Separable Transition Density in the Hybrid Model for Tumor-Immune System Competition

A hybrid model, on the competition tumor cells immune system, is studied under suitable hypotheses. The explicit form for the equations is obtained in the case where the density function of transition is expressed as the product of separable functions. A concrete application is given starting from a modified Lotka-Volterra system of equations

Separable Transition Density in the Hybrid Model for Tumor-Immune System Competition

A hybrid model, on the competition tumor cells immune system, is studied under suitable hypotheses. The explicit form for the equations is obtained in the case where the density function of transition is expressed as the product of separable functions. A concrete application is given starting from a modified Lotka-Volterra system of equations

Geometric Distribution Weight Information Modeled Using Radial Basis Function with Fractional Order for Linear Discriminant Analysis Method

Fisher linear discriminant analysis (FLDA) is a classic linear feature extraction and dimensionality reduction approach for face recognition. It is known that geometric distribution weight information of image data plays an important role in machine learning approaches. However, FLDA does not employ the geometric distribution weight information of facial images in the training stage. Hence, its recognition accuracy will be affected. In order to enhance the classification power of FLDA method, this paper utilizes radial basis function (RBF) with fractional order to model the geometric distribution weight information of the training samples and proposes a novel geometric distribution weight information based Fisher discriminant criterion. Subsequently, a geometric distribution weight information based LDA (GLDA) algorithm is developed and successfully applied to face recognition. Two publicly available face databases, namely, ORL and FERET databases, are selected for evaluation. Compared with some LDA-based algorithms, experimental results exhibit that our GLDA approach gives superior performance

Construction of Fusion Frame Systems in Finite Dimensional Hilbert Spaces

We first investigate the construction of a fusion frame system in a finite-dimensional Hilbert space F when its fusion frame operator matrix is given and provides a corresponding algorithm. The matrix representations of its local frame operators and inverse frame operators are naturally obtained. We then study the related properties of the constructed fusion frame systems. Finally, we implement the construction of fusion frame systems which behave optimally for erasures in some special sense in signal transmission

Construction of Fusion Frame Systems in Finite Dimensional Hilbert Spaces

We first investigate the construction of a fusion frame system in a finite-dimensional Hilbert space n when its fusion frame operator matrix is given and provides a corresponding algorithm. The matrix representations of its local frame operators and inverse frame operators are naturally obtained. We then study the related properties of the constructed fusion frame systems. Finally, we implement the construction of fusion frame systems which behave optimally for erasures in some special sense in signal transmission

Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation

Metzler et al. introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a Boltzmann thermal heat bath. In this paper, we present an interval Shannon wavelet numerical method for the FFPE. In this method, a new concept named “dynamic interval wavelet” is proposed to solve the problem that the numerical solution of the fractional PDE is usually sensitive to boundary conditions. Comparing with the traditional wavelet defined in the interval, the Newton interpolator is employed instead of the Lagrange interpolation operator, so, the extrapolation points in the interval wavelet can be chosen dynamically to restrict the boundary effect without increase of the calculation amount. In order to avoid unlimited increasing of the extrapolation points, both the error tolerance and the condition number are taken as indicators for the dynamic choice of the extrapolation points. Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA)

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam. The beam is attached to multi single-degree-of-freedom (SDOF) fractionally-damped systems, and it is subjected to a vehicle moving with a constant velocity. The damping characteristics of the beam and SDOF systems are described in terms of fractional derivatives. Three coupled second-order fractional differential equations are produced and then they are solved by combining the Laplace transform with the decomposition method. The obtained numerical results show that the dynamic response decreases as (a) the number of absorbers attached to the beam increases and (b) the damping-ratios of used absorbers and beam increase. However, there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. Furthermore, the obtained results show very good agreements with special case studies that were published in the literature

High Performance Numerical Computing for High Energy Physics: A New Challenge for Big Data Science

The publication of this article was funded by SCOAP 3 . Modern physics is based on both theoretical analysis and experimental validation. Complex scenarios like subatomic dimensions, high energy, and lower absolute temperature are frontiers for many theoretical models. Simulation with stable numerical methods represents an excellent instrument for high accuracy analysis, experimental validation, and visualization. High performance computing support offers possibility to make simulations at large scale, in parallel, but the volume of data generated by these experiments creates a new challenge for Big Data Science. This paper presents existing computational methods for high energy physics (HEP) analyzed from two perspectives: numerical methods and high performance computing. The computational methods presented are Monte Carlo methods and simulations of HEP processes, Markovian Monte Carlo, unfolding methods in particle physics, kernel estimation in HEP, and Random Matrix Theory used in analysis of particles spectrum. All of these methods produce data-intensive applications, which introduce new challenges and requirements for ICT systems architecture, programming paradigms, and storage capabilities

On Analytical Methods in Neuroblastoma Detection

Nonlinear dynamics of cancer recurrence are known to be governed by several factors as initial tumour size, number of metastatic sites, or quantity of drug resistant cells. The precise extent and location of tumours are very important factors so quantitative and consistent methods of evaluation are needed to assess reponse to patient therapy.Whole-body 123I-metaiodobenzylguanidine (mIBG) scintigraphy is used as primary medical image modality to detect neuroblastoma tumours due to its high specificity and sensitivity.However, current oncological guidelines are based on qualitative observer-dependent analysis. This fact makes it difficult to compare results of scintigraphies taken at different moments during therapy or at different institutions. In this paper, we review analytical methods used in neuroblastoma detection and propose an observer-independent method to quantitatively analyse a 123I-mIBG scintigraphy.Martínez Díaz, R.; Balaguer, J.; Sánchez Ruiz, LM.; Bello, P.; Castel, V.; Peris Fajarnes, G. (2013). On Analytical Methods in Neuroblastoma Detection. Abstract and Applied Analysis. 2013:1-5. doi:10.1155/2013/341346S152013Foo, J., & Leder, K. (2013). Dynamics of cancer recurrence. The Annals of Applied Probability, 23(4), 1437-1468. doi:10.1214/12-aap876Bellomo, N., & Delitala, M. (2008). From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Physics of Life Reviews, 5(4), 183-206. doi:10.1016/j.plrev.2008.07.001Bianca, C., & Delitala, M. (2011). On the modelling of genetic mutations and immune system competition. Computers & Mathematics with Applications, 61(9), 2362-2375. doi:10.1016/j.camwa.2011.01.024Cattani, C., & Ciancio, A. (2012). Separable Transition Density in the Hybrid Model for Tumor-Immune System Competition. Computational and Mathematical Methods in Medicine, 2012, 1-6. doi:10.1155/2012/610124Cattani, C., Ciancio, A., & d’ Onofrio, A. (2010). Metamodeling the learning–hiding competition between tumours and the immune system: A kinematic approach. Mathematical and Computer Modelling, 52(1-2), 62-69. doi:10.1016/j.mcm.2010.01.012Mueller, W. P., Coppenrath, E., & Pfluger, T. (2012). Nuclear medicine and multimodality imaging of pediatric neuroblastoma. Pediatric Radiology, 43(4), 418-427. doi:10.1007/s00247-012-2512-1Bombardieri, E., Giammarile, F., Aktolun, C., Baum, R. P., Bischof Delaloye, A., Maffioli, L., … Chiti, A. (2010). 131I/123I-Metaiodobenzylguanidine (mIBG) scintigraphy: procedure guidelines for tumour imaging. European Journal of Nuclear Medicine and Molecular Imaging, 37(12), 2436-2446. doi:10.1007/s00259-010-1545-7Matthay, K. K., Shulkin, B., Ladenstein, R., Michon, J., Giammarile, F., Lewington, V., … Cohn, S. L. (2010). Criteria for evaluation of disease extent by 123I-metaiodobenzylguanidine scans in neuroblastoma: a report for the International Neuroblastoma Risk Group (INRG) Task Force. British Journal of Cancer, 102(9), 1319-1326. doi:10.1038/sj.bjc.6605621MAISEY, M. N., NATARAJAN, T. K., HURLEY, P. J., & WAGNER, H. N. (1973). Validation of a Rapid Computerized Method of Measuring99mTc Pertechnetate Uptake for Routine Assessment of Thyroid Structure and Function1. The Journal of Clinical Endocrinology & Metabolism, 36(2), 317-322. doi:10.1210/jcem-36-2-317Chen, W., Cao, Q., & Dilsizian, V. (2011). Variation of Heart-to-Mediastinal Ratio in 123I-mIBG Cardiac Sympathetic Imaging: Its Affecting Factors and Potential Corrections. Current Cardiology Reports, 13(2), 132-137. doi:10.1007/s11886-010-0157-

High Performance Numerical Computing for High Energy Physics: A New Challenge for Big Data Science

Modern physics is based on both theoretical analysis and experimental validation. Complex scenarios like subatomic dimensions, high energy, and lower absolute temperature are frontiers for many theoretical models. Simulation with stable numerical methods represents an excellent instrument for high accuracy analysis, experimental validation, and visualization. High performance computing support offers possibility to make simulations at large scale, in parallel, but the volume of data generated by these experiments creates a new challenge for Big Data Science. This paper presents existing computational methods for high energy physics (HEP) analyzed from two perspectives: numerical methods and high performance computing. The computational methods presented are Monte Carlo methods and simulations of HEP processes, Markovian Monte Carlo, unfolding methods in particle physics, kernel estimation in HEP, and Random Matrix Theory used in analysis of particles spectrum. All of these methods produce data-intensive applications, which introduce new challenges and requirements for ICT systems architecture, programming paradigms, and storage capabilities