Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painlev\'{e} equation ($P_{II}$). Here we define two-variable polynomials $Y_{n}(t,h)$ on a lattice with spacing $h$, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when $h=0$. They also provide rational solutions for a particular discretisation of $P_{II}$, namely the so called {\it alternate discrete} $P_{II}$, and this connection leads to an expression in terms of the Umemura polynomials for the third Painlev\'{e} equation ($P_{III}$). It is shown that B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete $P_{II}$, which recovers Jimbo and Miwa's Lax pair for $P_{II}$ in the continuum limit $h\to 0$.Comment: 23 pages, IOP style. Title changed, and connection with Umemura polynomials adde

Spectral characteristics for a spherically confined -1/r + br^2 potential

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure

Increasing the capacity of health surveillance assistants in community mental health care in a developing country, Malawi.

Mental health services in Malawi are centralized in the three tertiary units which are located one in each of the three regions of Malawi and this means that most people with mental health problems do not get help. With severe shortages of mental health professionals in the country, integration of mental health into existing primary and community health services is the most  feasible way of increasing access to services for people with mental health problems. This paper discusses a pilot program of integrating mental health in the activities of Health Surveillance Assistants (HSAs) who are community health workers in Malawi

Small-amplitude excitations in a deformable discrete nonlinear Schroedinger equation

A detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schr\"{o}dinger equation is performed. For generic deformations the system possesses "singular" points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicinity of the singular points are described by the Toda-lattice equation while away from the singular points are described by the Korteweg-de Vries equation. Depending on the value of the deformation parameter and of the background level several kinds of solutions are possible. In particular we delimit the regions in the parameter space in which dark solitons are stable in contrast with regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidly spreading solutions may exist.Comment: 18 pages (RevTex), 13 figures available upon reques

Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.Comment: 27 pages, LaTeX2e (IOP style

Mapping and characterization of structural variation in 17,795 human genomes

Structural variants in more than 17,000 human genomes are mapped and characterized using whole-genome sequencing, showing how this type of variation contributes to rare deleterious coding and noncoding alleles. A key goal of whole-genome sequencing for studies of human genetics is to interrogate all forms of variation, including single-nucleotide variants, small insertion or deletion (indel) variants and structural variants. However, tools and resources for the study of structural variants have lagged behind those for smaller variants. Here we used a scalable pipeline(1)to map and characterize structural variants in 17,795 deeply sequenced human genomes. We publicly release site-frequency data to create the largest, to our knowledge, whole-genome-sequencing-based structural variant resource so far. On average, individuals carry 2.9 rare structural variants that alter coding regions; these variants affect the dosage or structure of 4.2 genes and account for 4.0-11.2% of rare high-impact coding alleles. Using a computational model, we estimate that structural variants account for 17.2% of rare alleles genome-wide, with predicted deleterious effects that are equivalent to loss-of-function coding alleles; approximately 90% of such structural variants are noncoding deletions (mean 19.1 per genome). We report 158,991 ultra-rare structural variants and show that 2% of individuals carry ultra-rare megabase-scale structural variants, nearly half of which are balanced or complex rearrangements. Finally, we infer the dosage sensitivity of genes and noncoding elements, and reveal trends that relate to element class and conservation. This work will help to guide the analysis and interpretation of structural variants in the era of whole-genome sequencing.Peer reviewe

Mixtures of independent component analyzers for EEG prediction

This paper presents a new application of independent component analysis mixture modeling (ICAMM) for prediction of electroencephalographic (EEG) signals. Demonstrations in prediction of missing EEG data in a working memory task using classic methods and an ICAMM-based algorithm are included. The performance of the methods is measured by using four error indicators: signal-to-interference (SIR) ratio, Kullback-Leibler divergence, correlation at lag zero and mean structural similarity index. The results show that the ICAMM-based algorithm outperforms the classical spherical splines method which is commonly used in EEG signal processing. Hence, the potential of using mixtures of independent component analyzers (ICAs) to improve prediction, as opposed on estimating only one ICA is demonstrated.This work has been supported by Generalitat Valenciana under grants PROMETEO/2010/040 and ISIC/2012/006Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Gonzalez, A.; Vidal Maciá, AM. (2012). Mixtures of independent component analyzers for EEG prediction. En Green and smart technology with sensor applications. Springer Verlag (Germany). 338:328-335. doi:10.1007/978-3-642-35251-5_46S328335338Common, P., Jutten, C.: Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press, USA (2010)Salazar, A., Vergara, L., Serrano, A., Igual, J.: A general procedure for learning mixtures of independent component analyzers. Pattern Recognition 43(1), 69–85 (2010)Lee, T.W., Lewicki, M.S., Sejnowski, T.J.: ICA mixture models for unsupervised classification of non-gaussian classes and automatic context switching in blind signal separation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(10), 1078–1089 (2000)Salazar, A., Vergara, L.: ICA mixtures applied to ultrasonic nondestructive classification of archaeological ceramics. Eurasip Journal on Advances in Signal Processing 2010, article ID 125201, 11 pages (2010), doi:10.1155/2010/125201Klein, C., Feige, B.: An independent component analysis (ICA) approach to the study of developmental differences in the saccadic contingent negative variation. Biological Psychology 70, 105–114 (2005)Makeig, S., Westerfield, M., Jung, T.P., Covington, J., Townsend, J., Sejnowski, T.J., Courchesne, E.: Functionally Independent Components of the Late Positive Event-Related Potential during Visual Spatial Attention. Journal of Neuroscience 19(7), 2665–2680 (1999)Wibral, M., Turi, G., Linden, D.E.J., Kaiser, J., Bledowski, C.: Decomposition of working memory-related scalp ERPs: Crossvalidation of fMRI-constrained source analysis and ICA. Internt J. of Psychol. 67, 200–211 (2008)Castellanos, N.P., Makarov, V.A.: Recovering EEG brain signals: Artifact suppression with wavelet enhanced independent component analysis. Journal of Neuroscience Methods 158, 300–312 (2006)Salazar, A., Vergara, L., Miralles, R.: On including sequential dependence in ICA mixture models. Signal Processing 90, 2314–2318 (2010)Dayan, P., Abbot, L.F.: Theoretical neuroscience: computational and mathematical modeling of neural systems. The MIT Press (2001)Sternberg, S.: High-speed scanning in human memory. Science 153(3736), 652–654 (1966)Raghavachari, S., Lisman, J.E., Tully, M., Madsen, J.R., Bromfield, E.B., Kahana, M.J.: Theta oscillations in human cortex during a working-memory task: evidence for local generators. J. of Neurophys. 95, 1630–1638 (2006)Gorriz, J.M., Puntonet, C.G., Salmeron, G., Lang, E.W.: Time series prediction using ICA algorithms. In: Proc. of 2nd IEEE Internat. W. on Intellig Data Acquisition and Advanc. Comp. Systems: Tech. and App., pp. 226–230 (2003)Lin, C.-T., Cheng, W.-C., Liang, S.-F.: An On-line ICA-Mixture-Model-Based Self-Constructing Fuzzy Neural Network. IEEE Transactions on Circuits and Systems I: Regular Papers 52(1), 207–221 (2005)Lee, T.W., Girolami, M., Sejnowski, T.J.: Independent component analysis using an extended InfoMax algorithm for mixed sub-gaussian and super-gaussian sources. Neural Computation 11(2), 417–441 (1999)Perrin, F., Pernier, J., Bertrand, D., Echallier, J.F.: Spherical splines for scalp potential and current density matching. Electroencep. and Clin. Neurophys. 72, 184–187 (1989)Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing 13(4), 600–612 (2004

Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

Artificial drainage of peatlands: hydrological and hydrochemical process and wetland restoration

Peatlands have been subject to artificial drainage for centuries. This drainage has been in response to agricultural demand, forestry, horticultural and energy properties of peat and alleviation of flood risk. However, the are several environmental problems associated with drainage of peatlands. This paper describes the nature of these problems and examines the evidence for changes in hydrological and hydrochemical processes associated with these changes. Traditional black-box water balance approaches demonstrate little about wetland dynamics and therefore the science of catchment response to peat drainage is poorly understood. It is crucial that a more process-based approach be adopted within peatland ecosystems. The environmental problems associated with peat drainage have led, in part, to a recent reversal in attitudes to peatlands and we have seen a move towards wetland restoration. However, a detailed understanding of hydrological, hydrochemical and ecological process-interactions will be fundamental if we are to adequately restore degraded peatlands, preserve those that are still intact and understand the impacts of such management actions at the catchment scale

GOPHER, an HPC framework for large scale graph exploration and inference

Biological ontologies, such as the Human Phenotype Ontology (HPO) and the Gene Ontology (GO), are extensively used in biomedical research to investigate the complex relationship that exists between the phenome and the genome. The interpretation of the encoded information requires methods that efficiently interoperate between multiple ontologies providing molecular details of disease-related features. To this aim, we present GenOtype PHenotype ExplOrer (GOPHER), a framework to infer associations between HPO and GO terms harnessing machine learning and large-scale parallelism and scalability in High-Performance Computing. The method enables to map genotypic features to phenotypic features thus providing a valid tool for bridging functional and pathological annotations. GOPHER can improve the interpretation of molecular processes involved in pathological conditions, displaying a vast range of applications in biomedicine.This work has been developed with the support of the Severo Ochoa Program (SEV-2015-0493); the Spanish Ministry of Science and Innovation (TIN2015- 65316-P); and the Joint Study Agreement no. W156463 under the IBM/BSC Deep Learning Center agreement.Peer ReviewedPostprint (author's final draft