Sequence Of Spaces Research Articles

Dedicated isotropic 3-D T1 SPACE sequence imaging for radiosurgery planning improves brain metastases detection and reduces the risk of intracranial relapse

BackgroundStereotactic radiosurgery (SRS) is increasingly used for brain metastases (BM) patients, but distant intracranial failure (DIF) remains the principal disadvantage of this focal therapeutic approach. The objective of this study was to determine if dedicated SRS imaging would improve lesion detection and reduce DIF. MethodsBetween 02/2020 and 01/2021, SRS patients at a tertiary care institution underwent dedicated treatment planning MRIs of the brain including MPRAGE and SPACE post-contrast sequences. DIF was calculated using the Kaplan–Meier method; comparisons were made to a historical consecutive cohort treated using MPRAGE alone (02/2019–01/2020). Results134 patients underwent 171 SRS courses for 821 BM imaged with both MPRAGE and SPACE (primary cohort). MPRAGE sequence evaluation alone detected 679 lesions. With neuroradiologists evaluating SPACE and MPRAGE, an additional 108 lesions were identified (p < 0.001). Upon multidisciplinary review, 34 additional lesions were identified. Compared to the historical cohort (103 patients, 135 SRS courses, 479 BM), the primary cohort had improved median time to DIF (13.5 vs. 5.1 months, p = 0.004). The benefit was even more pronounced for patients treated for their first SRS course (18.4 vs. 6.3 months, p = 0.001). SRS using MPRAGE and SPACE was associated with a 60% reduction in risk of DIF compared to the historical cohort (HR: 0.40; 95% CI: 0.28–0.57, p < 0.001). ConclusionsAmong BM patients treated with SRS, a treatment planning SPACE sequence in addition to MPRAGE substantially improved lesion detection and was associated with a statistically significant and clinically meaningful prolongation in time to DIF, especially for patients undergoing their first SRS course.

Radiomics and machine learning analysis based on magnetic resonance imaging in the assessment of liver mucinous colorectal metastases.

The purpose of this study is to evaluate the Radiomics and Machine Learning Analysis based on MRI in the assessment of Liver Mucinous Colorectal Metastases.Query METHODS: The cohort of patients included a training set (121 cases) and an external validation set (30 cases) with colorectal liver metastases with pathological proof and MRI study enrolled in this approved study retrospectively. About 851 radiomics features were extracted as median values by means of the PyRadiomics tool on volume on interest segmented manually by two expert radiologists. Univariate analysis, linear regression modelling and pattern recognition methods were used as statistical and classification procedures. The best results at univariate analysis were reached by the wavelet_LLH_glcm_JointEntropy extracted by T2W SPACE sequence with accuracy of 92%. Linear regression model increased the performance obtained respect to the univariate analysis. The best results were obtained by a linear regression model of 15 significant features extracted by the T2W SPACE sequence with accuracy of 94%, a sensitivity of 92% and a specificity of 95%. The best classifier among the tested pattern recognition approaches was k-nearest neighbours (KNN); however, KNN achieved lower precision than the best linear regression model. Radiomics metrics allow the mucinous subtype lesion characterization, in order to obtain a more personalized approach. We demonstrated that the best performance was obtained by T2-W extracted textural metrics.

Invariant convergent and invariant ideal convergent sequence in intuitionistic fuzzy normed space

The main purpose of this paper is to introduce invariant convergence in intuitionistic fuzzy normed space. Following which we present some characteristics of this notion with respect to intuitionistic fuzzy norm. We also define strongly invariant convergence, ideal invariant convergence and invariant ideal convergence in intuitionistic fuzzy normed space. After that, we establish the relationship between these notions with respect to intuitionistic fuzzy norm. Lastly, we define ideal invariant Cauchy and invariant ideal Cauchy criteria for sequences in intuitionistic fuzzy normed space and relate it to their convergence notion.

Value of High-Resolution MRI in the Diagnosis of Brachial Plexus Injury in Infants and Young Children.

PurposeTo investigate the value of high-resolution MRI based on 3D-short inversion time inversion recovery sampling perfection with application-optimized contrasts (3D-STIR SPACE) sequence for the diagnosis of brachial plexus injury in infants and young children.MethodsPhysical examination, electromyography (EMG) and MRI data of 26 children with brachial plexus injury were retrospectively analyzed. Sensitivity, specificity, and accuracy were calculated for the three tests. The agreement among these examinations was analyzed with the Kappa test. P<0.05 was considered statistically significant.ResultsOf the 26 children, 3 cases had normal MRIs, 23 cases had unilateral brachial plexus injury diagnosed with MRI, and a total of 73 nerve roots and/or sheaths were involved. Among the 23 cases with aberrant MRI findings, there were 19 cases of nerve root thickening (42 nerve roots), 4 cases of nerve root sleeve expansion (5 nerve roots), 17 cases of pseudomeningeal cysts (34 nerve roots), 2 cases of nerve root loosening (2 nerve roots), 8 cases of nerve root dissection (11 nerve roots), 19 cases with increased nerve signal (43 nerve roots), and 9 cases with an increased signal of the muscles on the affected side. As for the diagnosis of brachial plexus injury, the sensitivity and the accuracy of physical examination, EMG and MRI were 0.92, 0.86, and 0.88, respectively. The agreement between MRI and physical examination was substantial (κ=0.780, P=0.000), as did the agreement between MRI and EMG (κ=0.611, P=0.005).ConclusionHigh-resolution MRI based on 3D-STIR SPACE sequence plays a role in the diagnosis and evaluation of brachial plexus injury in infants and young children. It can accurately identify the injured nerve and characterize related pathological alterations. Besides EMG and physical examination, it can be used as a valuable tool for screening and monitoring of brachial plexus injury in infants and children.

General metric spaces warped along submetry

In this paper, we generalize the notion of a warped product to submetries between to general metric spaces. We study the sequences of warped geodesic general metric spaces in the generalized Gromov-Hausdorff topology. For general metric spaces with commonly bounded finite asymmetry factor, we provide a necessary and sufficient condition for a sequence of warped metrics along submetry to converge, in the generalized Gromov-Hausdorff topology, to the base of the submetry.

An efficient multigrid method for semilinear interface problems

In this paper, we study an efficient multigrid method to solve the semilinear interface problems. We first give an optimal finite element error estimate for the semilinear interface problems under a weak condition for the nonlinear term compared with the existing conclusions. Then next based on the finite element error estimate, we design a novel multigrid method for semilinear elliptic problems. The proposed multigrid method only requires to solve a linear interface problem in each level of the multilevel space sequence and a small-scale semilinear interface problem in a correction space. The involved linear interface problem can be solved efficiently by the multigrid iteration. The dimension of the correction space is small and fixed, which is independent from the fine spaces. Thus the computational time of the correction step is negligible compared with that of the linear interface problems in the fine spaces. On the whole, the efficiency of the presented multigrid method is nearly the same as that of the multigrid method for linear interface problems. Additionally, unlike the existing finite element error estimates and the multigrid methods for semilinear interface problems, which always require the bounded second order derivatives of the nonlinear terms, all the analysis in our paper only requires a Lipschitz continuous condition.

Discrete vector-valued nonuniform Gabor frames

Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying modulation and shift operators to non-zero functions in signal spaces. In many applications, for example, signal processing related to Gabor systems, the corresponding shifts may not be uniform. That is, the set associated with shifts may not be a group under usual addition. We analyze discrete vector-valued nonuniform Gabor frames (DVNUG frames, in short) in discrete vector-valued nonuniform signal spaces, where the indexing set associated with shifts may not be a subgroup of real numbers under usual addition, but a spectrum which is based on the theory of spectral pairs. First, we give necessary and sufficient conditions for the existence of DVNUG Bessel sequences in discrete vector-valued nonuniform signal spaces in terms of Fourier transformations of the modulated window sequences. We provide a characterization of DVNUG frames in discrete vector-valued nonuniform signal spaces. It is shown that DVNUG frames are stable under small perturbation of window sequences associated with given discrete vector-valued nonuniform Gabor systems. We observed that the arithmetic mean sequences associated with window sequences of a given DVNUG frame collectively constitute a discrete nonuniform Gabor frame. Finally, we discuss an interplay between window sequences of DVNUG systems and their corresponding coordinates.

Radiomics and Machine Learning Analysis Based on Magnetic Resonance Imaging in the Assessment of Colorectal Liver Metastases Growth Pattern.

To assess Radiomics and Machine Learning Analysis in Liver Colon and Rectal Cancer Metastases (CRLM) Growth Pattern, we evaluated, retrospectively, a training set of 51 patients with 121 liver metastases and an external validation set of 30 patients with a single lesion. All patients were subjected to MRI studies in pre-surgical setting. For each segmented volume of interest (VOI), 851 radiomics features were extracted using PyRadiomics package. Nonparametric test, univariate, linear regression analysis and patter recognition approaches were performed. The best results to discriminate expansive versus infiltrative front of tumor growth with the highest accuracy and AUC at univariate analysis were obtained by the wavelet_LHH_glrlm_ShortRunLowGray Level Emphasis from portal phase of contrast study. With regard to linear regression model, this increased the performance obtained respect to the univariate analysis for each sequence except that for EOB-phase sequence. The best results were obtained by a linear regression model of 15 significant features extracted by the T2-W SPACE sequence. Furthermore, using pattern recognition approaches, the diagnostic performance to discriminate the expansive versus infiltrative front of tumor growth increased again and the best classifier was a weighted KNN trained with the 9 significant metrics extracted from the portal phase of contrast study, with an accuracy of 92% on training set and of 91% on validation set. In the present study, we have demonstrated as Radiomics and Machine Learning Analysis, based on EOB-MRI study, allow to identify several biomarkers that permit to recognise the different Growth Patterns in CRLM.

Ruang l^p pada Norm-2 Lengkap

The space l^p with 1≤p∞ is the set of real numbers that satisfy _(n=1)^∞▒〖|x_n |^p∞〗.The function in the vector space X which has real value which fulfills the norm-2 properties is denoted by ,⋅‖ and the pair (X,‖⋅,⋅‖) is called the norm-2 space.A norm-2 space is said to be complete or called a Banach-2 space if every Cauchy sequence in the space converges to an element in that space.This research was conducted to prove the l^p space in the complete norm-2.The first step to prove the completeness is to prove that the norm contained in l^p with 1≤p∞ satisfies the properties of norm-2.Next, prove that the norm derived from norm-2 is equivalent to the norm in l^p.Next shows that every Cauchy sequence in space l^p converges to an element in space l^p.Based on this proof, it is found that (l^p,‖⋅,⋅‖) is a complete norm-2 space.

On Statistical Convergence in Credibility Space

In this paper, we present the notions of statistically convergent sequence for fuzzy variables, statistically Cauchy sequence in credibility space, and present a kind of statistical completeness for credibility space. Furthermore, the conditions of statistical convergence almost surely (a.s.), statistical convergence in credibility, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) of fuzzy variable sequences are examined. We have proved relations between these notions.

Approximating the Geometric Edit Distance

Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a geometric space. Therefore, the geometric edit distance (GED) has been studied. In this paper, we describe the first strictly sublinear approximate near-linear time algorithm for computing the GED of two point sequences in constant dimensional Euclidean space. Specifically, we present a randomized \(O(n\log ^2n)\) time \(O(\sqrt{n})\)-approximation algorithm. Then, we generalize our result to give a randomized \(\alpha \)-approximation algorithm for any \(\alpha \in [\sqrt{\log n}, \sqrt{n/\log n}]\), running in time \(O(n^2/\alpha ^2 \log n)\). Both algorithms are Monte Carlo and return approximately optimal solutions with high probability.

STURE: Spatial–Temporal Mutual Representation Learning for robust data association in online multi-object tracking

Online multi-object tracking (MOT) is a longstanding task for computer vision and intelligent vehicle platform. At present, the main paradigm is tracking-by-detection, and the main difficulty of this paradigm is how to associate current candidate detections with historical tracklets. However, in the MOT scenarios, each historical tracklet is composed of an object sequence, while each candidate detection is just a flat image, which lacks temporal features of the object sequence. The feature difference between current candidate detections and historical tracklets makes the object association much harder. Therefore, we propose a Spatial–Temporal Mutual Representation Learning (STURE) approach which learns spatial–temporal representations between current candidate detections and historical sequences in a mutual representation space. For historical tracklets, the detection learning network is forced to match the representations of sequence learning network in a mutual representation space. The proposed approach is capable of extracting more distinguishing detection and sequence representations by using various designed losses in object association. As a result, spatial–temporal feature is learned mutually to reinforce the current detection features, and the feature difference can be relieved. To prove the robustness of the STURE, it is applied to the public MOT challenge benchmarks and performs well compared with various state-of-the-art online MOT trackers based on identity-preserving metrics.

K -frames for Banach Spaces

In order to reconstruct elements from the range of a linear bounded operator K on a separable Banach space, concepts of K -frames and K ∗ -atomic systems for Banach spaces are introduced, the relationship between the two is discussed, and the sufficient condition for a Banach space to have a K -frame is given. In addition, the duality of K -frames for Banach spaces is studied, the pair of K , K ∗ -dual Bessel sequences and the pair of approximate K , K ∗ -dual Bessel sequences for Banach spaces are introduced, and their important properties are discussed.

A General Framework for Flight Maneuvers Automatic Recognition

Flight Maneuver Recognition (FMR) refers to the automatic recognition of a series of aircraft flight patterns and is a key technology in many fields. The chaotic nature of its input data and the professional complexity of the identification process make it difficult and expensive to identify, and none of the existing models have general generalization capabilities. A general framework is proposed in this paper, which can be used for all kinds of flight tasks, independent of the aircraft type. We first preprocessed the raw data with unsupervised clustering method, segmented it into maneuver sequences, then reconstructed the sequences in phase space, calculated their approximate entropy, quantitatively characterized the sequence complexity, and distinguished the flight maneuvers. Experiments on a real flight training dataset have shown that the framework can quickly and correctly identify various flight maneuvers for multiple aircraft types with minimal human intervention.

Multi-scale dendritic patterns sequentially superimposed in a primary semi-solid matrix

• The base of conventional dendritic arms is constituted by a primary semi-solid matrix. • The sequential formation of multi-scale dendrites were in-situ and real time verified. • The formation mechanism for multi-scale dendrites is attributed to temperature superimposition. • Multi-scale dendrites are important to microstructures and segregation control. The principle and control for solidification present crucial challenges. Through in situ and real time observation on the solidification of M50 bearing steel, here we discovered that the base of conventional dendritic arms is constituted by a primary semi-solid matrix. Due to the superimposition of temperature fluctuations from the large to the subtle scale, multi-scale dendritic patterns will sequentially emerge and evolve in the primary semi-solid matrix. These findings redefine the essence of multi-scale dendrites as the multi-scale segregation patterns in the primary semi-solid matrix, reconstitute the time and space sequence in the formation of multi-scale dendrites, and reveal the superimposition of temperature fluctuation as the driving principle. These new understandings will fundamentally influence the solidification field. These results also indicate important engineering applications, such as designing multi-scale dendrites, controlling the dendritic segregation and eliminating the detrimental eutectics.

Statistically Convergent Sequences in Intuitionistic Fuzzy Metric Spaces

In this paper, we introduce the concepts of statistical convergence and statistical Cauchy sequences with respect to the intuitionistic fuzzy metric spaces inspired by the idea of statistical convergence in fuzzy metric spaces. Then, we give useful characterizations for statistically convergent sequences and statistically Cauchy sequences.

An investigation on the triple ideal convergent sequences in fuzzy metric spaces

The notion of ideal convergence is a process of generalizing of statistical convergence which is dependent on the idea of the ideal $I$ of subsets of the set positive integer numbers. In this study we also present the concept of ideal convergence for triple sequences in fuzzy metric spaces (FMS) in the manner of George and Veeramani and the terms of ideal Cauchy sequence and $I^{∗}$-Cauchy sequence in FMS and study their certain properties.

The Neoantigen Landscape of the Coding and Noncoding Cancer Genome Space

Tumor mutation burden (TMB) is a measure to predict patient responsiveness to immune checkpoint immunotherapy because with increased mutation frequency, the likelihood of a greater neoantigen burden is increased. Although neoantigen prediction tools exist, tumor neoantigen burden has not been adopted as a measure to predict immunotherapy response. With both measures, current guidelines are limited to the coding regions, but ectopic expression of sequences in the noncoding space may potentially be a source of neoantigens. A pan-cancer cohort of 574 advanced disease stage patients with whole genome and transcriptome sequencing was analyzed to report mutation burden and neoantigen counts within the coding and noncoding regions. The efficacy of tumor neoantigen burden, reported as tumor neoantigen count (TNC), including neoantigens derived from the expression of noncoding regions, compared with TMB as a predictor of response to immunotherapy for 80 patients who had received treatment, was evaluated. TMB was found to be the best predictor of response to immunotherapy, whereas expression-derived TNC from the noncoding regions did not improve prediction of response. Therefore, there is minimal benefit in extending the calculation of TNC to the noncoding space for the purposes of predicting response. However, it is likely that there is a wealth of neoantigens derived from the noncoding space that may impact patient outcomes and treatments.

Abundance of independent sequences in compact spaces and Boolean algebras

It follows from a theorem of Rosenthal that a compact space is ccc if and only if its every Eberlein continuous image is metrizable. Motivated by this result, for a class of compact spaces {mathcal {C}} we define its orthogonal {mathcal {C}}^perp as the class of all compact spaces for which every continuous image in {mathcal {C}} is metrizable. We study how this operation relates classes where centeredness is scarce with classes where it is abundant (like Eberlein and ccc compacta), and also classes where independence is scarce (most notably weakly Radon-Nikodým compacta) with classes where it is abundant. We study these problems for zero-dimensional compact spaces with the aid of Boolean algebras, and show the main difficulties that arise when we deal with general settings. Our main results are the constructions of several relevant examples.

Statistically Convergent Sequences in Neutrosophic Metric Spaces

In this study, the introduction of statistical convergence and statistical Cauchy sequences with respect to neutrosophic metric spaces is motivated by the notion of statistical convergence in fuzzy metric spaces. We offer useful characterizations for statistically convergent and statistically Cauchy sequences.