2,579 research outputs found
A conservative numerical method for a time fractional diffusion equation
No full textGeometric numerical integration, the branch of numerical analysis with the goal of finding approximate solutions of differential equations that preserve some structure of the continuous problem, is a well established field of research [5]. In particular, requiring that invariants or conservation laws are preserved, on one hand, applies on the approximations some constraints that are satisfied also by the exact solutions. On the other hand, it guarantees a better propagation of the error over long integration times [3].
In the last two decades, new techniques for finding conservation laws of fractional differential equations have been derived by suitably generalising methods for PDEs [4, 6]. However, the numerical preservation of conservation laws of time fractional differential
equations is a research topic still at an embryonic state. This talk deals with the numerical solution of diffusion equations in the form
D^α_t u = D^2_x K(u), α ∈ R,
where D_x is the partial derivative in space, K is an arbitrary regular function, and D^α_t
denotes the Riemann-Liouville fractional derivative of order α.
The proposed numerical method combines a finite difference scheme in space with a spectral time integrator and preserves discrete versions of the conservation laws of the original differential equation [1, 2].
The conservative and convergence properties of the proposed method are verified by the computational solution of some numerical experiments.
References
[1] K. Burrage, A. Cardone, R. D’Ambrosio, B. Paternoster. Numerical solution of time fractional diffusion systems. Appl. Numer. Math., 116 (2017), 82–94.
[2] A. Cardone, G. Frasca-Caccia. Numerical conservation laws of time fractional diffusion PDEs. arXiv.2203.01966, (2022).
[3] A. Dur ́an, J. M. Sanz-Serna. The numerical integration of relative equilibrium solutions. Geometric theory. Nonlinearity, 11, 1547–1567, (1998).
[4] G. S. F. Frederico, D. F. M. Torres. Fractional conservation laws in optimal control theory. Nonlinear Dyn., 53 (2008), 215–222.
[5] E. Hairer, C. Lubich, G. Wanner. Geometric Numerical Integration. Structure Preserving Algorithms for Ordinary Differential Equations, volume 31 of Springer Series in Computational Mathematics. Springer, Berlin, second edition, 2006.
[6] S. Y. Lukashchuk. Conservation laws for time-fractional subdiffusion and diffusionwave equations. Nonlinear Dyn., 80 (2015), 791–80
Characterization of Neoparamoeba pemaquidensis strains: PCR-RFLP of the internal transcribed spacer region from the amoeba and endosymbiont
No full textNeoparamoeba pemaquidensis continues to be an ongoing problem for commercial finfish aquaculture and has also sporadically been associated with mass mortalities of commercially relevant marine invertebrates. Despite the ubiquity and importance of this amphizoic amoeba, our understanding of the biology as it applies to host range, pathogenicity, tissue tropism, and geographic distribution is severely lacking. This may stem from the inability of current diagnostic tests based on morphology, immunology, and molecular biology to differentiate strains at the subspecies level. In the present study, we developed a polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method based on the internal transcribed spacer (ITS) region that can accurately differentiate amoeba strains of N. pemaquidensis. The investigation focused on the complications of the amoeba ITS microheterogeneity in the development of a subspecies marker and the use of the endosymbiont, Ichthyobodo necator related organism (IRO), ITS region as an alternative marker. The combination of host amoeba and endosymbiont ITS PCR-RFLP analyses was successfully used to correctly identify and characterize an N. pemaquidensis isolate from an outbreak of amoebic gill disease in Atlantic salmon Salmo salar from the west coast of North America (Washington State, USA).Charles G. B. Caraguel, Nathanaëlle Donay, Salvatore Frasca Jr., Charles J. O’Kelly, Richard J. Cawthorn Spencer J. Greenwoo
SOUND FROM THE CRADLE, UN PERCORSO PER IMMAGINI DELLA MUSICA DEGLI ITALIANI IN AMERICA NEGLI ANNI NOVANTA
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COSNet: An R package for label prediction in unbalanced biological networks
No full textSeveral problems in computational biology and medicine are modeled as learning problems in graphs, where nodes represent the biological entities to be studied, e.g. proteins, and connections different kinds of relationships among them, e.g. protein-protein interactions. In this context, classes are usually characterized by a high imbalance, i.e. positive examples for a class are much less than those negative. Although several works studied this problem, no graph-based software designed to explicitly take into account the label imbalance in biological networks is available. We propose COSNet, an R package to serve this purpose. COSNet deals with the label imbalance problem by implementing a novel parametric model of Hopfield Network (HN), whose output levels and activation thresholds of neurons are parameters to be automatically learnt. Due to the quasi-linear time complexity, COSNet nicely scales when the number of instances is large, and application examples to challenging problems in biomedicine show the efficiency and the accuracy of the proposed library
A neural network based algorithm for gene expression prediction from chromatin structure
No full textGene expression is a very complex process, which is finely regulated and modulated at different levels. The first step of gene expression, the transcription of DNA into mRNA, is in turn regulated both at the genetic and epigenetic level. In particular, the latter, which involves the structure formed by DNA wrapped around histones (chromatin), has been recently shown to be a key factor, with post-translational modifications of histones acting combinatorially to activate or block transcription. In this work we addressed the problem of predicting the level of expression of genes starting from genome-wide maps of chromatin structure, that is, of the localization of several different histone modifications, which have been recently made available through the introduction of technologies like ChIP-Seq. We formalized the problem as a multi-class bipartite ranking problem, in which for each class a gene can be under-or over-expressed with respect to a given reference expression value. In order to deal with this problem, we exploit and extend a semi-supervised method (COSNet) based on a family of Hopfield neural networks. Benchmark genome-wide tests performed on six different human cell lines yielded satisfactory results, with clear improvements over the alternative approach most commonly adopted in the literature
SOUND FROM THE CRADLE, AN IMAGE JOURNEY OF THE MUSIC OF ITALIANS IN AMERICA IN THE 1990S
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