Given a set of nucleotide sequences we consider the problem of identifying conserved substrings occurring in homologous genes in a large number of sequences. The problem is solved by identifying certain nodes in a suffix tree containing all substrings occurring in the given nucleotide sequences. Due to the large size of the targeted data set, our approach employs a truncated version of suffix trees. Two methods for this task are introduced: (1) The annotation guided marker detection method uses gene annotations which might contain a moderate number of errors; (2) The probability based marker detection method determines sequences that appear significantly more often than expected. The approach is successfully applied to the mitochondrial nucleotide sequences, and the corresponding annotations that are available in RefSeq for 2989 metazoan species. We demonstrate that the approach finds appropriate substrings. Mitochondria inherited a genome (mitogenome) from their bacterial ancestors, which has been reduced dramatically in most lineages  nearly 3000 metazoan mitochondrial genomes are contained in NCBI RefSeq. This makes them a particularly interesting data set for phylogenetic studies among various taxonomic units . They arThe NCBI GenBank and RefSeq data bases provide genome sequences and their corresponding annotations ,10, i.e.de-novo annotation of metazoan mitogenomes is possible with MITOS  the suffix of S starting at position i including the empty suffix S(|S|+1). The suffix tree T of a sequence S is a specific rooted tree whose edges are labeled with substrings of S$, for a symbol $ ∉ Σ. In the following we describe the main properties of the suffix tree $.Let e, e.g., ). The pasuffix links as introduced by , i.e., the index of the sequence where v occurs and the positions of the first nucleotide and the last nucleotide of the occurrence. Let gann be the annotation information for gene g over all available sequences. Then overlap(iocc(v), gann) is defined as the total number of common nucleotide positions of the ith occurrence of v and the annotation of gene g on sequence S where S is the sequence of the ith occurrence of v. The score for a gene g and any node v is defined as:To define the score formally, let g, because the path label of an inner node is shorter than the path labels of its child nodes. The score values that an inner node v receives from its child nodes rather count the respective overlaps of a genes annotation and all words of length k where the path label of v is a prefix.Note that the score function does not count the overlap of the occurrences of the path label of an inner node with the given annotation of a gene We are not aware of a possibility to determine the genes overlaps with the path labels of an inner node in a time and memory efficient way because the coordinates of the occurrences are unknown in this subsequent step after the tree construction. However, the scores provide a sufficient approximation of the exact distribution of gene overlaps for the inner nodes.w is a repetitive sequence if it contains a substring of the form ′rq where r′ is maximal and r′ ≥ r for a parameter r ≥ 2 that is called the repeat threshold. See [For the marker detection the nodes whose path labels occur only once in the input sequences or are repetitive are dismissed in the further search for markers. A word old. See  for a rew is a repetitive string that contains a repeated string of up to l nucleotides in O(l · |w|) time. To this end it counts the occurrences of each word q with |q| ∈ [1 : l]. All words containing repeated substrings are considered unsuitable markers.Algorithm 1 detects whether a word w for repeated substrings of length j + 1 in the outer for-loop starting in line 1. A window of length j + 1 is moved over word w from left to right starting in line 3. Whenever the first and last character in that window are unequal (iw ≠ wi−j−1 in line 4) the count is reset and the offset is set to the current window shift modulo j. The offset is used to check when the window was shifted by j + 1 positions without a single mismatch to increase the variable count which counts the number of repeats of word wi−j−1 … wi−1.Algorithm 1 analyses word Algorithm 1: Repeat Detection applied on a word w = w0 …ww|−1| with repeat threshold r1forj = 0 : l − 1 do2offset←j; w//modulo of start of repeat in 3count←1; //current count of repetitions4fori = j + 1 : |w| − 1 do 5ifiw ≠ wi−j−1then  6count←1;   i−j−1 …wi−1 is not repeated// substring w7offset← i mod (j + 1);   8else if offset= i mod (j + 1) then  9count ++;   10ifcount > rthen   11end with: w contains a repeated substring;    12end with: w contains no repeated substrings;T nodes whose path labels are suitable as markers are detected. A node v is considered to be a suitable marker for a gene g if Inequality 2 holds and g = arg maxg score.In a depth first search over the annotation guided suffix tree v is found whose path label is suitable as marker the corresponding test is omitted for all nodes below of v. Since the path labels of the nodes below v have the path label of v as common prefix they cannot occur more frequently in the input sequences than the path label of their ancestor node v. As approximated by the score at least 95% of v's path label's occurrences in the given nucleotide sequences overlap with a single gene g. This information was gathered from v's child nodes. If there is at least one occurrence of v's path label overlapping with some gene g′ different from g it is possible that some node below v might indicate an association of its path label with g′. However, we discard this information and consider it as an erroneous annotation.If a node v with path label w = w′w″ is suitable as marker, i.e., it satisfies Inequality 2, and v's parent node v′ has path label w′ but does not satisfy Inequality 2. Then m = w′u where u is the first character of w″, i.e., the edge label from v′ to v, is added to a set of candidate markers. Note that, w′u is the shortest prefix of w satisfying Inequality 2.Assume that a node v whose ancestor v′ suffices Inequality 2 is tested for Inequality 2 it is ensured that no marker in the candidate set is prefix of another marker in this set. However, all markers that contain other markers as suffixes or infixes have to be removed. This is achieved by a search for all suffixes and infixes of a marker (see Algorithm 2). Of the remaining markers none is prefix, suffix or infix of any other marker.In a final step, the set of candidate markers is filtered such that no marker is suffix, prefix, or infix of another marker in the final set of markers. The filtering step is done as follows. Since no node Algorithm 2: Suffix Search applied on a node. For a node v with path label w = w′w″ and parent node v′ with path label w′ the marker of a node is defined as m = w′u where u is the first character of w″ (in case of the annotation guided suffix tree) or as m = w′a where a is the shortest prefix of w″ such that m is significant (in case of the probability based suffix tree). If w does not suffice the requirements of the corresponding methods m is the empty word.1m ← marker of this node2fori ← 1 : |m| − 1 do3v ← node with the shortest path label containing im… m|m|−1 as prefix; 4m′← marker of v 5ifm′ exists and |m′| ≤ |m| − i + 1 then 6end with: m contains another marker as infix  7end with: m contains no other marker as infix2.3.The marker detection method that is described in Subsection 2.2 relies on a given annotation. In this section we present the probability based marker detection method that detects markers using statistical tests and does not require annotation data. The tests are based on a Markov model of third degree derived from the given sequences. The Markov model is used to determine an expected number of occurrences for a word in a sequence whose {1,2,3,4}-mers occur with the same frequency as in the input sequences. These expected number of occurrences are compared with the actual number of occurrences.k-truncated generalized suffix tree that is called probability based suffix tree. The construction of this tree is similar to the construction of the standard k-truncated generalized suffix tree but it needs a simple additional procedure to store for each leaf the total number of occurrences of its path label. To do so each leaf has a counter. During the construction of the tree all possible infixes of length k and suffixes shorter than k of the sequences S1$, …, nS$ are included into the tree. During the inclusion, the algorithm traverses the nodes of the tree until it reaches a leaf node. The leaf node increases its counter by one as the newly included infix or suffix equals the leaf's path label. When the inclusion process is finished and the counter values have been determined for all leaves, the counted number of occurrences are passed iteratively to the parent nodes. The number of occurrences of each inner node is computed as the sum of the values from the child nodes. The bottom up procedure takes linear run time.The probability based marker detection method uses an extension of the When the probability based suffix tree has been constructed it can be used to detect markers. The path labels of the nodes are tested for their statistical significance by using their total number of occurrences as described in detail in the following. Similarly to the annotation guided marker detection method, this is done in a depth first search that does not search underneath nodes that proved to be significant.w = w0w1 … ww|−1| be the path label of some node v with n(v) occurrences. Let α ∈ Σ and s ∈ Σ+ then P denotes the probability that a follows directly after s in a nucleotide sequence. For an empty string s we simply write P(a) denoting the probability of letter a occurring in a string. These probabilities are derived from a Markov model of third degree that is derived from the input sequences. We compute a probability for node v's path label to occur based on the probabilities from the Markov model by:Let 2 significance test. The χ2 test takes the expected (ke) and the observed (ko) number of occurrences of m different categories that are a partition of the sample to compute a score To identify whether a word can be used as a marker the statistical significance is derived from a χw starts at the current nucleotide or (2) not. The sample size N is the summed length of all input sequences. The expected and observed number of occurrences  of a word w that leads to the incoming edge, i.e., the path label or a prefix of the path label (including at least the path label of the parent), of node v and the complements of the number of occurrences  are derived from the following equations:In our case there are only two categories: (1) The word This givesw does occur randomly, is rejected whenz > 0 such that the error of wrongly rejecting the null hypothesis (α) is small. In that case w occurs significantly more often than expected in random sequences based on the used Markov model.The null hypothesis, i.e., w of a node vv are dismissed, i.e., the significance of their path labels is not investigated. The reasoning for this is analogous to the corresponding reasoning for the annotation guided marker detection method. However, it is possible that a prefix of w would also satisfy v′ be the parent node of v with path label w′. We test each string w′w″ where w″ is a prefix of the edge label from v′ to v and take the shortest string as a candidate marker that satisfies If for the path label Equally to the guided marker detection method the set of candidate markers is reduced such that in the final set of markers no marker contains another marker as infix or suffix or contains a repeated substring.probabilistic suffix trees (PST) [E. coli DNA [Note, that with es (PST) ,41 a reles (PST) . Probabicoli DNA  and for coli DNA  PSTs havcoli DNA .2.4.target gene for each marker. The target gene of a marker is the gene this marker is associated with. Using the annotation guided method the target gene for every marker is clear. The probability based marker detection method, however, does not define a marker's target gene. To classify the markers, i.e., to detect their target genes, annotation information is necessary. Therefore, we assume for the following that an annotation is given. The annotation data is solely used to assign target genes to the markers not to determine the markers themselves.In the following we describe how to determine the Once the set of markers is determined all sequences are queried for these markers in a fast search over the suffix tree. The position of all occurrences of the markers are thus determined. In the next step these positions are compared with the gene annotations. The number of overlapping base pairs is counted for all gene annotations overlapping with a specific marker. Each marker gets a score for each gene that is defined by the summed size of overlaps with that gene. The gene with the highest score is finally chosen as the target gene of the marker.2.5.de-novo annotation pipeline or the fast prediction of the presence or absence of genes.Having a set of markers with their respective target genes can be useful in various applications that are to a certain extend based on the detection of genes. One possible application is the detection and correction of errors in annotation databases. Other applications can be the inclusion into a The knowledge of the positions of markers in the nucleotide sequences and of the marker's target genes is used to produce a rough annotation of the sequences where subsequent overlapping markers with identical target genes are concatenated. The quality of the derived annotation is then compared with the original annotation.The comparison of the rough annotation with the original annotation might show that some gene is placed in a different location or on the inverse strand. In these cases either our prediction, i.e., the rough annotation, or the original annotation is erroneous. It is not always clear which of the two possible ones is the case.equal if both annotate the same gene and strand; (2) Δ± if they annotate the same gene but give different strands; (3) false negatives (FN) if a RefSeq annotation is unpaired; (4) false positive (FP) if a predicted fragment remains unpaired; and (5) different if the pair annotates different genes.The comparison of the two annotations is done as in . For eac3.k = 30 as the vast majority of markers is shorter than 30 base pairs. Confronted with rather short words we set l = 4 and the repeat threshold r = 3. For the significance parameter we set z ∈ {25 000, 50 000, 25 000 000}. The algorithms are run on a PC with Six-Core AMD Opteron(tm) Processor 2435 with 32 GB RAM.To test our methods we use the annotations from the RefSeq data base (release 57) containing 2989 metazoan mitochondrial genomes . Additio4.The annotation guided and probability based marker detection methods were run on the 2989 mitochondrial genome sequences contained in RefSeq and their reverse complements. Both approaches are very efficient see , i.e., t4.1.The structure of the 30-truncated suffix trees, i.e., the annotation guided suffix tree and the probability based suffix tree, is identical for both methods. The number of nodes and leaves depends only on the chosen depth of the tree. For depth 30 the suffix tree consists of 133 786 893 nodes. The characteristics of the sequences that are chosen as markers differs strongly between the two methods .z = 50 k detected more markers than the annotation guided method (3 119 929 markers). The results illustrate the trade off between marker length and number of occurrences. Clearly, short markers are more frequent than longer markers. The annotation guided method detected markers from 4 to 30 base pairs with an average marker length of 13.27 nucleotides and an average frequency of 6.31. The probability based method with z = 50 k detects markers with 8 to 27 nucleotides and an average length of 19.97 nucleotides. The markers frequency ranges from 2 to 3409 and is in average 6.61. z is very large).With 3 511 781 markers the probability based method with z = 25 k and a very large value of z = 25 M. With z = 25 k the marker length ranges from 7 to 27 nucleotides with an average of 19.45. The marker frequency ranges from 2 to 48 285 and is in average 6.93. Markers occurring more often than the number of sequences, i.e., the number of species, that are included in the analysis are qualitatively questionable as specifiers for certain genes because the genes usually occur at most once per genome. One of the markers with such a high frequency is the repeat (ATATATA) that is too short to be detected by Algorithm 1.For the probability based method the length and frequency of the markers depends on the value chosen for z. z the expected frequency of a marker has to be very small. Due to the underlying Markov model the expected frequency of a marker decreases with increasing length. Thus, only long sequences are declared as markers for a large value of z. For z = 25 M the obtained marker lengths range from 11 to 30 base pairs with an average of 24.63.A very large value for z (25 M) reduces the frequencies of the detected markers to a range from 2 to 2642 and an average of 5.05. To satisfy g is x then on average each nucleotide of the gene overlaps with x markers for g. In most cases  the probability based method covers the genes more densely than the annotation guided method. But differences between the two methods are larger for the tRNA genes and rRNA genes than for the protein coding genes.The different approaches used by the two marker detection methods also show an effect on the number of markers for the different genes. nad1  is shown. Clearly there are regions in the gene that are more densely covered than others. Whether this is due to the conservation of specific functional or structural important regions in the gene is yet to be investigated. Both methods show the same distinctive peaks but the variation of the density is different. The slopes in the density produced by the probability based method are far steeper than the slopes in the comparative plot for the annotation guided method.trnF are shown. Mind that the tRNA genes consist of less than a hundred nucleotides but the density for every hundredth part of a gene is measured. Thus a bar in the histogram represents less than one nucleotide and gives a rougher distribution than the respective distributions of longer genes. The distribution of the coverage does not immediately hint on the typical clover leaf structure of the tRNAs. However, in most tRNAs a central peak is visible where the anti codon is situated. In case of the trnF  the coverage with markers is generally higher towards the middle of the gene for both methods. However the annotation guided method shows a lower density in the very center of the gene than in the proximate areas around it.In 4.2.The structural analysis of the methods gives insight on the basic characteristics of the markers. However, the quality of the markers cannot be derived by such means. In the following we compare the annotations given by the RefSeq database and the MitoZoa database with the rough annotations produced by the different marker detection methods.b ≠ a in the RefSeq annotations. The probability based method also switches the strandedness of the genes more often.z, where z sets the significance threshold for the markers. The percentage of correct hits among all hits is the highest with z = 25 M, but the absolute number of correct hits per gene is the smallest compared to the other algorithms.For protein coding genes it is quite obvious that the probability based method improves the number of false positives with an increased threshold. However, by reducing the number of false positives it also increases the number of false negatives (FN). A false negative (FN) is every gene of the annotation that does not overlap with any prediction produced by the algorithm. The number of correct predictions per gene decreases for stricter significance threshold values. The relative amount of false predictions is vastly reduced with large values for z = 25 k the quality of the markers is lower than those for the protein coding genes for the respective method, i.e., predictions are less correct.The results for the control region are similar to those of the protein coding genes. Aside from the probability based method with z = 50 k 80 are associated with rrnL  and 16 with rrnS . Due to their near perfect conservation, i.e., 6 of the 8 most frequent markers and their reverse complements are associated with rrnL and occur in over 2850 sequences, each of these short sequences may serve as an indicator for the corresponding rRNA.For the rRNA genes the absence of false negatives is most striking. The remaining results are similar to those for the protein coding genes and control region. Among the 100 most frequent markers determined by the probability based method with The tRNA genes are generally shorter than the other genes considered. This complicates the detection of markers as the total number of markers is lower for these genes. The annotations for the tRNAs produced by the marker detection methods miss many genes (FN) or lie in regions of other genes based on the annotations provided by the RefSeq data base. The annotation guided method collected the highest number of correct predictions per gene for the tRNAs compared to the probability based method.Bear in mind that the annotations provided by the RefSeq may contain some errors possibly distorting these results. In an additional analysis we compared our results that were produced using the RefSeq annotations with the curated annotations provided by the MitoZoa database see .The comparison gives similar values to those shown in z = 25 M) there are more false negatives. The number of false positives is equal or lower except for the control region where an increase for the probability based methods is registered. The number of differently predicted genes is higher in three cases, lower in four cases , and similar otherwise.Aside from the annotations for the control region the comparison of the annotations provided by our methods score more true positives than in the comparison with the RefSeq. There are equally or less strand differences in the comparison with MitoZoa than with the RefSeq. Only in two cases  a large number (38 369) of predictions fall into the category different, i.e., the prediction overlaps most with a different feature of the RefSeq annotation. In 9971 of these cases the predicted gene and the annotated gene are adjacent in the genome. This large number can be explained by the fact that the method determines conserved sequences. If gene boundaries are conserved our methods will find conserved sequences spanning the boundary of two genes. In mitogenomes the same genes are often adjacent. In particular the mitogenomes of most chordates and many insects share a common gene order. Furthermore, mitochondrial genes are tightly packed on the mitogenome, i.e., there is mostly no or extremely small non-coding regions between genes or they might even overlap by a few nucleotides [For the probability based marker detection method (with leotides .z = 50 k) finds a correct marker, for only 67% of the annotated control regions in protostomia but in 98% for the Deuterostomia. Within the Protostomia consistent results are found. For the very sparsely sampled and annotated Lophotrochozoa 39% of the predictions match the RefSeq annotations and for the better sampled and annotated Ecdysozoa 68% do match.The control region harbors most of the signals for replication and transcription of the metazoan mitogenome , see alsz = 50 k) that are classified as different is on average 15.53 for Deuterostomia and only 6.55 for Protostomia (Ecdysozoa 6.16 and Lophotrochozoa 7.87).Prediction quality differs between taxa. The number of predictions of the probability based method  huge number of sequences renders this computationally difficult; (2) large number of genome rearrangements excluded all methods using a global chaining of anchors; and (3) due to the large taxonomic range the sequences are highly divergent which makes exact matches over all sequences, that are the base of most aligning programs, basically impossible. The substrings identified by our method might be useful for constructing a whole genome alignment if an efficient local chaining algorithm for sets of anchors appearing in a subset of the sequences becomes available.


Purpose: Traumatic brain injury involving loss of consciousness has focal effects in the human brainstem, suggesting that it may have particular consequences for eye movement control. This hypothesis was investigated by measurements of vergence eye movement parameters.Methods: Disparity vergence eye movements were measured for a population of 123 normally sighted individuals, 26 of whom had suffered diffuse traumatic brain injury (dTBI) in the past, while the remainder served as controls. Vergence tracking responses were measured to sinusoidal disparity modulation of a random-dot field. Disparity vergence step responses were characterized in terms of their dynamic parameters separately for the convergence and divergence directions.Results: The control group showed notable differences between convergence and divergence dynamics. The dTBI group showed significantly abnormal vergence behavior on many of the dynamic parameters.Conclusion: The results support the hypothesis that occult injury to the oculomotor control system is a common residual outcome of dTBI. If there was independent eye movement control of the two eyes, vergence and saccadic movements should be equally rapid, since there is no obvious evolutionary value in downregulating the speed of fixation at different distances if the capability had been available. The inference from this differential behavior is that vergences and saccades must be considered strong evidence that they are controlled by separate neurophysiological mechanisms , althou that the diffuse effects tend to be concentrated in the core brain structures. Thus, dTBI corresponds roughly to the category of mild-to-moderate (or non-penetrating) TBI, diagnosed as levels 9–15 on the GCS. However, dTBI is intended to include the additional criterion of lack of focal contusions on an MRI scan.)Remarkably, what is generally considered to be diffuse brain trauma does, in fact, have a focal effect centered on the core brain structures, such as the basal ganglia and brainstem. Brain impacts entailing loss of consciousness are generally considered to cause diffuse axonal injury through the brain. Thus, the idea that the brainstem would be the focus of long-term damage, with specific reference of the oculomotor pathways in the upper brainstem, has neither been widely expressed nor used in diagnosis/treatment of dTBI deficits. Note, in particular, that the GCS assesses only eye opening and closing responses, and does not include any eye movement indices.Significantly, in this context, recent studies have discovered that a high proportion of patients diagnosed with dTBI exhibit binocular vision dysfunctions, particularly deficiencies in the binocular coordination of eye movements –12. Up tA primary indication that diffuse impacts should have a focal effect in the core brain structures comes from a study of helmet-to-helmet American football impacts by Viano et al. , in whicThe innovative approach taken here is to consider this system as a whole, as an interconnected network of basal ganglia structures controlling all aspects of the dynamics of attentional interactions with the environment through movements of the eyes. In this sense, the approach instantiates the concept that various movements of the eyes, including the pupil and the lens accommodation, are a window into the functional status of the respective components of this complex of oculomotor control pathways. The present study focuses on the binocular aspect of oculomotor control, and specifically the control of symmetrical vergence in the median plane, which excludes any saccadic involvement.per se. All recruitment and experimental procedures in this study adhered to the Declaration of Helsinki. The study was approved by the Institutional Review Board of the Smith-Kettlewell Eye Research Institute and informed consent was obtained from all participants, none of whom withdrew from the study.This study involved a recruited base of 123 participants  from a non-academic population via a social media website for the normative study of oculomotor dynamics, passing the exclusion criterion of having no clinical history of brain or ocular abnormalities, including any form of strabismus or TBI events defined as involving head trauma, resulting in a loss of consciousness for a period of 5 min or more, or loss of memory of the traumatic event The participants were included in the analysis if they met the criteria of letter acuity of 20/40 or better in both eyes , of no visible ocular abnormalities, and of passing a random-dot stereopsis test at a disparity of 4 arcmin, consisting of reporting the quadrant and depth sign of a stereoscopically defined square of 10° on a side with a disparity of 4 arcmin. The individuals were assigned to the control group if they reported no past history of dTBI events . They were assigned to the dTBI group  if they reported a positive past history of one or more dTBI events characterized at levels 13–15 on the extended Glasgow Coma Scale [GCS-E; , which provides chirally-distinct circularly polarized output to the two eyes when viewed with appropriate polarizing filters in front of the two eyes. The stimulus was a 20° × 40° black and white random-dot array with a central 1° cross-hair monocular fixation target. The motion of the fields could be the same or opposite for the two eyes .Binocular eye movements were recorded with the Visagraph III  binocular infrared differential limbal eye tracker Figure , with a To calibrate the linearity of the recorded position function, the 1° cross-hair monocular fixation target (without the random-dot field) underwent two randomized sets of horizontal position shifts over the range from −16° to 16° for each eye, with button presses indicating when fixation was accurate at each position. The full set of points was fitted with a third-order polynomial to provide a linear calibration of the horizontal position separately for each eye.Horizontal conjunctive tracking eye movements were recorded while the 40° binocular random-dot field, including the fixation target, underwent a continuous sinusoidal change of horizontal position of ±2° around the central fixation position at 0.25 Hz. This task was a designed as a control condition for the vergence tracking task (next section), using the identical stimulus but with the two fields oscillating in phase for the conjunctive tracking and in counterphase for the vergence tracking. Thus, the monocular stimuli are identical for both tasks, the only difference being the interocular phase of the sinusoidal movements.Horizontal vergence eye movements were recorded while the 40° random-dot field, including the fixation target, underwent a continuous sinusoidal change of horizontal disparity from 8° to 12° of absolute disparity at 0.25 Hz, which is comfortably within the vergence range for normal subjects.The oculomotor position waveform for the 60 s tracking period (15 cycles) was subjected to Fourier analysis for each cycle to determine the amplitude and phase of the component at the stimulus frequency, the proportion of overall energy at the stimulus frequency . The amplitude and phase calculations were performed only on cycles in which >50% of the energy was at the stimulus frequency, to ensure that the assessment was applied when the participant was effectively engaged in tracking behavior. This analysis was performed with a sliding window of one cycle following each sample point. The fraction of cycles passing the 50% criterion was also tabulated.Binocular eye movements were recorded while the 20° × 40° noise field including the 1° fixation target that underwent 2° horizontal square-wave disparity changes every 2–3 s, with random jitter over 1 s from a uniform distribution to avoid predictability of the onset time. The minimum interval of 2 s allowed comfortable completion of 24 repeated normal vergence movements within a 60 s sequence.The vergence (left-eye minus right eye) signal waveforms were extracted from a period around the times of the instantaneous transitions of the stimulus in a window from 1 s prior to the transition to 2.5 s after the transition  consisting of a two-component cosine + gamma function fit:t, T are time variables, A1, A2 are scaling factors, δ1, δ2 are delays, w is the period of the cosine, β is the exponential time constant, and α is the order of the gamma function.To quantify the vergence dynamics, the average convergence and divergence waveforms were fitted with a canonical time waveform v(t). Peak velocity was defined for the peak of its derivative. Temporal asymmetry is defined in the following section.The fit of this equation, as characterized for one example in Figure Temporal asymmetry of the velocity trace was defined by computing the ratio of the post-peak area minus the pre-peak area to the total area of the vergence interval defined from the velocity trace. In principle, this temporal asymmetry index has a value of 0 for a time-symmetric waveform and a value of 1 for a pure exponential waveform. In practice, the smoothing applied to the waveform reduces the maximum value for the pure exponential response after the filtering of the waveforms, so we defined a normalized temporal asymmetry index (γ) as the ratio of the empirical temporal asymmetry index to the theoretical temporal asymmetry index for a filtered exponential decay. .t-tests. Unless otherwise noted, significant results are reported at level of p < 0.01.The statistical analyses were performed by p < 0.01 are highlighted in yellow.An overview of the vergence tracking behavior is provided by averaging the sinusoidal tracking performance separately for the control and dTBI groups in relation to the target disparity variation  The difference function reveals that the vergence tracking is adhering relatively closely to the target disparity, though significantly delayed.In the uppermost dTBI case in Figure conjunctive tracking is substantially advanced in phase relative to the target. The disjunctive tracking of the two eyes are again largely conjunctive in nature, with any difference barely noticeable. Yet, the vergence angle (interocular difference) function reveals that there is a reportable vergence tracking of about half the target amplitude, though with much larger error than in the control case.The center dTBI case in Figure conjunctive tracking is heavily disrupted, with jerky behavior, large differences between the eyes and wide error ranges, indicating inconsistent behavior from trial to trial. The right-eye variability is again large, although the left-eye shows a consistent tendency of anti-tracking, as though it is driven by the right-eye signal. The disjunctive tracking behavior shows inversion of the left-eye response, though with reduced amplitude, and a much noisier response for the right eye. These combine to produce a vergence tracking response with little adherence to the target disparity, and may be regarded as essentially noise, or perhaps even inverted on the basis of the inverted left-eye response.In the third dTBI case in Figure To quantify these results, the average response to the sinusoidal disparity stimulus may be encoded by the following parameters: amplitude and phase delay in terms of absolute response lag, together with their SEM over cycles, and a parameter for the goodness of fit to the sinusoidal waveform. In order to avoid artifacts due to blinks and inattention, the analysis was based only on cycles in which the goodness of fit to the sinusoidal waveform was better than a correlation value of 0.9 (based on a 1-cycle moving average).(kx−1) × e−x/σ), where k and σ are constants, which has a long tail for small k.The full results for these four parameters are shown in Figure x − ox)(k−1) × e−(x−xo)/σ), where x is phase lag, to avoid biasing the peak of the distribution while allowing for an asymmetry of the distribution.The fit to the phase distribution Figure C is a spThe goodness of fit distributions Figure D show thThe fit for the amplitude distribution gives a peak-to-peak value of 3.34° ± 0.076°, implying that the typical behavior is to track at a significantly lower disparity amplitude than the stimulus demand . However, 17% of the population show amplitudes >1.5 (3°), forming the long tail to the right of the main peak, and this result cannot be attributed to simply noisy tracking behavior because the amplitude analysis is based only on good-quality tracking cycles.The peak phase lag was 222 ± 17 ms, implying that the normal behavior is to track the target with a neural processing delay typical for unpredictable saccades. Here, the surprise is that virtually all cases are showing a phase lag despite the fact that the stimulus disparity was entirely predictable after the first cycle. The asymmetry in the fitted gamma function implies that a small proportion of the control group have atypically long tracking lags see . The relThe same set of analysis was performed for the dTBI group  and the peak velocities . We therefore turn to a more detailed analysis of the parameter distributions plotted in Figure p < 0.01, and the average chi square across the six distributions showed that they were significantly non-Gaussian at this level for both the convergence and the divergence sets. We therefore fitted the distributions with a two-component model consisting of a normal Gaussian function summed with a three-parameter gamma function that could allow for long tails and/or a second peak . This interpretation implies that the Gaussian component is the best estimate of the normal behavior for the control group, and that the Gaussian component for the dTBI group captures the predominant behavior for this subgroup (with the range of diverse forms of damage captured by the gamma component for both groups). The analysis of abnormality for the dTBI group is consequently evaluated in relation to the Gaussian component of the control group. We have therefore tabulated the mean values for the Gaussian component for the control group for comparison with the values in the dTBI group.Table Table t-tests at p < 0.01). Remarkably, the convergence/divergence performance for the dTBI group were significantly enhanced (pink highlighting) relative to controls for the onset latency parameter for convergence and for the amplitude and duration parameters for divergence.For the dTBI group, Table This table also provides an analysis for the variability of the parameters over trials, which was significant higher for the dTBI than for the control group for the amplitude and duration parameters in the convergence (but not the divergence) direction. The lack of an effect in the divergence directions is partly due to the significant tendency for the variabilities for the control group to be higher for divergence than convergence movements (significant for the onset and duration parameters). In summary, the Gaussian model fits provide strong evidence for notable differences in vergence eye movement dynamics for dTBI sufferers relative to the control population, building on the basic information of significant differences between divergence and convergence movements in the control population itself. Most of the differences are in the direction of weaker responses in the dTBI population.p < 0.01 (uncorrected), implying that they would be even further from significance if an appropriate correction level was employed for the 20 applications of the significance test. Thus, we can conclude that there was no significant variance introduced by the wide range of ages or time since the concussion event.As a final form of analysis, correlations were run for each of the step disparity convergence and divergence parameters of Table The average vergence tracking waveform for the control group showed a mean vergence error of about 1° less than the target vergence angle of 9°, implying that the vergence was relaxed somewhat behind the screen (at the 48 cm viewing distance).The control convergence/divergence comparisons in the controls are of interest in assessing the dynamics of the vergence control system in its near-field operating range . The preThe long tails on many of the normal distribution functions imply that they are not well described by Gaussian distributions, which are the asymptotic form to be expected from the combination of many independent sources of noise . The long tails may thus be interpreted to imply that some proportion of the individuals categorized as normal should be suspected of exhibiting abnormal oculomotor dynamics on the respective indices. In the context of the deficits shown by the dTBI sufferers, it needs to be asked whether the clinical history could have missed some TBI incidents in these cases. Although our clinical history asked about all TBI incidents in the individuals’ past, it is unlikely that the history would unearth all TBI incidents in a person’s life, particularly those due to birth trauma or falls during infancy. The analysis thus suggests that the long tails of the “control” distribution functions represent an occult subpopulation of dTBI cases.In the convergence/divergence comparison in the controls, the primary result is the combined weakness in the divergence response relative to the convergence responses on all parameters except temporal asymmetry. The lack of a significant difference for the temporal asymmetry parameter implies that the general weakness is not attributable to a change in the operating principle (active vs. passive) between the two directions of movement as indexed by a change in the waveform of the saccadic responses. Evidently, there is just a net tendency toward a weaker response in the divergence direction on a population basis, although the analysis of Tyler et al.  made cleFor the dTBI group, the mean values of most parameters were significantly weaker than those of the control group for both convergence and divergence movements. The mean vergence angle was reduced by 1.8° relative to the 9° vergence angle of the screen, implying that the dTBI group exhibiting a further degree of convergence relaxation on average, although the tracking amplitude was similar to that for the control group. This result corresponds to a quantification of the condition known as “convergence insufficiency” that is typically associated with dTBI. We emphasize that all the dTBI individuals had normal stereoscopic vision for the random-dot depth discrimination targets of our screening test, so this difference is not attributable to a sensory weakness. Remarkably, however, the convergence/divergence comparisons for the dTBI group go in the reverse direction from the controls for the amplitude and onset latency parameters, although there is no obvious reason why this should be the case. The variability of the parameters over trials was also significantly higher for the dTBI than for the control group for the amplitude and duration parameters in the convergence direction.The sinusoidal vergence tracking data show a significant proportion of deficits in the dTBI, with up to a quarter of cases showing weakness on three of the vergence tracking parameters, where only about 7–9% should be expected from the criteria set for the control distributions. It thus should be worthwhile to include this form of tracking behavior in a test for binocular deficits in dTBI cases.The reduced amplitudes of convergence responses in the dTBI subgroup is not surprising in light of the higher proportion of convergence insufficiency reported in clinical studies of this population , 16, 17,One hypothesis for the effect of dTBI could be that it might tend to knock out the active drive of the vergence response in one direction and convert it to a passive response. If this were to occur, an index of its occurrence might be the switch from a time-symmetric waveform to a high-asymmetry exponential waveform corresponding to relaxation process . HoweverThis study shows that the variety of human vergence dynamics contributes substantially to the understanding of the oculomotor control mechanisms underlying the generation of these movements, and their susceptibility to mild TBI. A large proportion of the dTBI group showed abnormal vergence behavior on one or more of the dynamic parameters. The results suggest that occult injury to the oculomotor control system is a common residual outcome of dTBI. Severe brain injury is often visible by structural brain imaging, such as X-radiography or magnetic resonance imaging (MRI), but milder effects that are invisible to these techniques may nevertheless cause substantial oculomotor disruptions. Effective treatment of these oculomotor problems will require accurate diagnosis of the source of the problem.The 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.


Walking impairment after stroke can be addressed with the use of drop foot stimulators (DFS). Many studies have demonstrated that DFS improves walking speed, reduces spasticity and reduces the physiologic effort of walking. Current DFS, through activation of the common peroneal nerve, elicit ankle dorsiflexion during swing phase of gait. DFS are generally piloted by force sensing resistor placed in the shoe of the affected side with stimulation triggered ON by heel rise and triggered OFF by heel strike. A tilt sensor can also be used with stimulation triggered by the tilt of the shank of the affected leg. These triggering approaches are the standard for initiating stimulation. However, the real-time modulation of FES intensity to provide more optimized delivery of stimulation and also to regulate dorsiflexion in the presence of disturbances, such as fatigue and spasticity may increase the number of potential users of DFS. Concerning research domain, stimulators that would allow modulating the stimulation pattern in between heel rise and strike events would allow exploring new stimulation strategies. We propose to extract continuous information: the gait cycle index (GCI), from one inertial measurement unit (IMU) measuring shank tilt angle. In order to illustrate the use of this real-time information, we show the feasibility of piloting an electrical stimulator.12 subjects with post-stroke hemiplegia participated. A wireless IMU was placed on the unaffected shank and was used to estimate GCI. Subjects performed 3 trials in each of the 3 conditions: C1 no stimulation aid, C2 electrical stimulation assistance triggered by heel switch, C3 electrical stimulation assistance triggered from GCI.1) the proposed algorithm was able to real-time estimate GCI, 2) events could be extracted from GCI information in order to trig a DFS.The estimation of the continuous GCI in individuals with stroke is possible. Events can be extracted from this information in order to trig a stimulator. These results are a first step towards the possibility to investigate new DFS paradigms based on real-time modulation of stimulation parameters. Walking impairment after stroke is a common and universal problem, 2 that However, real-time control of stimulation intensity is still not available in existing devices. The modIt would also be of great importance to be able to analyze the orthotic and clinical outcome of other type of stimulation strategies other than triggering ON and OFF a fixed pattern based on gait events. Some research studies have suggested that improvement in orthotic performance could be achieved using stimulus intensity shapes matching more closely the natural tibialis anterior biphasic activation pattern than the trapezoidal shape classically used in the stimulators–31.In this article we propose to extract continuous tilt angle information from one inertial sensor fixed on patient shank. As a first attempt to use this real-time information, we show the feasibility of triggering an electrical stimulator based this information. We embedded our gait observation algorithm within a system involving a commonly used Odstock stimulator. The goal was to show the feasibility of processing the gait cycle index (GCI) from one sensor, and to use it to pilot the stimulator.In the present study, we: 1) explore the feasibility of continuous tracking gait cycle in individuals with foot drop using one sensor placed on the unaffected leg shank and 2) validate the feasibility of combining the observation algorithm with a DFS controller.12 subjects  with hemiplegia were included. Subject characteristics are given in Table  The algorithm was first introduced and described by Heliot and Espiau in, where m0 and a frequency of ω0. The equation of Van der Pol oscillator used in this study is given by (1).Our algorithm is based on defining OFFLINE a model of a system, which in our case is human gait. In the field of control of locomotion in humanoid robots, the bipedal gait has been modeled as a non-linear oscillator, 34. Two0 are positive constants. The choice of μ, ω0, and b constants is explained bellow.where μ, and ωIn the phase plane (position versus velocity), periodic stable solution of the oscillator is a trajectory called a limit cycle Figure . The phaThe phase grows uniformly in the direction of motion and gains 2π at each rotation. There is a need to define the φ variable in such a way that it rotates uniformly in the cycle of the oscillator. We therefore define OFFLINE an isochron matrix that allows us to associate a phase value to any point in the vicinity of the limit cycle. Each point in the vicinity of the limit cycle is associated with a point in the limit cycle Figure . This maBased on control theory framework, it is theoretically possible to build an observer of this system that will be able to estimate the internal state of the system, in our case gait of a person with drop foot modeled as Van der Pol oscillator, from the system output measurement. In control theory, a state observer is defined as a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system, and couwhere: y is the output of the system, and x1, and x2 are the states of the system which should be estimated. In our case, y corresponds to a measurement of shank angle of the unaffected leg. The shank angle was chosen because it is the easiest to be obtained by the sensor technology used in this study. Knowing the value of y, and solving the system of equations , we can The principle of described algorithm is given in Figure 0, and b constants in (1) that would fit the sensor measurement into this oscillator model. This problem can be solved by using dynamic optimization technique called Feasible Sequential Programming Technique (SQP)[0, and b constants that minimize a quadratic function of the error between measurement and output of our model. The mathematical details about the calculations are given in[The last step is defending the values of μ, ωue (SQP). SQP tecgiven in. Prior tOscillator design (OFFLINE)The subject is asked to walk a few steps during which the shank angle is measured.0, and b are identified through a dynamic optimization problem: the error between the measured shank angle and the oscillator output is minimized. The isochron matrix is computed.The oscillator parameters μ, ωThe oscillator parameters are updated in the observer of the system.We summarize the different steps of the method  - the observer computes φ and GCI variables in real-time based on the measured shank angle y.https://www.iot-lab.info/). A WSN430 node is an electronic system which insures 3 functions: data acquisition using daughter board sensor-specific, data processing based on a micro-controller (Texas Instruments MSP430) and wireless radio- frequency communication (based on Texas Instruments CC1100). In our architecture, 3 types of WSN430 nodes are used: one sink node connected to a laptop via a serial port, one sensor node placed on the participants’ lower limbs, and one control node which triggers the stimulator as shown in Figure The developed system is based on a wireless architecture of sensors and actuators using WSN430 technology  are triggered offline on the patient in order to obtain efficient dorsiflexion/eversion movement without discomfort or pain. The stimulator can be used in “normal” mode using a footswitch placed under the affected side heel in order to switch the stimulation ON at heel off and OFF at heel strike. To test the algorithm described in the “Observation algorithm for gait phases estimation”, the actuator node was plugged onto the switch connector of the stimulator in order to trigger ON/OFF the stimulation depending on the information received from the sink node Figure .Figure 5In the protocol, each subject walked along the GAITRite walkway. Each subject performed 3 successive trials for each of the 3 conditions: C1) No stimulation, C2) Stimulation triggered on the basis of heel switch information, C3) stimulation triggered on the basis of the GCI information. C2 and C3 were applied in a randomized order among the patients  events extracted from GAITRite software.A t-test was carried out to compare the average walking speed in each condition .Table In Figure The GAITRite walkway was used as a gold standard to verify heel on and heel off moments of affected leg for each trial of each subject. The GCI values computed in the C3 condition, corresponding to Heel OFF and Heel ON were compared with events extracted from GAITRite data for the affected leg. The comparison between heel ON and heel OFF instants estimated using GAITRite system and proposed Observation algorithm for gait phases estimation is shown in Table In Figure In this study we used the observation of the unaffected leg shank angle to detect the heel strike moment instead of commonly used heel-floor contact. Strong positive correlation between unaffected leg shank inclinations demonstrates that the shank angle is a variable, which has similar repeatable shape during the gait of a person with drop foot, and could be potentially used to trigger the electrical stimulator.In order to validate the relevance of the GCI information, we compared the GCI values computed in the C3 condition, corresponding to Heel OFF and Heel ON events extracted from GAITRite data for the affected leg Figure . The aimFrom the Table 2 ranging from 30% to 70%. Patients 1 to 4 and 7 to 12 were stimulated for GCI values ranging from 0% to 40%. Indeed, for these patients the swing phase duration was similar to normal gait. Patient 6 was stimulated for GCI values ranging from 0% to 50%.Among all 12 subjects, 282 strides were analyzed for the trials in the C3 condition. In only 4% of the cases, the stimulation was not triggered in affected leg heel strike moment, as expected. That was due to problems with the wireless communication such as loss of wireless signal . We will also develop new controllers with auto-adaptive properties in order to automatically modulate stimulation parameters in order to assess walking in more challenging conditions .


A method has been developed and tested to determine the body length of living daphnids. The purpose of the method was the simple, accurate, repeatable, quick, and to the living organism, harmless measurement of body length of all individuals in a population to enhance the capability of observing population development over time. Generally, organisms are transferred to a petri dish and temporarily fixed by removing access medium. A picture of the petri dish is taken using an ordinary flatbed scanner. Pictures are manually analysed with purposely developed software. We found no significant impact of the method on either individual performance (growth and reproduction) or population development (abundance and structure) of daphnids in comparison to the previously used method for data gathering . The disadvantage of our method, an increased demand in time for picture analysis, is negligible compared to the advantages this method has. Data generated with the new method do represent the population structure more accurately than those data generated with the previously used method. Scanning organisms does also allow a retrospective quality control for generated data as pictures can securely be stored. The quality of the pictures is furthermore sufficient to include additional endpoints to the analysis . Here, we present, test and discuss an alternative approach to automated image analysis for data gathering in single and multiple individual and species experiments.The online version of this article (doi:10.1007/s10646-015-1490-0) contains supplementary material, which is available to authorized users. Daphnia magna . Organisms are fixed to the petri dish by carefully removing excess water until no movement of the organisms is observed, while leaving enough water around the individuals to continue filtering water. The petri dish is placed at the scanner and a picture is taken using the preliminary set scanner settings. So far the method of body length measurement has been calibrated using the colour image scanners CanoScan 8800F and 9000F from Canon at 1200 dpi and the CanoScan D-1250U at 300 dpi.A video demonstrating the whole process of generating a picture using a group of different sized daphnids is provided in the Online Resource 2.For the accurate measurement of body length it is necessary to calibrate the software to the scanner and the scanner settings chosen to generate the picture. To do so, millimetre scale has been placed face down on the bottom of a petri dish and was scanned using the identical scanner setting as chosen for scanning the daphnids. The software incorporates a measurement procedure for standards  which can be used to identify the number of dots per inch (dpi) for a chosen length (for example 1 mm). This standard measure can be saved to allow measurements of all pictures taken with the same scanner and scanning settings without further need of length calibration.Purposely developed software is used to manually measure the body length of individuals in the picture. The software has been developed using Delphi (Embacadero RAD Studio XE2). A version of the software is provided in the Online Resource 3.Overall, the software allows opening the picture in its original size, the user can identify the standard to measure against and needs to manually identify the starting and ending point of a measurement by clicking on it. The processed picture (indicating the measurement) can be saved as jpg-file. Generated data can be stored as Excel readable csv-files. A demonstration of the software is provided in the Online Resource 4.The body length of three daphnids of three different size classes  was measured using a microscope (WILD Heerbrugg). Subsequently, the individuals were transferred to a petri dish and pictures were taken as described above at four different settings for the resolution of the scanner . Pictures were analysed using the purposely developed software (Online Resource 3) and measured body length was compared to the measurements generated using the microscope Mayer .Desmodesmus subspicatus.The body length of 20 neonates (<24 h) was measured 2–3 times a week for a total of 30 days. Body length was determined using the microscope for half of the organisms. The remaining organisms were scanned and body length was measured via picture analysis. Organisms were treated identically except for the method used to generate length data. Individuals were kept individually in 90 ml M4-medium Elendt  at 20 ± A population experiment was conducted over 5 weeks to determine whether frequent data acquisition itself and the type of data acquisition via scanning and microscopy influence the population development. The experiment consisted of four treatments with three replicates each. Three treatments (scanning (1), sieving with microscopy (2) and sieving without microscopy (3)) were set up to be semi-static; thus populations were handled frequently. Three times a week populations were transferred to fresh medium via sieving. During this process data acquisition took place every time (treatments 1 and 2) or only twice in total . Next to these semi-static populations treated with frequent sieving the experiment consisted of populations where medium had not been changed (treatment 4) and populations were not handled frequently. Data acquisition for treatment 4 took only place twice (day 19 and 35) via sieving with microscopy.Desmodesmus subspicatus (per day and population).All populations were started with five neonate (<24 h) and three adult (2.9–4.0 mm in length) daphnids, kept in 950 ml M4-medium Elendt  at 20 ± Four sieves differing in their mesh diameter were used to separate individuals in four categories. These categories were proposed to be adults , juveniles , neonates  and aborts. Sieves used were scanned and measured. Mesh diameters were found to be 1.36, 0.66, 0.40 and 0.27 mm for the sieves for adults, juveniles, neonates and aborts, respectively. A cascade of all sieves was used on days of data acquisition for treatments using microscopy for length measurement to allow the immediate count of individuals belonging to the different size classes prior to length measurement of a subsample (n ~ 10). Only the sieve with the smallest mesh size (Ø 0.27 mm) was used to collect the whole population for scanning and for transfer to fresh medium without data acquisition Mayer .After the observation of population development was completed individuals of one population were classed using the sieving with the sieve cascade and the scanning method. All groups and their corresponding sieves were scanned to compare the presumed and actual separation via the sieving method Mayer .A series of more than 200 pictures (each consisting of one mother with their offspring <24 h) were generated for an independent reproduction test. Pictures were taken and analysed as described above in consecutive order within a period of 10 h. Analysis of all pictures was conducted by two analysts. The main difference between both analysts was the familiarity with the method .Two-way analysis of variance (ANOVA) was performed with the data on individual growth and reproduction and the total population abundance. The Shapiro–Wilk test for normal distribution and the Levene-Median test for equal variance were performed prior to the ANOVA. The all pairwise multiple comparison was conducted following the Holm-Sidak method. All statistical analysis was performed using SigmaPlot 12.3.The test revealed that at 360 dpi the picture quality was not high enough to identify both the spine and the base of the spine. We therefore disregarded this resolution from further analysis as the body length of daphnids  illustrated in Fig. Since minimal movement of individuals (and with this movement of filtering appendices inside the carapax) is recorded during the scanning process generated pictures have the advantage to disclose additional information. The movement of filtering appendices (shown in the picture as rainbow-coloured areas) combined with the colour of the algae in the upper part of the gut can be used to distinguish living and dead individuals. A detailed illustration is shown in the Online Resource 1, Fig. 1. The picture quality also allows the investigation of further endpoints. It is for example possible to count and measure offspring in the brood pouch or measure spine length and other morphological characteristics.There was no statistically significant difference in body length and reproduction when comparing the microscopy and scanning method  with the exception of a single significant difference in body length on day 25 . This difference is however very low and is not observable at any other time point. This experiment illustrates that handling procedures involved in scanning does not alter individual behaviour in terms of growth and reproduction differently than those procedures involved in the usually used method for body length determination .per se cannot be ruled out. However, it is more likely that populations not sieved frequently reached higher abundances because they were kept in a static system without medium change. Not renewing the medium likely increases the food availability for the population through both a lack of removing not eaten algae and growth of bacteria. It has frequently been observed that daphnids can graze on bacteria  much higher total population abundance as all other populations . If sieving through the smallest sieve took place three times a week to transfer the population to fresh medium total abundances were significantly smaller on both days of data acquisition Fig. , top. Whper se does not disturb population development in semi-static experiments; making high temporal-resolution observations possible without reducing the potential of lab experiments reflecting field populations.Whether one sieve or a sieve cascade is used to transfer populations to fresh medium does not show any impact  on the total population abundance . The relative decline towards the equilibrium however is similar to that of the other populations treated to scanning. This data set has been included to illustrate that fluctuations between experiments can occur throughout the population development towards the equilibrium. More importantly it shows that an impact of scanning on population abundance might not be ruled out but does, if at all having an impact, influences population development consistently. Meaning that treatments are comparable to their control and experiments are comparable to each other.Sieving the population through a sieve cascade and counting individuals in each sieve certainly requires some time but allows the investigation of the population structure by classifying certain groups of the population. The comparison of population structure shows that frequent change of medium does not influence the composition of a population Fig. b vs. d. Figure Overlapping size distribution occurs to such an extent that a precise classification via sieving is not possible. This could result in a high variability between replicates and an increased chance of differences in population structures between treatments thoroughly reflecting errors in categorisation rather than true treatment effects. Intensification of the sieving process  could be a solution to reduce the amount of overlapping size distribution but will increase the handling time, will most certainly increase the stress for the organisms and does not allow distinguishing demographic shifts and morphological plasticity.Using the scanning method furthermore has the advantage that it can reduce handling time. No individuals need to be counted during the actual experiment for data acquisition providing the possibility to increase the number of replicates or treatments within one experiment. Generating the data via picture analysis on the other hand can increase the overall duration of an experiment. Depending on the number of pictures and population abundances, time spend to analyse pictures might be higher than time saved not sieving through a sieve cascade and counting on the go. The advantage is that picture analysis can be conducted at any time, pictures can be stored for quality control and reanalysis, and picture analysis provides the opportunity to investigate other endpoints. The number of reproducing mothers and the number of eggs per mother can be measured and could be used to predict population growth. Such measures increase the information an experiment can deliver and increases the benefit of whole population experiments. Enabling a better understanding of population development in general and widen the potential to assess changes in populations from biotic and abiotic stresses.The comparison of the results from both analysts (experienced vs. unexperienced) revealed that it is of advantage to get familiar with this method to reduce the coefficient of variance for the measurements and thus increase the statistical power for experiments. Comparing the measured averages and standard deviations for neonates in the first 20 pictures revealed that the coefficient of variance is twice the coefficient of variance for an experienced analyst. Nevertheless, this experiment showed that unexperienced analysts can reach a relatively low coefficient of variance to start with . For the experienced analyst the coefficient of variance remains fairly stable over time with an overall average of 0.032 ± 0.013 and a maximum of 0.075. For the unexperienced analyst the coefficient of variance increases over time and reaches on average of 0.085 ± 0.033 with a maximum of 0.244. An inconsistency of picture analysis over time  exacerbates the analysis of the whole experiment especially when comparing different treatments over time. This analysis indicates that experience, most likely determined by the concentration level to click at the accurate spot is an important factor for consistency in accuracy.A further factor influencing the analysis is the definition of body length itself. Usually, body length for daphnids is defined as the diagonal measurement from the top of the eye to the apical base of the spine as illustrated in Fig. A comparison of the measured body length of mothers in all pictures analysed using both mentioned definitions for body length show a constant difference of the measured length of 0.13 mm .Using the scanning method gives the possibility to increase the number of treatments within one experiment as handling time of populations is decreased. Users are able to accurately determine the population structure accounting for all individuals in the population. They are no longer restricted to group the individuals in a population into age/size classes specified by the sieves used, and they have the opportunity to greatly enhance the amount of information gathered in their test. Users have the chance to fit the type of endpoint to be measured to the underlying research question without having to change the method to be used or the need of changing the analysis programme.There are disadvantages compared to other methods. Predominantly the additional time needed for picture analysis and a chance of analytical differences between two experimentalists could be seen negative. Automated image analysis as proposed frequently Online Resource 2 (MP4 88495 kb)Online Resource 3 (ZIP 672 kb)Online Resource 4 (PDF 1108 kb)


Correction for incomplete transfer of energy from transverse to longitudinal degrees of freedom, and the violation of the adiabatic conditions on reflection at the mirror, is carried out by alternately measuring the spectrum at trapping times of 1 ms and 2 ms. The results a0 = −0.1054 ± 0.0055 and |λ | = 1.271 ± 0.018 are comparable in precision with existing measurements of a0.The coefficient  Δ S = 0) semi-leptonic decay, whose rate is governed by the weak vector and axial vector coupling constants GV and GA. The anomalously long lifetime of the neutron  may be derived from the neutron lifetime as before, and the value of λ from observations on the parity-violating neutron-spin electron-momentum correlation coefficient A in polarized neutron decay [Although nfidence . An alteon decay .λ | which has not been fully explored, namely the measurement of the electron-antineutrino angular correlation coefficient a. This is given in lowest order by the expression [There is, however, another route to the determination of |pression :a0=[ rather than to |λ| itself.Since this is a parity conserving correlation which does not contain interference terms proportional to a0 relies on a measurement [g(E) which has the form [g1(E) ≥ 0 reaches a maximum near the middle of the spectrum at about the same point where the function g2(E) changes sign from negative to positive. The behaviour of g2(E) is a reflection of the fact that, for a Fermi (Gamow-Teller) transition, the momenta pe and pν are predominantly parallel . It should be remarked that a0 as it appears in To date the most successful method for determining surement  of the pthe form g(E)=g1 of protons trapped behind a barrier of variable height V0. This is what is meant by the “one-dimensional integrated spectrum,” since protons are trapped if the energy in their longitudinal degree of freedom is less than eV0. However Monte Carlo simulations based on the known spatial variation of the magnetic and electric fields [a0. It was therefore found advantageous to exploit the action of a nonuniform magnetic field by establishing the mirror electrode in a region where the magnetic field has fallen to a very low value. The modified apparatus and magnetic field map are shown in In the simplest method the potential on the gate electrode is kept constant at about 0.85 kV while the mirror electrode may be set at different potentials c fields  and the high magnetic field, nearly all the transverse energy is transferred into the longitudinal mode, an effect described as adiabatic focusing or collimation. Thus the measured integrated spectrum coincides very closely with the full three-dimensional spectrum. It is, however, essential that the magnetic field be uniform at the position of the mirror electrode, and to this end a permanent magnet in the form of an annulus has been built into the mirror electrode. Under these conditions, and assuming exact adiabatic invariance, approximately 90 % of the total proton energy should appear in the longitudinal degree of freedom [N3(V0) of protons created in the region of high uniform magnetic field and trapped in the region of low uniform magnetic field [In this variant, which is the inverse of the normal magnetic mirror effect whereby energy is transferred from the longitudinal to the transverse mode when a charged particle is transported into a region of  freedom . In ordeic field . At the B≈2 T is such that the field changes by about 7 % in one period of cyclotron oscillation for a proton of average energy moving with a velocity ≈250 km s−1. This change might reasonably be described as adiabatic. However at B≈1 T the field change per cycle increases to about 30 % per period and the assumption of exact adiabaticity fails. Thus transverse and longi-tudinal motions are coupled in this region and an oscillating proton visits every state open to it by conservation of energy and angular momentum. The result is that “unbound” protons with energy above the barrier set by the mirror, but with initial longitudinal energy below the barrier, will ultimately escape. However, the time scale must be determined from the experimental data.According to the field plot shown in −1 with a background/signal ratio less than 1 %. The integral spectra observed in both long and short 10 ms traps were recorded in 50 V steps of V0 up to a maximum of 900 V with the same statistical error at each point corresponding to about 1 % at the highest counting rate. Approximately 106 events were recorded in total [The first experiments were performed during two cycles of beam-time on the high-flux cold neutron beam PF1 at the Institut Laue-Langevin in Grenoble, France in 1997. The maximum count rate for trapped protons was about 4 sin total .−1 to about 20 s−1. Thus, to keep the deadtime correction [The final experiments were performed during two cycles in 1998 and the results including many of the technical details have been published . For thirrection  associatassumption that all particles which are not energy bound escape over a time scale which is negligible compared with the trapping time are displayed in The results of an analysis based on the a0 is non-zero at a level of significance < 0.1 %, the hypothesis of an infinitesimal lifetime for unbound particles in the trap must be rejected. Indeed, since unbound particles are released at a constant rate into the trap, whereas the loss rate is proportional to the number present at any one time, it follows that the number of unbound particles which are trapped must eventually reach an equilibrium value. The difference in the measured values of a0 may then be used to determine this lifetime, under the weaker hypothesis that the number of unbound trapped particles reaches equilibrium in a time < 1 ms. The results of this re-analysis are shown in Since the difference between the two mean values of a0 derived from all the measurements listed isλ |is obtained by application of The mean value of


In the GRID technique one measures Doppler-broadened line profiles of γ transitions using the high resolution crystal spectrometers GAMS, which are installed at the high flux reactor of the ILL Grenoble. One of the essential applications of this technique is the measurement of nuclear state lifetimes. In the present contribution the precision and the principal limits of the technique are discussed. A general scheme of the experimental set-up is shown in During the last three decades, crystal spectrometers have been developed and installed at the high flux reactor of the Institut Laue-Langevin. Currently, three devices are available: the single bent crystal spectrometer GAMS2/3 and the two double flat crystal spectrometers GAMS4 and GAMS5. They are installed in line to an in-pile tangential beam tube. In this beam tube targets can be placed at a distance of 55 cm to the reactor core where the thermal neutron flux equals 5×10A detailed description of the GRID technique has been given in a series of publications ,2,3 and Thermal neutron capture produces an excited nucleus, which deexcites either by γ emission or other decay processes. Whenever an emission process takes place, the nucleus is recoiling due to momentum conservation. In the particular case of a γ cascade this means that the measured energy of any secondary γ ray might be Doppler shifted by a recoil induced during a prior emission of another γ ray. Due to the spatial distribution of the recoil directions, it is a Doppler broadening, which will be obtained. The broadening depends on the velocities of the recoiling nuclei at the time of the secondary emission and therefore on three factors: i) the initial recoil velocity, ii) the time between the initial recoil and the emission of the observed γ ray e.g., the lifetime of the intermediate level and iii) the slowing down of the recoiling particles. The measurement of the Doppler-broadening allows extraction of information on one of these quantities, assuming the other two to be known.Eγ1. As the initial recoil velocity is known to be υR = Eγ1/Mc, where M is the mass of the recoiling isotope and c the velocity of light, the Doppler-broadened lineshape of the secondary transition Eγ2 depends only on the lifetime of the intermediate nuclear state and the slowing down of the recoiling atoms.For illustration, we consider first the very simple case of a two step γ cascade, where the intermediate level is fed to 100 % by a primary transition of energy t) of all recoiling atoms. This assumption is strongly based on the use of powder targets. In this case, the γ rays are emitted from a large number of microcrystals and any microscopic anisotropy of the slowing down process is averaged out due to the random alignment of the microcrystals. Assuming υ(t) to be known, the Doppler-broadened γ lineshape is given by the equationΓ represents the natural width and τ the lifetime of the depopulated nuclear state. The calculation of υ(t) was first solved within the so-called Mean Free Path Approach (MFPA) [In order to have a description for the slowing down process of the recoiling atoms Jolie et al. , 4 have h (MFPA)  or Restrh (MFPA)  have beet) would allow extraction of a nuclear state lifetime and a direct comparison with the experiment. However, there exist two further factors which must be taken into account: i) the instrumental response function and ii) the Doppler-broadening due to thermal motion. Both of them can be determined experimentally. In fact, with the double flat crystal spectrometers GAMS4 and GAMS5 the determination of the instrument response function is possible with very high accuracy in the so-called nondispersive mode  within the different slowing down models. Consequently, the Doppler-broadened lineshape ID(E) will depend on the target temperature. The total lineshape, which needs to be compared to an experiment can be written asIT(E) denotes the total lineshape obtained as a convolution of a Doppler-broadened lineshape ID(E) and the instrumental response function R(E). Assuming the knowledge of υ(t) it has been shown that it is possible to extract lifetimes of nuclear states in the range of 10−15 s to 10−11 s using the least squares fitting routine GRIDDLE [τ is known and the function υ(t) has to be extracted, which allows the study of the atomic motion in solids.If there are no other sources of additional broadening, see Ref. . The the GRIDDLE . Also tht). Due to the low recoil velocities, the theoretical description of the atomic motion can be restricted to classical mechanics, i.e., to the solution of Newton’s equations of motion for point mass particles interacting via a classical interatomic potential.The structure of k describes the mean free paths between two collisions. They can be calculated knowing the density of the target material and assuming an atomic interaction potential [Within the MFPA the slowing down process is considered to be on average a sequence of binary atomic collisions, where the recoiling atom looses in every collision half of its kinetic energy. Between collisions the atoms are on average assumed to move with constant velocity. The result of this assumption can be summarized as a step functiont). This technique is quite common in the computer simulation of ion beam solid interaction [N atoms, where N = 500 to 1000. Newton’s equations of motion of all N atoms, interacting via an interatomic potential, are simultaneously integrated. However, the computational procedure is rather complicated as N(N – 1)/2 equations have to be solved. Therefore, a slightly simplified approach (Restricted Molecular Simulations) has been introduced to the GRID-technique [A more precise approach for the calculation has been introduced to the GRID technique by Kuronen et al. , who useeraction  and is eechnique . It can t) deduced afterwards. As these two models do not directly calculate the average velocity they can be used to test the model of an isotropic slowing down. This can be done by replacing In both MD and RMD simulations, a large number of recoil events  is calculated and an average velocity υ the velocity of the j-th recoiling atom and θ is the angle under which the j-th particle moves with respect to the direction of observation. The summation goes over M recoil events. The first integration takes account for the isotropic alignment of the microcrystals and the second integration introduces the emission probability of the second γ ray. Comparing lineshapes, which were calculated via Here t) was calculated for 36Cl atoms recoiling in NaCl, using different theoretical approaches. Within a time interval of up to 2×10−13 s the choice of the interatomic potential seems to introduce the dominating uncertainty in the slowing down description. Later, the difference of the slowing down models becomes dominating.In all three models mentioned above, the basic input is defined by the assumption of an interatomic potential. Essentially two potentials are used: The MFPA is based on a Born-Mayer type repulsive potential . The MD −14 s, the function υ(t) was approximated by an exponential behavior υ(t) = υ0 exp(–t/T). The parameters υ0 and T represent the initial recoil velocity and the average slowing down time, respectively. Although this model is rather simple, it gives a surprisingly good fit to the simulated υ(t) curves for time intervals up to 2×10−13 s. Using this approximation the function ID(E) can be analytically calculated to beC denotes a normalization constant. The nuclear state lifetime enters into equation [T. From this it can be concluded that any relative uncertainty of the average slowing down time T gives the same relative uncertainty for the lifetime extraction. An analysis of the calculations presented in T and therefore τ of about 36 %. A similar result was obtained in [−13 s and a check for longer lifetimes is still missing. This is mainly caused by the bad numerical efficiency of MD simulations.In order to quantify the influence of the uncertainty in the slowing down description on the lifetime determination up to 5×10Up to now considerations have been based on the assumption of a fully primarily fed nuclear level of interest. In the more general (and more frequent) case, the level of interest is fed by several γ cascades passing several intermediate levels. Here, it is difficult to estimate the velocity distribution of the recoiling nucleus, when the level of interest is reached. If the intensities of all γ transitions and the lifetimes of all intermediate levels are known, this distribution can be calculated. In most of the cases this does not apply and the uncertainty of this missing knowledge has to be quantified with respect to the extraction of nuclear state lifetimes from Doppler-broadened lineshapes. For this purpose several approaches are used:A rather conservative estimation can be done within the so-called extreme feeding assumptions. They are based on the comparison of the summary intensities populating and depopulating the level of interest. If the summary intensity of all depopulating transitions is greater then the populating one, the missing populating intensity can be used to formulate the extreme feeding assumptions. In one extreme all missing intensity is assigned to a primary feeding and in the other one it may be assigned to a transition depopulating a very long lived state, which has an energy of about 1 MeV higher then the level of interest. In the first case the velocity distribution contains a maximum possible number of high energetic recoils. This means that in order to obtain a certain given Doppler broadening, the lifetime of the level of interest has to be rather long. In such a way an upper limit for the lifetime estimation can be obtained. In the second case, the velocity distribution contains a maximum number of low energetic recoils, yielding such the lower limit for the lifetime.χ2 analysis of the experimental data. Here, a certain parametrization of the missing part of the recoil velocity distribution is chosen. The parameter values are then included in the fit procedure for the evaluation of the experimental data. A typical parametrization is given by a two step cascade  can not be given in analytical form. However, numerically it is easy to handle and can be used to demonstrate the sensitivity of the GRID technique to the different parameters, which have to be used for an evaluation of a measured lineshape. As the evaluation of the data is done by means of a least square fitting, the following function shall be considerediE are discrete points with a certain spacing of ΔE on the energy axis representing the analog to experimental data sampling within a scan. The function Ψ2 has the same analytical structure as the partial derivative of the optimization function χ2 in a least square fit. Thus, an increase in the values of Ψ2 means an increase in sensitivity in lifetime extraction. In Ψ2 has been calculated as function of τ for assumed parameters of υ0 = 0.5 Å/fs for the initial velocity Δτ/τ = 0.1 for a desired precision of the lifetime measurement, T = 50 fs for the average slowing down time, ΔEi = 10 eV for the scan spacing and Tυ = 0.03 Å/fs for the thermal velocity and σHW = 20 eV as FWHM of the instrument response function. In general it can be outlined that the highest sensitivity of the technique is given in the lifetime region of 10−14 to 10−12 s. At lower lifetime values the decreasing sensitivity will be compensated by an increasing influence of the natural width of the intermediate level. For lifetimes longer than one picosecond the technique loses strongly in sensitivity. This can partly be compensated by increased statistics. For example, for the extraction of a lifetime of τ ≈ 2 × 10−12 there have to be taken twice as many scans as for τ ≈ 1 × 10−12.The simple model of an exponential slowing down can be extended to include thermal motion. This can be done by folding ψ2 the influence of the instrument resolution, the target temperature and the slowing down time on the sensitivity have been investigated. Following the upper left plot in Tυ (upper right plot) appears to be a strongly limiting factor for the sensitivity to lifetimes longer than 10−12 s, as with increasing target temperature more and more statistics is required to extract a certain lifetime. The scan interval (lower left plot) appears to be of no significance for the sensitivity. A strong influence comes from the slowing down time. As expected from Using the function −15 to 10−12 s. It requires the knowledge of atomic motion with several hundreds of eV kinetic energy and the feeding scenario of the nuclear level of interest.The GRID technique has been shown to be a sensitive experimental technique for the investigation of nuclear state lifetimes in the range of 10−15 to 10−13 s measured with the GRID technique have the same relative uncertainty as the slowing down description. Recently, efforts have been made to improve the current status and to study explicitly the atomic interaction using the GRID technique itself. This can be done using single crystal targets , which allows a significant increase in the amount of information obtained. Further details can be found in Refs. [The relative uncertainty of the theoretical description of atomic motion can be quantified in certain cases. It results mainly from the unknown atomic interaction. Lifetimes in the range of 10in Refs. , 13.An additional uncertainty for the lifetime extraction is caused by an unknown feeding scenario for the level of interest. It can be quantified using the concept of extreme feeding scenarios, which yields the maximum variation of the measured lifetime value as it can be produced by the unknown feeding. Using the approximation of a two step cascade for the missing feeding one can find a most likely recoil velocity distribution and extract the most likely directly from the experimental data. Alternativelly, the missing feeding can be calculated using statistical models of the nucleus .


Obstructive Sleep Apnoea/Hypopnoea Syndrome (OSAHS) is a common disorder in the general population but often underestimated and underdiagnosed.This questionnaire-based study evaluated the overall level of knowledge about OSAHS among Italian General Practitioners (GPs), who are frequently involved in the management of this complex disease. This represents an interesting aspect, because GPs intercept many of the patients with OSAHS, in which C-PAP could be potentially indicated. Randomly-selected GPs were provided with questionnaires, which were then returned anonymously.80 questionnaires have been validated; the participants in the sample examined were represented by 43 females and 37 males; the average age of participants was 51 years. The general knowledge on OSAHS is overall satisfactory among GPs; it is recognized by most of the GPs interviewed as pathology in constant increase, and associated with predisposing factors such as obesity. High blood pressure is perceived as an independent cardiovascular risk factor in patients with OSAHS, in line with the majority of international studies. The C-PAP has been identified as the care gold standard in patients with OSAHS, despite the lack of patient compliance in relation to this procedure, while polysomnography was found to be the main instrumental procedure used in the diagnostic workup of OSAS. The pulmonologist and a multidisciplinary team have been identified as the specialist figures of reference to which to direct the patient through the diagnostic workup. Respiratory therapists and nurses represent the role of educator in the proper management of the C-PAP in the opinion of 62% of respondents, while only 34% think that this role should be played by the GPs and/or other specialists.In conclusion, this survey about the perception of OSAHS among GPs in Italy highlighted a satisfactory overall knowledge of OSAHS and only few weak points. OSAHS is a common disorder in the general population but often underestimated and underdiagnosed . The defad hoc” and based on the guidelines and the current literature, by a panel of experts composed by General Practitioners (GPs) and Specialists . It consists of 16 items (Table The results of this study were obtained through the completion of an anonymous questionnaire, created ““Sleepiness Epworth Scale” is still poor. The latter assesses the likelihood of falling asleep or dozing off in various situations, which is a useful metric to suspecting OSAHS. 78% of the GPs surveyed did not know about it, while only 28% indicated to be aware but not to use it (Figure As a general result, a good knowledge of the definition of OSAHS emerged from the results, with 67% of correct answer to the corresponding question in the questionnaire Figure . An adeqt Figure A. 60% oft Figure B, emphast Figure A and in t Figure B the diaOSAHS is a common disorder in the general population but often underestimated and underdiagnosed. OSAHS is an independent risk factor for hypertension and cardiovascular disease and is the frequent underlying disease of secondary hypertension and resistant hypertension . Randomi