6 resultados para Improved Fourier series method

em Duke University


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While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

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In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

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We present measurements of morphological features in a thick turbid sample using light-scattering spectroscopy (LSS) and Fourier-domain low-coherence interferometry (fLCI) by processing with the dual-window (DW) method. A parallel frequency domain optical coherence tomography (OCT) system with a white-light source is used to image a two-layer phantom containing polystyrene beads of diameters 4.00 and 6.98 mum on the top and bottom layers, respectively. The DW method decomposes each OCT A-scan into a time-frequency distribution with simultaneously high spectral and spatial resolution. The spectral information from localized regions in the sample is used to determine scatterer structure. The results show that the two scatterer populations can be differentiated using LSS and fLCI.

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Gliomagenesis is driven by a complex network of genetic alterations and while the glioma genome has been a focus of investigation for many years; critical gaps in our knowledge of this disease remain. The identification of novel molecular biomarkers remains a focus of the greater cancer community as a method to improve the consistency and accuracy of pathological diagnosis. In addition, novel molecular biomarkers are drastically needed for the identification of targets that may ultimately result in novel therapeutics aimed at improving glioma treatment. Through the identification of new biomarkers, laboratories will focus future studies on the molecular mechanisms that underlie glioma development. Here, we report a series of genomic analyses identifying novel molecular biomarkers in multiple histopathological subtypes of glioma and refine the classification of malignant gliomas. We have completed a large scale analysis of the WHO grade II-III astrocytoma exome and report frequent mutations in the chromatin modifier, alpha thalassemia mental retardation x-linked (ATRX), isocitrate dehydrogenase 1 and 2 (IDH1 and IDH2), and mutations in tumor protein 53 (TP53) as the most frequent genetic mutations in low grade astrocytomas. Furthermore, by analyzing the status of recurrently mutated genes in 363 brain tumors, we establish that highly recurrent gene mutational signatures are an effective tool in stratifying homogeneous patient populations into distinct groups with varying outcomes, thereby capable of predicting prognosis. Next, we have established mutations in the promoter of telomerase reverse transcriptase (TERT) as a frequent genetic event in gliomas and in tissues with low rates of self renewal. We identify TERT promoter mutations as the most frequently mutated gene in primary glioblastoma. Additionally, we show that TERT promoter mutations in combination with IDH1 and IDH2 mutations are able to delineate distinct clinical tumor cohorts and are capable of predicting median overall survival more effectively than standard histopathological diagnosis alone. Taken together, these data advance our understanding of the genetic alterations that underlie the transformation of glial cells into neoplasms and we provide novel genetic biomarkers and multi – gene mutational signatures that can be utilized to refine the classification of malignant gliomas and provide opportunity for improved diagnosis.

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BACKGROUND: Controversies exist regarding the indications for unicompartmental knee arthroplasty. The objective of this study is to report the mid-term results and examine predictors of failure in a metal-backed unicompartmental knee arthroplasty design. METHODS: At a mean follow-up of 60 months, 80 medial unicompartmental knee arthroplasties (68 patients) were evaluated. Implant survivorship was analyzed using Kaplan-Meier method. The Knee Society objective and functional scores and radiographic characteristics were compared before surgery and at final follow-up. A Cox proportional hazard model was used to examine the association of patient's age, gender, obesity (body mass index > 30 kg/m2), diagnosis, Knee Society scores and patella arthrosis with failure. RESULTS: There were 9 failures during the follow up. The mean Knee Society objective and functional scores were respectively 49 and 48 points preoperatively and 95 and 92 points postoperatively. The survival rate was 92% at 5 years and 84% at 10 years. The mean age was younger in the failure group than the non-failure group (p < 0.01). However, none of the factors assessed was independently associated with failure based on the results from the Cox proportional hazard model. CONCLUSION: Gender, pre-operative diagnosis, preoperative objective and functional scores and patellar osteophytes were not independent predictors of failure of unicompartmental knee implants, although high body mass index trended toward significance. The findings suggest that the standard criteria for UKA may be expanded without compromising the outcomes, although caution may be warranted in patients with very high body mass index pending additional data to confirm our results. LEVEL OF EVIDENCE: IV.

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In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.