 %, Germany—15 %, France—18 %, United Kingdom—27 %; in Eastern Europe: Croatia—18.9 %, Serbia—18.4 %, Russia—9.7 %, Slovenia: 6.7 %; and in the United States—13 % (Smedberg et al. An important finding of this study is that majority of smoking women in small towns in Poland continue to smoke during pregnancy. Future studies need to explore the barriers towards quitting that smoking women who live in rural area in Poland may experience. Polańska et al. addressed the lack of studies to analyze the prevalence of smoking at different stages into pregnancy (Polańska et al. Although an interview-based survey is the least expensive method of assessing tobacco smoke exposure, and the survey results are immediately ready for evaluation, there are possible sources of bias when smoking status information is based on self-report only, such as respondents forgetting about relevant facts, their unwillingness to disclose the information sought by researchers, and intentionally providing misleading information Solberg . It has Although there is strong evidence that tobacco smoking is highly associated with lower socioeconomic status (Escobedo et al. Rates of active smoking among population of pregnant women living in small towns in Poland are very high. Our study indicates an urgent need for public health interventions aimed at reducing the incidence of smoking during pregnancy in this disadvantaged population. Effective methods of reducing the tobacco epidemic at both the individual and population levels, including smoking cessation treatment and counseling are available in Poland; however, the access to these resources in small towns may be significantly limited. Since the correlates of smoking during pregnancy are a low education level and a low economic status of the pregnant woman, these are the socioeconomic groups that should be targeted as the first priority. Poland is a country with a high level of socioeconomic inequalities and there is a need to close these gaps.The fact that a considerable proportion of women spontaneously quit smoking after being found pregnant indicates that pregnancy is a strong motivating factor behind the cessation of smoking. This is why it is worthwhile to use the time of pregnancy as a period in which interventions should be applied.


To estimate conduction velocities from activation times in myocardial tissue, the “average vector” method computes all the local activation directions and velocities from local activation times and estimates the fastest and slowest propagation speed from these local values. The “single vector” method uses areas of apparent uniform elliptical spread of activation and chooses a single vector for the estimated longitudinal velocity and one for the transversal. A simulation study was performed to estimate the influence of grid size, anisotropy, and vector angle bin size. The results indicate that the “average vector” method can best be used if the grid- or bin-size is large, although systematic errors occur. The “single vector” method performs better, but requires human intervention for the definition of fiber direction. The average vector method can be automated. The assessment of the conduction velocity of the cardiac impulse is an important aspect of the study of arrhythmogenesis, especially where it involves arrhythmias based on reentry . It is fastest in the direction of the myocardial fibers and slow transverse to fiber direction. The normal anisotropic ratio  is for ventricular myocardium about 2:1 , therefore, is essential. Ideally, conduction velocities are calculated from high density surface mapping  studies following pacing from the center of the grid of mapping electrodes . Using the activation times in a subgrid, the best fitting vector (direction and velocity) of the activation front at the central point of the subgrid is estimated. This procedure yields a local activation vector for every point except for border points.  method has a larger overestimation of the longitudinal velocity for almost all grid sizes at a bin size of 15°, except for very large grids (approximately 22 by 22) and using 5 by 5 subgrids  empty bin. Overestimation in the transverse direction results from a large number of vectors that are a mix of transversal and longitudinal and therefore longer being put in the same bin as the pure transversal ones.l with the average vector method is more difficult and less reliable with smaller bin sizes, small grid sizes and larger anisotropy.At a bin-size of 15° and small grid-sizes it may happen that no vector is present in some of the bins . The table shows the results of these simulations. The table shows for instance that a grid-size of at least 14 by 14 at an anisotropy-ratio of 2 and a noise-level of 0.5 ms is required to keep the chance below 5% that no vector is present in the bin representing the fiber direction  conduction nor the transversal conduction (slowest) conduction are along the long and short axis of the elliptical pattern. From Figure l and CVt. One should, however, be aware that breakthrough patterns may yield unrealistic high CVl values, because transmural rotation of myocardial fibers affects the epicardial activation pattern . When the anisotropic ratio is large, the overestimation at smaller sizes is larger and also the chance that no vectors are in the fastest bin. Using a 5 by 5 grid in general improves the quality of the estimate, but larger grid sizes are required to be able to reliably measure at all. Using 30° bins instead of 15° gives better overall results.Both methods perform relatively well for the determination of transverse conduction velocity, and are not dependent on grid size, bin size (average vector method) and anisotropy. For small anisotropy and small grid sizes (<about 20 × 20) the average vector method underestimates transverse CVA limitation of this study is that these simulations assume that the activation spreads from a single stimulus point in the middle of the grid.The assumption in this paper is that the myocardium is homogeneously anisotropic. As the example in Figure For the simulation experiments the direction of the longitudinal direction was known . Bin boundaries were selected in such a way that this 45° was in the middle of the bin. So, for 30° bins boundaries were 0, 30, 60,… and for the 15° bins −7.5, 7.5, 22.5, 37.5, 62.5,… For experiments in real hearts, this information is in general not known; using this knowledge may have positively skewed the results for the average method.Multielectrode mapping with regular grid electrodes in patients has been reported to determine the arrhythmogenic site of a tachycardia  that the largest possible distance over which linear conduction takes place is selected. The latter obviates the influence of breakthrough activation and allows greater time resolution (less influence of sampling rate). The single vector method is the preferred method when manual processing is an option.The single vector method performs better than the average vector method when grid size is small, bin size is small, sampling rate is low and anisotropy is large. This is at least in part related to the fact that (1) the identification of fiber direction allows selection of a single vector in the correct direction (and perpendicular to it); (2) the intrinsic assumption that CVThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Clostridium botulinum are the most poisonous substances known to mankind. However, toxin regulation and signals triggering synthesis as well as the regulatory network and actors controlling toxin production are unknown. Experiments show that the neurotoxin gene is growth phase dependent for C. botulinum type A1 strain ATCC 19397, and toxin production is influenced both by culture conditions and nutritional status of the medium. Building mathematical models to describe the genetic and molecular machinery that drives the synthesis and release of BoNT requires a simultaneous description of the growth of the bacterium in culture. Here, we show four plausible modelling options which could be considered when constructing models describing the pattern of growth observed in a botulinum growth medium. Commonly used bacterial growth models are unsuitable to fit the pattern of growth observed, since they only include monotonic growth behaviour. We find that a model that includes both the nutritional status and the ability of the cells to sense their surroundings in a quorum-sensing manner is most successful at explaining the pattern of growth obtained for C. botulinum type A1 strain ATCC 19397.Botulinum neurotoxins (BoNTs) produced by the anaerobic bacterium  Clostridium botulinum is one of the significant organisms associated with foodborne hazards, and improved mathematical models which account for complex growth patterns make important contributions to improved food safety.  Clostridium botulinum is a Gram-positive obligately anaerobic, endospore-forming bacterium that produces a lethal neurotoxin called botulinum neurotoxin (BoNT)  produce seven distinct BoNTs (Serotypes A-G) and more than 40 different neurotoxin subtypes  expression is not fully understood. Furthermore, the environmental signals that trigger the synthesis of the BoNTs and the regulatory network and actors that control the production of the toxin (and hence expression of the encoding bont gene) remain to be elucidated. What is known is that the bont gene expression appears to be tightly regulated through positive regulatory elements, including the participation of BotR  has also been reported -PCR and quantitative RT-PCR . However, as growth proceeded at 25°C, nicking of the single chain led to a steady and substantial increase in the proportion of neurotoxin in the dichain form . At 25°C, as the bacteria entered late exponential phase, and the logarithm of the viable count increased from 6.9 to 8.7 cfu ml−1, the concentration of type A toxin in the culture supernatant increased by six orders of magnitude to reach more than 105 MLD50 ml−1 , we have generated several working hypotheses on the nature of the ‘signal/s’ that could have generated the pattern of growth observed for type A1 strain ATCC 19397. The growth pattern of type A1 strain ATCC 19397 could be dependent on a signal from either the levels of a nutrient or nutrients in the culture or from a quorum-sensing mechanism. Four mathematical models describing how the signalling species could exert an effect on the adaptation, reproduction and sporulation of strain ATCC 19397 have been generated and tested. The commonly used bacterial growth models, i.e. logistic, Gompertz and Baranyi  ). For this reason, we chose to use the experimental data reported in Sharma . It is a typical C. botulinum Group I type A1 strain with the bont gene in an ha neurotoxin gene cluster  peptone-yeast-glucose-starch medium at 37°C (Sharma 2/H2 (10:90 v/v). The reported data also includes measurements of the amount of toxin released in the supernatant over time. This was quantified using an endopeptidase activity assay developed by Ekong, Feavers and Sesardic . Simulation is realized via the numerical integration of the ODEs. The whole process is supported by the COPASI modelling and simulation software package , which generates a spike in the pattern of the interpolating curve and several inflection points in a small time interval. We have assumed that this point may be erroneous and have replaced it with the average value of the two adjacent experimental data points to give a smoother curve that is illustrated in Fig. The growth of strain ATCC 19397 is illustrated in Fig. A slow growth phase in the time interval  h, which is often described as the lag phase of the culture.An exponential growth phase in the time interval  h, where the curve of the logarithm of the counts can be approximated as a straight line.A late exponential growth and a stationary phase  followed by a rapid decline of the population in the interval [21–30] h.Another nearly stationary phase with a possible slow growth tendency during the period [30–45] h.From a direct observation of the time course in Fig. et al. et al. None of the classical models of bacterial population growth  that determines the limiting effect on growth. Both AC and RC types of cells consume nutrients over time, which we include in the model with two additional reactions:In this case, the basic population dynamics  can be modelled by three reactions:\documentN is encoded into the model by a proper selection of the rates of reactions , and for reaction . This function is used to model rates that decrease in a sigmoidal way as the concentration of nutrients (N) diminishes . With this modelling choice, we model both the positive effects of N on growth and the inhibitory effect that occurs when the concentration of N falls back to a tuneable threshold level.The dependence of the growth dynamics that is associated with the consumption of eactions , 2) and andN is eactions , which wreaction  and (2),reaction  it decrereaction  and (2),tex − mathid = "IM0002" > nK/(nN + nK), which also provides a sigmoidal behaviour. The mathematical form of this function allows us to define a sporulation rate that grows as N decreases. The rates of reactions   tex − mat = 0 with a number of cells in the AC compartment, equal to the size of the inoculum in the experimental setting (Sharma N be one (in arbitary units).We initialized the model at time g Sharma , and we The model was simulated with COPASI and the results of the best fit obtained are shown in Fig. With a hypothesis that considers that dynamics is controlled by a single limiting factor (which decreases over time), the corresponding population dynamics indicates growth and decline Fig. . Howevertex − mathid = "IM0003" > N/RC n) an inverse Hill function where the regulatory species is < tex − mathid = "IM0005" > N/RC). This quantity represents a scaling of the concentration of nutrients with respect to the number of reproducing cells. At the early stage of cell growth, when the reproducing cells’ numbers are low and the concentration of nutrients high, the < tex − mathid = "IM0006" > N/RC ratio is large but this reduces quickly as the population grows. The growth of the population also means that the concentration of available nutrient/s diminishes during the exponential phase. As a result of the depletion of nutrient/s, the ratio is eventually expected to fall below a threshold that could in turn trigger sporulation. Due to the drop in nutrient concentration, the population of reproducing cells should decrease quickly, arresting the decreasing trend of the ratio < tex − mathid = "IM0007" > N/RC, which in turn decreases the propensity of the cells to sporulate. Ultimately, the culture reaches a state with a small population of surviving cells.In an extension it is natural to consider a scenario that includes the possibility for cells to sense not just the availability of nutrient/s, but also the density of the population in the medium. This is implemented in a model by making the rates of the sporulation reaction  dependentex − mathid = "IM0008" > N/RC through an inverse Hill function. The simulated dynamics is compared with the experimental data in Fig. This model follows from the previous one, with reactions –5), sub, sub5), In order to elucidate the growth pattern observed in the later stages of the culture (between time 30 and 48 h), we consider the possibility that the bacterial cells could be using in a quorum-sensing mechanism, a chemical signal to measure local population density, to regulate sporulation. If this signal is short lived, then it would be possible that, following a drop in the population density, the culture could enter a stage where sporulation is unlikely and a slow growth may resume.S, is introduced to represent the ‘chemical signal’ produced within the cells in culture. The dynamics of the cells following the introduction of S is modelled with three reactions:Again a model is constructed using reactions –3) but  but 3) bS whereas reaction  are removed.Reaction  represenreaction  models treaction  models teactions  and 3),,S whereaS accumulates in the botulinum growth medium, whereas the sporulation reaction   2) folloreaction  has Hillted Fig. . Again tC. botulinum, it was necessary to build a model that described the growth of the bacterium in a culture. Since bont gene expression is growth phase dependent and the concentration of toxin released in the botulinum growth medium is related to the number of bacterial cells, creating a comprehensive computational model of BoNT production required an understanding of the population dynamics regulating neurotoxin production and thus modelling of the bacterium's population dynamics.In order to elucidate the genetic and molecular machinery that drive the synthesis and release of BoNT by C. botulinum Group I type A1 strain ATCC 19397 in a botulinum growth medium were proposed, implemented and examined. In turn the models captured the dependence of the growth dynamics on  as drivers of population dynamics.Four plausible modelling options that could be considered when constructing models describing the growth pattern observed for amics on  the avaiamics on  both then et al. , commonlC. botulinum.Although this approach is relatively qualitative, and we have not included detailed methods to compare goodness of fit, it acts as an important precursor to the development of new, quantitative models for toxin production by