Dual Sequence Research Articles

Scaffold Diversity through a Branching Double-Annulation Cascade Strategy: Iminium-Induced One-Pot Synthesis of Diverse Fused Tetrahydroisoquinoline Scaffolds.

A branching double-annulation cascade (BDAC) strategy for diverse and complex fused THIQ scaffolds via a highly reactive iminium-induced one-pot double-cyclization sequence involving Pictect-Spengler-type cyclization has been developed for the first time. The salient features of this protocol are that it allows direct and rapid access to unprecedented diverse fused THIQ skeletons, is metal/catalyst free, has a cleaner reaction profile, provides good to excellent yields, and is a convenient approach. This catalyst-free domino process facilitates the double annulation with a variety of scaffold building agents via two C-N and one C-X (X = C, N, O) bond formation in a single step under uniform reaction conditions. Furthermore, we reveal an unusual dual BDAC sequence leading to N-N-linked isoquinoline dimer.

Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allow lags in operator processing, permitting asynchronous implementation. The decomposition phase of each iteration of our methods is to generate points in the graphs of the selected monotone operators, in order to construct a half-space containing the Kuhn–Tucker set associated with the system. The coordination phase of each iteration involves a projection onto this half-space. We present two related methods: the first method provides weakly convergent primal and dual sequences under general conditions, while the second is a variant in which strong convergence is guaranteed without additional assumptions. Neither algorithm requires prior knowledge of bounds on the linear operators involved or the inversion of linear operators. Our algorithmic framework unifies and significantly extends the approaches taken in earlier work on primal-dual projective splitting methods.

Canonical dual K-Bessel sequences and dual K-Bessel generators for unitary systems of Hilbert spaces

In this paper, firstly we explore some properties of K-frames in terms of decompositions of operators. Then we pay more attention to characterize the dual K-Bessel sequences of a given K-frames. Since the frame operator for a K-frame may not be invertible, there is no classical canonical dual for a K-frame. We introduce the concept of canonical dual K-Bessel sequence of a K-frame which generalizes the classical dual of a frame. We prove its existence and uniqueness and some other properties. We also give a simple way to construct new K-frames from given ones. For the K-frame generators of a unitary system, we give a condition such that a K-frame generator for a unitary group has a dual K-Bessel generator so that both of them share the same group structure. We characterize the K-frame generators in terms of operators and we also consider the construction of new K-frame generators from given ones.

BioCode gold-nanobeacon for the detection of fusion transcripts causing chronic myeloid leukemia.

BackgroundGold-nanobeacons (Au-nanobeacons) have proven to be versatile systems for molecular diagnostics and therapeutic actuators. Here, we present the development and characterization of two gold nanobeacons combined with Förster resonance energy transfer (FRET) based spectral codification for dual mode sequence discrimination. This is the combination of two powerful technologies onto a single nanosystem.ResultsWe proved this concept to detect the most common fusion sequences associated with the development of chronic myeloid leukemia, e13a2 and e14a2. The detection is based on spectral shift of the donor signal to the acceptor, which allows for corroboration of the hybridization event. The Au-nanobeacon acts as scaffold for detection of the target in a homogenous format whose output capability (i.e. additional layer of information) is potentiated via the spectral codification strategy.ConclusionsThe spectral coded Au-nanobeacons permit the detection of each of the pathogenic fusion sequences, with high specificity towards partial complementary sequences. The proposed BioCode Au-nanobeacon concept provides for a nanoplatform for molecular recognition suitable for cancer diagnostics.Electronic supplementary materialThe online version of this article (doi:10.1186/s12951-016-0192-y) contains supplementary material, which is available to authorized users.

Dual and triple equations and q-orthogonal polynomials

In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included.

T2 relaxation time is related to liver fibrosis severity

The grading of liver fibrosis relies on liver biopsy. Imaging techniques, including elastography and relaxometric, techniques have had varying success in diagnosing moderate fibrosis. The goal of this study was to determine if there is a relationship between the T2-relaxation time of hepatic parenchyma and the histologic grade of liver fibrosis in patients with hepatitis C undergoing both routine, liver MRI and liver biopsy, and to validate our methodology with phantoms and in a rat model of liver fibrosis. This study is composed of three parts: (I) 123 patients who underwent both routine, clinical liver MRI and biopsy within a 6-month period, between July 1999 and January 2010 were enrolled in a retrospective study. MR imaging was performed at 1.5 T using dual-echo turbo-spin echo equivalent pulse sequence. T2 relaxation time of liver parenchyma in patients was calculated by mono-exponential fit of a region of interest (ROI) within the right lobe correlating to histopathologic grading (Ishak 0-6) and routine serum liver inflammation [aspartate aminotransferase (AST) and alanine aminotransferase (ALT)]. Statistical comparison was performed using ordinary logistic and ordinal logistic regression and ANOVA comparing T2 to Ishak fibrosis without and using AST and ALT as covariates; (II) a phantom was prepared using serial dilutions of dextran coated magnetic iron oxide nanoparticles. T2 weighed imaging was performed by comparing a dual echo fast spin echo sequence to a Carr-Purcell-Meigboom-Gill (CPMG) multi-echo sequence at 1.5 T. Statistical comparison was performed using a paired t-test; (III) male Wistar rats receiving weekly intraperitoneal injections of phosphate buffer solution (PBS) control (n=4 rats); diethylnitrosamine (DEN) for either 5 (n=5 rats) or 8 weeks (n=4 rats) were MR imaged on a Bruker Pharmascan 4.7 T magnet with a home-built bird-cage coil. T2 was quantified by using a mono-exponential fitting algorithm on multi-slice multi echo T2 weighted data. Statistical comparison was performed using ANOVA. (I) Histopathologic evaluation of both rat and human livers demonstrated no evidence of steatosis or hemochromatosis There was a monotonic increase in mean T2 value with increasing degree of fibrosis (control 65.4±2.9 ms, n=6 patients); mild (Ishak 1-2) 66.7±1.9 ms (n=30); moderate (Ishak 3-4) 71.6±1.7 ms (n=26); severe (Ishak 5-6) 72.4±1.4 ms (n=61); with relatively low standard error (~2.9 ms). There was a statistically significant difference between degrees of mild (Ishak <4) vs. moderate to severe fibrosis (Ishak >4) (P=0.03) based on logistic regression of T2 and Ishak, which became insignificant (P=0.07) when using inflammatory markers as covariates. Expanding on this model using ordinal logistic regression, there was significance amongst all 4 groups comparing T2 to Ishak (P=0.01), with significance using inflammation as a covariate (P=0.03) and approaching statistical significance amongst all groups by ANOVA (P=0.07); (II) there was a monotonic increase in T2 and statistical significance (ANOVA P<0.0001) between each rat subgroup [phosphate buffer solution (PBS) 25.2±0.8, DEN 5-week (31.1±1.5), and DEN 9-week (49.4±0.4) ms]; (III) the phantoms that had T2 values within the relevant range for the human liver (e.g., 20-100 ms), demonstrated no statistical difference between two point fits on turbo spin echo (TSE) data and multi-echo CPMG data (P=0.9). The finding of increased T2 with liver fibrosis may relate to inflammation that may be an alternative or adjunct to other noninvasive MR imaging based approaches for assessing liver fibrosis.

In Vivo Reconstruction of Lumbar Erector Spinae Architecture Using Diffusion Tensor MRI.

Diffusion tensor magnetic resonance imaging (DT-MRI) reconstruction of lumbar erector spinae (ES) compared with cadaver dissection. The aim of this study was to reconstruct the human lumbar ES from in vivo DT-MRI measurements and to compare the results with literature and cadaver dissection. DT-MRI enables 3-dimensional in vivo reconstruction of muscle architecture. Insight in ES architecture may improve the understanding of low back function. Furthermore, DT-MRI reconstructions allow individualized biomechanical modeling, which may serve as a clinical tool in injury evaluation and in improvement of understanding of pathologies like scoliosis. The lumbar spine of 1 healthy male volunteer was scanned using a 3.0 T clinical MRI scanner. MRI data acquisition consisted of 3 parts: (1) high-resolution T1-weighted turbo spin echo for anatomical reference; (2) DT-MRI measurements for fiber tractography; (3) dual echo gradient echo sequence for signal correction purposes. After processing, DT-MRI data were exported to a custom-built software program for fiber tractography. The resulting reconstructions were anatomically validated by comparison with cadaver dissection and literature. DT-MRI reconstruction of 4 parts of the lumbar ES (thoracic part of iliocostalis lumborum, lumbar part of iliocostalis lumborum, thoracic part of longissimus thoracis, and lumbar part of longissimus thoracis) adequately reflected its complex geometry. Some inaccuracies were found in reconstruction details. DT-MRI reconstructions were generally in agreement with anatomical descriptions from literature and with findings in a dissected cadaver specimen. DT-MRI enables anatomically valid reconstruction of ES architecture. However, for reliable reconstruction of the smallest fascicles and attachments a higher resolution or application of higher-order models is needed. Reconstructions can be used as input for estimation of muscle architecture parameters in individualized biomechanical modeling. Such models are promising as a tool in clinical evaluation and in research of low back pain mechanisms.

Time Efficient 3D Radial UTE Sampling with Fully Automatic Delay Compensation on a Clinical 3T MR Scanner

This work’s aim was to minimize the acquisition time of a radial 3D ultra-short echo-time (UTE) sequence and to provide fully automated, gradient delay compensated, and therefore artifact free, reconstruction. The radial 3D UTE sequence (echo time 60 μs) was implemented as single echo acquisition with center-out readouts and improved time efficient spoiling on a clinical 3T scanner without hardware modifications. To assess the sequence parameter dependent gradient delays each acquisition contained a quick calibration scan and utilized the phase of the readouts to detect the actual k-space center. This calibration scan does not require any user interaction. To evaluate the robustness of this automatic delay estimation phantom experiments were performed and 19 in vivo imaging data of the head, tibial cortical bone, feet and lung were acquired from 6 volunteers. As clinical application of this fast 3D UTE acquisition single breath-hold lung imaging is demonstrated. The proposed sequence allowed very short repetition times (TR~1ms), thus reducing total acquisition time. The proposed, fully automated k-phase based gradient delay calibration resulted in accurate delay estimations (difference to manually determined optimal delay −0.13 ± 0.45 μs) and allowed unsupervised reconstruction of high quality images for both phantom and in vivo data. The employed fast spoiling scheme efficiently suppressed artifacts caused by incorrectly refocused echoes. The sequence proved to be quite insensitive to motion, flow and susceptibility artifacts and provides oversampling protection against aliasing foldovers in all directions. Due to the short TR, acquisition times are attractive for a wide range of clinical applications. For short T2* mapping this sequence provides free choice of the second TE, usually within less scan time as a comparable dual echo UTE sequence.

Newton’s method may fail to recognize proximity to optimal points in constrained optimization

We will show examples in which the primal sequence generated by the Newton---Lagrange method converges to a strict local minimizer of a constrained optimization problem but the gradient of the Lagrangian does not tend to zero, independently of the choice of the dual sequence.

Projected shrinkage algorithm for box-constrained $$\ell _1$$ ℓ 1 -minimization

Box-constrained \(\ell _1\)-minimization in some cases performs remarkably better than the classical \(\ell _1\)-minimization when appropriate box constraints are available. And also many practical \(\ell _1\)-minimization models indeed involve box constraints. In this paper, we propose an efficient iteration scheme, dubbed the projected shrinkage (ProShrink) algorithm, to solve a class of box-constrained \(\ell _1\)-minimization problems. A key component in our technique is that the proximal point operator of \(\ell _1\)-norm with box constraints can be equivalently simplified into a projected shrinkage operator which can be calculated directly. Theoretically, we prove that ProShrink enjoys convergence of both the primal and dual point sequences. On the numerical level, we demonstrate the benefit of adding box constraints via sparse recovery experiments.

Plate/shell topological optimization subjected to linear buckling constraints by adopting composite exponential filtering function

In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function (CEF) is selected as filtering functions for element weight, the element stiffness matrix and the element geometric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete”. The buckling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algorithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.

7 Tesla quantitative hip MRI: T1, T2 and T2* mapping of hip cartilage in healthy volunteers.

To evaluate the technical feasibility and applicability of quantitative MR techniques (delayed gadolinium-enhanced MRI of cartilage (dGEMRIC), T2 mapping, T2* mapping) at 7T MRI for assessing hip cartilage. Hips of 11 healthy volunteers were examined at 7T MRI with an 8-channel radiofrequency transmit/receive body coil using multi-echo sequences for T2 and T2* mapping and a dual flip angle gradient-echo sequence before (T10) and after intravenous contrast agent administration (T1Gd; 0.2mmol/kg Gd-DTPA(2-) followed by 0.5h of walking and 0.5h of rest) for dGEMRIC. Relaxation times of cartilage were measured manually in 10 regions of interest. Pearson's correlations between R1delta = 1/T1Gd - 1/T10 and T1Gd and between T2 and T2* were calculated. Image quality and the delineation of acetabular and femoral cartilage in the relaxation time maps were evaluated using discrete rating scales. High correlations were found between R1delta and T1Gd and between T2 and T2* relaxation times (all p < 0.01). All techniques delivered diagnostic image quality, with best delineation of femoral and acetabular cartilage in the T2* maps (mean 3.2 out of a maximum of 4 points). T1, T2 and T2* mapping of hip cartilage with diagnostic image quality is feasible at 7T. To perform dGEMRIC at 7T, pre-contrast T1 mapping can be omitted. • dGEMRIC of hip cartilage with diagnostic image quality is feasible at 7 T. • To perform dGEMRIC at 7 T, pre-contrast T1 mapping can be omitted. • T2(*) mapping of hip cartilage with diagnostic image quality is feasible at 7 T. • T2 and T2* relaxation times of cartilage were highly correlated at 7 T. • Best delineation of femoral and acetabular cartilage was found in T2* maps.

Strong Stationary Duality for Diffusion Processes

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well-chosen sequence of approximating birth-and-death Markov chains, allowing for simultaneous numerical simulations of our primal and dual diffusion processes. Lastly, we show how our new definition of diffusion duality allows the spectral theory of cutoff phenomena to extend naturally from birth-and-death Markov chains to the present diffusion context.

Microstructural parameter estimation in vivo using diffusion MRI and structured prior information.

PurposeDiffusion MRI has recently been used with detailed models to probe tissue microstructure. Much of this work has been performed ex vivo with powerful scanner hardware, to gain sensitivity to parameters such as axon radius. By contrast, performing microstructure imaging on clinical scanners is extremely challenging.MethodsWe use an optimized dual spin‐echo diffusion protocol, and a Bayesian fitting approach, to obtain reproducible contrast (histogram overlap of up to 92%) in estimated maps of axon radius index in healthy adults at a modest, widely‐available gradient strength (35 mT m −1). A key innovation is the use of influential priors.ResultsWe demonstrate that our priors can improve precision in axon radius estimates—a 7‐fold reduction in voxelwise coefficient of variation in vivo—without significant bias. Our results may reflect true axon radius differences between white matter regions, but this interpretation should be treated with caution due to the complexity of the tissue relative to our model.ConclusionsSome sensitivity to relatively large axons (3–15 μm) may be available at clinical field and gradient strengths. Future applications at higher gradient strength will benefit from the favorable eddy current properties of the dual spin‐echo sequence, and greater precision available with suitable priors. Magn Reson Med, 2015. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Magn Reson Med 75:1787–1796, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance.

Identification of Chinese Traditional Medicine Cistanches Herba from Different Places by HPLC-ESI-MS and FTIR Methods

Five samples of Cistanches Herba from different places were analyzed by HPLC-ESI-MS and FTIR methods. The effective compositions in Cistanches Herba including cistanoside A, echinacoside, acteoside , isoacteoside, 2'-actylacteoside, cistanoside C and tubluoside B were determined by HPLC-MS. The common peak ratio and variant peak ratio were calculated by FTIR spectroscopy of the five samples and the dual index sequence of common peak ratio and variant peak ratio were established. The results showed that the evaluation results of the samples by the two methods were the same. The general fake plant Cynomorii Herba could be identified by FTIR. HPLC-ESI-MS, which has high sensitivity and rapid determination procedure, can be used to evaluate quality of Cistanches Herba by quantitative analysis of the primary compositions. FTIR is a non-destructive analysis method. without complicated extraction and separation procedures to the samples. The absorption strength and the absorption shape were the synergistic effect of the functional groups and the nestification of the components in Cistanches Herba. The provided method has some advantages such as rapid analysis process, good reproducibility, non-destructive, small quantity of sample, simple treatment, good specificity, low-cost and environment-friendly. The method meets the trend of complex analysis and whole analysis for the Chinese medicines. Combination of FTIR and HPLC-ESI-MS was a good method for identification and evaluation of quality of Chinese medicines.

On convergence analysis of dual proximal-gradient methods with approximate gradient for a class of nonsmooth convex minimization problems

In this paper, we consider the problem of minimizing a nonsmoothconvex objective which is the sum of a proper, nonsmooth, closed,strongly convex extend real-valued function with a proper,nonsmooth, closed, convex extend real-valued function which is acomposition of a proper closed convex function and a nonzeroaffine map. We first establish its dual problem which consists ofminimizing the sum of a smooth convex function with a closedproper nonsmooth convex function. Then we apply first orderproximal gradient methods on the dual problem, where an error ispresent in the calculation of the gradient of the smooth term.Further we present a dual proximal-gradient methods withapproximate gradient. We show that when the errors are summablealthough the dual lowest objective function sequence generated bythe proximal-gradient method with the errors converges to theoptimal value with the rate $O(\frac{1}{k})$, the rate ofconvergence of the primal sequence is of the order$O(\frac{1}{\sqrt{k}}$).

Patch‐based generation of a pseudo CT from conventional MRI sequences for MRI‐only radiotherapy of the brain

In radiotherapy (RT) based on magnetic resonance imaging (MRI) as the only modality, the information on electron density must be derived from the MRI scan by creating a so-called pseudo computed tomography (pCT). This is a nontrivial task, since the voxel-intensities in an MRI scan are not uniquely related to electron density. To solve the task, voxel-based or atlas-based models have typically been used. The voxel-based models require a specialized dual ultrashort echo time MRI sequence for bone visualization and the atlas-based models require deformable registrations of conventional MRI scans. In this study, we investigate the potential of a patch-based method for creating a pCT based on conventional T1-weighted MRI scans without using deformable registrations. We compare this method against two state-of-the-art methods within the voxel-based and atlas-based categories. The data consisted of CT and MRI scans of five cranial RT patients. To compare the performance of the different methods, a nested cross validation was done to find optimal model parameters for all the methods. Voxel-wise and geometric evaluations of the pCTs were done. Furthermore, a radiologic evaluation based on water equivalent path lengths was carried out, comparing the upper hemisphere of the head in the pCT and the real CT. Finally, the dosimetric accuracy was tested and compared for a photon treatment plan. The pCTs produced with the patch-based method had the best voxel-wise, geometric, and radiologic agreement with the real CT, closely followed by the atlas-based method. In terms of the dosimetric accuracy, the patch-based method had average deviations of less than 0.5% in measures related to target coverage. We showed that a patch-based method could generate an accurate pCT based on conventional T1-weighted MRI sequences and without deformable registrations. In our evaluations, the method performed better than existing voxel-based and atlas-based methods and showed a promising potential for RT of the brain based only on MRI.

An alternating direction method with increasing penalty for stable principal component pursuit

The stable principal component pursuit (SPCP) is a non-smooth convex optimization problem, the solution of which enables one to reliably recover the low rank and sparse components of a data matrix which is corrupted by a dense noise matrix, even when only a fraction of data entries are observable. In this paper, we propose a new algorithm for solving SPCP. The proposed algorithm is a modification of the alternating direction method of multipliers (ADMM) where we use an increasing sequence of penalty parameters instead of a fixed penalty. The algorithm is based on partial variable splitting and works directly with the non-smooth objective function. We show that both primal and dual iterate sequences converge under mild conditions on the sequence of penalty parameters. To the best of our knowledge, this is the first convergence result for a variable penalty ADMM when penalties are not bounded, the objective function is non-smooth and its sub-differential is not uniformly bounded. Using partial variable splitting and adopting an increasing sequence of penalty multipliers, together, significantly reduce the number of iterations required to achieve feasibility in practice. Our preliminary computational tests show that the proposed algorithm works very well in practice, and outperforms ASALM, a state of the art ADMM algorithm for the SPCP problem with a constant penalty parameter.

A multicontrast approach for comprehensive imaging of substantia nigra

We characterize the contrast behavior of substantia nigra (SN) in both magnetization transfer (MT) imaging, which is believed to be sensitive to neuromelanin (NM), and susceptibility weighted imaging (SWI). Images were acquired with a MT prepared dual echo gradient echo sequence. The first echo was taken as the MT contrast image and the second was used to generate the SWI image. SN volumes were segmented from these two types of images using a thresholding method. The spatial and signal characteristics of the extracted SWI and MT volumes were compared. Both images showed the presence of SN but the volumes of the SN identified in the two are spatially incongruent. The MT volume was more caudal than the SWI volume and with only a 12% overlap between the two volumes. Considering the SN volumes in each hemisphere separately, the average distances between the centers of mass of the volumes from the two types images are 5.1±1.1mm and 4.1±1.2mm, respectively. The frequency offsets (homodyne filtered phase/echo time) for the volumes derived from MT (NM) images and SWI images are 0.09±0.32radians/s and −1.12±0.57radians/s (p<0.0001), respectively. The MT contrasts for the two volumes are 0.16±0.02 and 0.10±0.03 (p<0.001), respectively. Our results indicate that the two contrasts are sensitive to different portions of the SN, with MT seeing the more caudal portion of the SN than SWI, likely due to variations of NM and iron content in the SN. Despite the small overlap, these regions are complementary. Our results provide a new understanding of the contrast behavior of the SN in the two imaging approaches commonly used to image it and indicate that using both may yield a more comprehensive visualization of the SN.

Leonard triples of Krawtchouk type

Let denote an algebraically closed field of characteristic 0. Let denote a vector space over of finite positive dimension. A Leonard pair on is an ordered pair of linear transformations in such that for each of these transformations there exists a basis for with respect to which the matrix representing that transformation is diagonal and the matrix representing the other transformation is irreducible tridiagonal. The diameter of the Leonard pair is defined as . Let be a Leonard pair of diameter . The Leonard pair is of Krawtchouk type whenever its eigenvalue sequence and its dual eigenvalue sequence are both . The notions of a Leonard triple and a Leonard triple of Krawtchouk type are similarly defined. In this paper, let be a Leonard pair of Krawtchouk type. We first determine all linear transformations in such that is a Leonard triple of Krawtchouk type. Then we classify up to isomorphism Leonard triples of Krawtchouk type.