Analysis of foveation sequences in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder that appears at birth or during the first few months of life; it is characterised by involuntary, conjugated, bilateral to and fro ocular oscillations. Pathogenesis of congenital nystagmus is still unknown. Eye movement recording allow to extract and analyse nystagmus main features such as shape, amplitude and frequency; depending on the morphology of the oscillations nystagmus can be classified in different categories (pendular, jerk, horizontal unidirectional, bidirectional). In general, CN patient show a considerable decrease of the visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations; however, image stabilisation is still achieved during the short foveation periods in which eye velocity slows down while the target image is placed onto the fovea. Visual acuity was found to be mainly dependent on foveation periods duration, but cycle-to-cycle foveation repeatability and reduction of retinal image velocities also contribute in increasing visual acuity. This study concentrate on cycle-to-cycle image position variation onto fovea, trying to characterise the sequences of foveation positions. Eye-movement (infrared oculographic or electro oculographic) recordings, relative to different gaze positions and belonging to more than 30 CN patients, were analysed. Preliminary results suggest that sequences of foveations show a cyclic pattern with a dominant frequency (around 0.3 Hz on average) much lower than that of the nystagmus (about 3.3 Hz on average). Sequences of foveations reveals an horizontal ocular swing of more than 2 degree on average, which can explain the low visual acuity of the CN patient. Current CN therapies, pharmacological treatment or surgery of the ocular muscles, mainly aim to increase the patient's visual acuity. Hence, it is fundamental to have an objective parameter (expected visual acuity) for therapy planning. The information about sequences of foveations can improve estimation of patient visual acuity. © 2008 Springer-Verlag.

Detection of foveation windows and analysis of foveation sequences in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder characterised by involuntary, conjugated ocular oscillations, that can arise since the first months of life. Pathogenesis of congenital nystagmus is still under investigation. In general, CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, image stabilisation is still achieved during the short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recording are routinely employed, allowing physicians to extract and analyse nystagmus main features such as shape, amplitude and frequency. Using eye movement recording, it is also possible to compute estimated visual acuity predictors: analytical functions which estimates expected visual acuity using signal features such as foveation time and foveation position variability. Use of those functions add information to typical visual acuity measurement (e.g. Landolt C test) and could be a support for therapy planning or monitoring. This study focus on robust detection of CN patients' foveations. Specifically, it proposes a method to recognize the exact signal tracts in which a subject foveates, This paper also analyses foveation sequences. About 50 eyemovement recordings, either infrared-oculographic or electrooculographic, from different CN subjects were acquired. Results suggest that an exponential interpolation for the slow phases of nystagmus could improve foveation time computing and reduce influence of breaking saccades and data noise. Moreover a concise description of foveation sequence variability can be achieved using non-fitting splines. © 2009 Springer Berlin Heidelberg.

Sequences of Maximal Degree Vertices in Graphs

2000 Mathematics Subject Classification: 05C35.

Topic Segmentation: How Much Can We Do by Counting Words and Sequences of Words

In this paper, we present an innovative topic segmentation system based on a new informative similarity measure that takes into account word co-occurrence in order to avoid the accessibility to existing linguistic resources such as electronic dictionaries or lexico-semantic databases such as thesauri or ontology. Topic segmentation is the task of breaking documents into topically coherent multi-paragraph subparts. Topic segmentation has extensively been used in information retrieval and text summarization. In particular, our architecture proposes a language-independent topic segmentation system that solves three main problems evidenced by previous research: systems based uniquely on lexical repetition that show reliability problems, systems based on lexical cohesion using existing linguistic resources that are usually available only for dominating languages and as a consequence do not apply to less favored languages and finally systems that need previously existing harvesting training data. For that purpose, we only use statistics on words and sequences of words based on a set of texts. This solution provides a flexible solution that may narrow the gap between dominating languages and less favored languages thus allowing equivalent access to information.

On a Theorem by Van Vleck Regarding Sturm Sequences

In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences with pivot, and (b) incomplete Sturm sequences. Despite its importance, the Pell-Gordon Theorem for polynomials in Q[x] has been totally forgotten and, to our knowledge, it is referenced by us for the first time in the literature. In this paper we go over Van Vleck’s theorem and method, modify slightly the formula of the Pell-Gordon Theorem and present a general triangularization method, called the VanVleck-Pell-Gordon method, that correctly computes in Z[x] polynomial Sturm sequences, both complete and incomplete.

Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.

Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)

Given the polynomials f, g ∈ Z[x] of degrees n, m, respectively, with n > m, three new, and easy to understand methods — along with the more efficient variants of the last two of them — are presented for the computation of their subresultant polynomial remainder sequence (prs). All three methods evaluate a single determinant (subresultant) of an appropriate sub-matrix of sylvester1, Sylvester’s widely known and used matrix of 1840 of dimension (m + n) × (m + n), in order to compute the correct sign of each polynomial in the sequence and — except for the second method — to force its coefficients to become subresultants. Of interest is the fact that only the first method uses pseudo remainders. The second method uses regular remainders and performs operations in Q[x], whereas the third one triangularizes sylvester2, Sylvester’s little known and hardly ever used matrix of 1853 of dimension 2n × 2n. All methods mentioned in this paper (along with their supporting functions) have been implemented in Sympy and can be downloaded from the link http://inf-server.inf.uth.gr/~akritas/publications/subresultants.py

Zeros of Sequences of Partial Sums and Overconvergence

2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

MSC 2010: 11B83, 05A19, 33C45

Accurate estimation of isoelectric point of protein and peptide based on amino acid sequences

Motivation: In any macromolecular polyprotic system - for example protein, DNA or RNA - the isoelectric point - commonly referred to as the pI - can be defined as the point of singularity in a titration curve, corresponding to the solution pH value at which the net overall surface charge - and thus the electrophoretic mobility - of the ampholyte sums to zero. Different modern analytical biochemistry and proteomics methods depend on the isoelectric point as a principal feature for protein and peptide characterization. Protein separation by isoelectric point is a critical part of 2-D gel electrophoresis, a key precursor of proteomics, where discrete spots can be digested in-gel, and proteins subsequently identified by analytical mass spectrometry. Peptide fractionation according to their pI is also widely used in current proteomics sample preparation procedures previous to the LC-MS/MS analysis. Therefore accurate theoretical prediction of pI would expedite such analysis. While such pI calculation is widely used, it remains largely untested, motivating our efforts to benchmark pI prediction methods. Results: Using data from the database PIP-DB and one publically available dataset as our reference gold standard, we have undertaken the benchmarking of pI calculation methods. We find that methods vary in their accuracy and are highly sensitive to the choice of basis set. The machine-learning algorithms, especially the SVM-based algorithm, showed a superior performance when studying peptide mixtures. In general, learning-based pI prediction methods (such as Cofactor, SVM and Branca) require a large training dataset and their resulting performance will strongly depend of the quality of that data. In contrast with Iterative methods, machine-learning algorithms have the advantage of being able to add new features to improve the accuracy of prediction. Contact: yperez@ebi.ac.uk Availability and Implementation: The software and data are freely available at https://github.com/ypriverol/pIR. Supplementary information: Supplementary data are available at Bioinformatics online.

Optimised phase disposition pulse-width modulation strategy for hybrid-clamped multilevel inverters using switching state sequences

This study describes an optimised modulation strategy based on switching state sequences for the hybrid-clamped multilevel converter. Two key control variables defined as 'phase shift angle' and 'switching state change' for a five-level hybrid-clamped inverter are proposed to improve all switches' operation, and by changing their values, different control methods can be obtained for modulation optimisation purposes. Two example methods can solve the voltage imbalance problem of the dc-link capacitors and furthermore avoid two switches' simultaneous switching transitions and improve the inverter's performance as compared with the traditional phase disposition pulse-width modulation strategy. A 6 kW prototype inverter is developed and a range of simulation and experiments are carried out for validation. It is found that simulation and experimental results are in a good agreement and the proposed modulation strategy is verified in terms of low-order harmonic reduction.

Ammonite biostratigraphy, lithofacies variations, and paleoceanographic implications for Barremian-Aptian sequences of northeastern Mexico

Two Barremian-Aptian sequences studied in Durango and Nuevo Leon States, northeastern Mexico include three lithic units which have been described as the Cupido Formation of Barremian-early Early Aptian age, its lateral equivalent, the Lower Tamaulipas Formation, and the La Peña Formation extending through the early Albian. ^ The present work improves the existing ammonite Aptian biozonation by considering constraints associated with a discontinuous spatial and temporal record of the different taxa within the La Peña Formation. ^ Four ammonite biozones are established: (1) The Dufrenoyia justinae Zone for the late Early Aptian, (2) The Burckhardtites nazasensis/Rhytidoplites robertsi Zone for the middle Aptian, (3) The Cheloniceras inconstans Zone for the early Late Aptian, and (4) The Hypacanthoplites cf. leanzae Zone for the late late Aptian. ^ Also, a detailed sedimentological analysis of the sections shed further light on the possible causes that controlled intermittent occurrences of the ammonites in relation to the prevailing paleoceanographic and paleoecologic conditions in northeastern Mexico during the late Barremian-Aptian. ^ Microfacies analyses show that the upper part of the Cupido facies are represented by biocalcirudite with rudists, biocalcarenites with oolites and algae, and rich benthonic foraminifera assemblages with ostracods. These facies are related to paleoceanographic conditions of sedimentation within a shallow-marine carbonate platform. Its lateral equivalent, deep-water facies extended to the southeast and it is represented by the Lower Tamaulipas Formation, which includes planktonic foraminifera, ostracods, and mollusk and echinoid fragments. The beginning of deposition of the La Peña Formation in the late Early Aptian is characterized by an increase in terrigenous materials and significant decrease in the abundance of benthic fauna. The La Peña Formation is recognized by an alternation of marls and shale limestones containing ammonites, planktonic foraminifera, ostracods, and radiolaria toward the top. Accumulation of the La Peña continued throughout the end of the Aptian and records changes in conditions of sedimentation and productivity in the water column, which abruptly terminated the carbonate deposition in the Cupido Platform. ^ Results of carbon/carbonate content analyses show that changes from the Cupido to the La Peña facies are also characterized by an increase of organic carbon, which indicate the onset of enhanced dysoxic/anoxic conditions in the lower water column. ^

Serial evolutionary networks of within-patient HIV-1 sequences reveal patterns of evolution of X4 strains

Background The HIV virus is known for its ability to exploit numerous genetic and evolutionary mechanisms to ensure its proliferation, among them, high replication, mutation and recombination rates. Sliding MinPD, a recently introduced computational method [1], was used to investigate the patterns of evolution of serially-sampled HIV-1 sequence data from eight patients with a special focus on the emergence of X4 strains. Unlike other phylogenetic methods, Sliding MinPD combines distance-based inference with a nonparametric bootstrap procedure and automated recombination detection to reconstruct the evolutionary history of longitudinal sequence data. We present serial evolutionary networks as a longitudinal representation of the mutational pathways of a viral population in a within-host environment. The longitudinal representation of the evolutionary networks was complemented with charts of clinical markers to facilitate correlation analysis between pertinent clinical information and the evolutionary relationships. Results Analysis based on the predicted networks suggests the following:: significantly stronger recombination signals (p = 0.003) for the inferred ancestors of the X4 strains, recombination events between different lineages and recombination events between putative reservoir virus and those from a later population, an early star-like topology observed for four of the patients who died of AIDS. A significantly higher number of recombinants were predicted at sampling points that corresponded to peaks in the viral load levels (p = 0.0042). Conclusion Our results indicate that serial evolutionary networks of HIV sequences enable systematic statistical analysis of the implicit relations embedded in the topology of the structure and can greatly facilitate identification of patterns of evolution that can lead to specific hypotheses and new insights. The conclusions of applying our method to empirical HIV data support the conventional wisdom of the new generation HIV treatments, that in order to keep the virus in check, viral loads need to be suppressed to almost undetectable levels.