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Differential equation

Salim Lahmiri
Variational mode decomposition (VMD) is a new adaptive multi-resolution technique suitable for signal denoising purpose. The main focus of this work has been to study the feasibility of several image denoising techniques in empirical mode decomposition (EMD) and VMD domains. A comparative study is made using 11 techniques widely used in the literature, including Wiener filter, first-order local statistics, fourth partial differential equation, nonlinear complex diffusion process, linear complex diffusion process (LCDP), probabilistic non-local means, non-local Euclidean medians, non-local means, non-local patch regression, discrete wavelet transform and wavelet packet transform...
February 2017: Healthcare Technology Letters
Yang Liu, Dapeng Xie, Dandan Yang, Chuanzhi Bai
In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.
2017: Journal of Inequalities and Applications
Katrin Göke, Heike Bunjes
Passive drug loading can be used to effectively identify suitable colloidal lipid carrier systems for poorly water-soluble drugs. This method comprises incubation of preformed carrier systems with drug powder and subsequent determination of the resulting drug load of the carrier particles. Until now, the passive loading mechanism is unknown, which complicates reliable routine use. In this work, the influence of drug characteristics on the course of passive loading was investigated systematically varying drug surface area and drug solubility...
May 18, 2017: European Journal of Pharmaceutics and Biopharmaceutics
H A Castro-Abril, J M Guevara, M A Moncayo, S J Shefelbine, L A Barrera, D A Garzón-Alvarado
The growth plate is the responsible for longitudinal bone growth. It is a cartilaginous structure formed by chondrocytes that are continuously undergoing a differentiation process that starts with a highly proliferative state, followed by cellular hypertrophy, and finally tissue ossification. Within the growth plate chondrocytes display a characteristic columnar organization that potentiates longitudinal growth. Both chondrocyte organization and hypertrophy are highly regulated processes influenced by biochemical and mechanical stimuli...
May 16, 2017: Journal of Theoretical Biology
Robert J Smith, Alexandra B Hogan, Geoffry N Mercer
Respiratory Syncytial Virus (RSV) is an acute respiratory infection that infects millions of children and infants worldwide. Recent research has shown promise for the development of a vaccine, with a range of vaccine types now in clinical trials or preclinical development. We extend an existing mathematical model with seasonal transmission to include vaccination. We model vaccination both as a continuous process, applying the vaccine during pregnancy, and as a discrete one, using impulsive differential equations, applying pulse vaccination...
May 18, 2017: Vaccines
Qiang Ren, Jogender Nagar, Lei Kang, Yusheng Bian, Ping Werner, Douglas H Werner
A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements...
May 18, 2017: Scientific Reports
Josef P Barnes, Peter R Johnston
This study presents a comparison of semi-analytical and numerical solution techniques for solving the passive bidomain equation in simple tissue geometries containing a region of subendocardial ischaemia. When the semi-analytical solution is based on Fourier transforms, recovering the solution from the frequency domain via fast Fourier transforms imposes a periodic boundary condition on the solution of the partial differential equation. On the other hand, the numerical solution uses an insulation boundary condition...
May 19, 2017: Computer Methods in Biomechanics and Biomedical Engineering
J E F Green, J P Whiteley, J M Oliver, H M Byrne, S L Waters
We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium...
May 16, 2017: Mathematical Medicine and Biology: a Journal of the IMA
Neil P Oxtoby, Daniel C Alexander
PURPOSE OF REVIEW: This article argues that the time is approaching for data-driven disease modelling to take centre stage in the study and management of neurodegenerative disease. The snowstorm of data now available to the clinician defies qualitative evaluation; the heterogeneity of data types complicates integration through traditional statistical methods; and the large datasets becoming available remain far from the big-data sizes necessary for fully data-driven machine-learning approaches...
May 16, 2017: Current Opinion in Neurology
Yiji Wang
This study examined parental proximal processes involving in the intergenerational transmission of depressive symptoms from parents to their children. Extant literature has predominantly focused on maternal depressive symptoms. Yet, the mechanisms that may underlie the transmission of paternal depressive symptoms is less often studied. Participants were Chinese parents of first-graders (N = 2282). Results of structural equation modeling suggested that maternal and paternal depressive symptoms may be transmitted to their children through differential processes...
May 17, 2017: Child Psychiatry and Human Development
Minfeng Chen, Zongsheng Gao, Yunfei Du
In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m, n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text]...
2017: Journal of Inequalities and Applications
Samuel H Rudy, Steven L Brunton, Joshua L Proctor, J Nathan Kutz
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis...
April 2017: Science Advances
D Avitabile, M Desroches, E Knobloch
Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed experimentally, but their existence and role in spatially extended systems is largely unexplored. We identify and describe a type of coherent structure in which a spatial pattern displays temporal canard behavior. Using interfacial dynamics and geometric singular perturbation theory, we classify spatiotemporal canards and give conditions for the existence of folded-saddle and folded-node canards...
April 2017: Physical Review. E
Peter W Stokes, Bronson Philippa, Daniel Cocks, Ronald D White
A generalized phase-space kinetic Boltzmann equation for highly nonequilibrium charged particle transport via localized and delocalized states is used to develop continuity, momentum, and energy balance equations, accounting explicitly for scattering, trapping and detrapping, and recombination loss processes. Analytic expressions detail the effect of these microscopic processes on mobility and diffusivity. Generalized Einstein relations (GER) are developed that enable the anisotropic nature of diffusion to be determined in terms of the measured field dependence of the mobility...
April 2017: Physical Review. E
Lesley A Inker, Andrew S Levey, Hocine Tighiouart, Tariq Shafi, John H Eckfeldt, Craig Johnson, Aghogho Okparavero, Wendy S Post, Josef Coresh, Michael G Shlipak
Background.: The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations are recommended for glomerular filtration rate (GFR) estimation in the general population. They have not been evaluated in community-based populations, including Blacks at higher levels of GFR, but are commonly applied in such populations. Methods.: In an ancillary study of Multi-Ethnic Study of Atherosclerosis conducted at one site, we evaluated the performance of the CKD-EPI equations for creatinine (eGFRcr), cystatin C (eGFRcys) or the combination (eGFRcr-cys) compared with GFR measured as plasma clearance of iohexol...
May 13, 2017: Nephrology, Dialysis, Transplantation
Richard F Spaide
PURPOSE: To investigate the relationship between subfoveal choroidal thickness and disease manifestation in a series of eyes with nonexudative age-related macular degeneration (AMD). METHODS: Retrospective study of eyes with nonexudative AMD. The extracellular deposits present, drusen and subretinal drusenoid deposits (SDD, pseudodrusen) along with a newly recognized form of drusen, pachydrusen, were graded and compared with choroidal thickness as determined by optical coherence tomography...
May 11, 2017: Retina
Inna Chervoneva, Boris Freydin, Terry Hyslop, Scott A Waldman
Quantitative reverse transcription polymerase chain reaction (qRT-PCR) is widely used for molecular diagnostics and evaluating prognosis in cancer. The utility of mRNA expression biomarkers relies heavily on the accuracy and precision of quantification, which is still challenging for low abundance transcripts. The critical step for quantification is accurate estimation of efficiency needed for computing a relative qRT-PCR expression. We propose a new approach to estimating qRT-PCR efficiency based on modeling dynamics of polymerase chain reaction amplification...
January 1, 2017: Statistical Methods in Medical Research
Miaomiao Chen, Chaoying Chen, Zhiwei Shen, Xiaolei Zhang, Yanzi Chen, Fengfeng Lin, Xilun Ma, Caiyu Zhuang, Yifei Mao, Haochuan Gan, Peidong Chen, Xiaodan Zong, Renhua Wu
Extracellular pH (pHe) decrease is associated with tumor growth, invasion, metastasis, and chemoresistance, which can be detected by chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI). Here, we demonstrated that ioversol CEST MRI can be exploited to achieve pHe mapping of the liver cancer microenvironment. In in vitro studies, we firstly explored whether ioversol signal is pH-dependent, and calculated the function equation between the CEST effects of ioversol and pH values, in the range of 6...
April 25, 2017: Oncotarget
Lingzhao Fang, Goutam Sahana, Peipei Ma, Guosheng Su, Ying Yu, Shengli Zhang, Mogens Sandø Lund, Peter Sørensen
BACKGROUND: A better understanding of the genetic architecture of complex traits can contribute to improve genomic prediction. We hypothesized that genomic variants associated with mastitis and milk production traits in dairy cattle are enriched in hepatic transcriptomic regions that are responsive to intra-mammary infection (IMI). Genomic markers [e.g. single nucleotide polymorphisms (SNPs)] from those regions, if included, may improve the predictive ability of a genomic model. RESULTS: We applied a genomic feature best linear unbiased prediction model (GFBLUP) to implement the above strategy by considering the hepatic transcriptomic regions responsive to IMI as genomic features...
May 12, 2017: Genetics, Selection, Evolution: GSE
Julien Jouganous, Will Long, Aaron P Ragsdale, Simon Gravel
Understanding variation in allele frequencies across populations is a central goal of population genetics. Classical models for the distribution of allele frequencies, using forward simulation, coalescent theory, or the diffusion approximation, have been applied extensively for demographic inference, medical study design, and evolutionary studies. Here we propose a tractable model of ordinary differential equations for the evolution of allele frequencies that is closely related to the diffusion approximation but avoids many of its limitations and approximations...
May 11, 2017: Genetics
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