Dimensional Sequence Research Articles

Three-Dimensional Magnetic Resonance Imaging in the Musculoskeletal System: Clinical Applications and Opportunities to Improve Imaging Speed and Resolution.

Although conventional 2-dimensional magnetic resonance (MR) sequences have traditionally comprised the foundational imaging strategy for visualization of musculoskeletal anatomy and pathology, the emergence of isotropic volumetric 3-dimensional sequences offers to advance musculoskeletal evaluation with comparatively similar image quality and diagnostic performance, shorter acquisition times, and the added advantages of improved spatial resolution and multiplanar reformation capability. The purpose of this review article is to summarize the available 3-dimensional MR sequences and their role in the management of patients with musculoskeletal disorders, including sports imaging, rheumatologic conditions, peripheral nerve imaging, bone and soft tissue tumor imaging, and whole-body MR imaging.

Poissonian pair correlation for higher dimensional real sequences

AbstractIn this article, we examine the Poissonian pair correlation (PPC) statistic for higher dimensional real sequences. Specifically, we demonstrate that for , almost all , the sequence in has PPC conditionally on the additive energy bound of . This bound is more relaxed compared to the additive energy bound for one dimension as discussed in [Aistleitner, El‐Baz, and Munsch, Geom. Funct. Anal. 31 (2021), 483–512]. More generally, we derive the PPC for for almost all . As a consequence we establish the metric PPC for provided that all of the are greater than two.

Randomized complexity of mean computation and the adaption problem

Recently the adaption problem of Information-Based Complexity (IBC) for linear problems in the randomized setting was solved in Heinrich (2024) [8]. Several papers treating further aspects of this problem followed. However, all examples obtained so far were vector-valued. In this paper we settle the scalar-valued case. We study the complexity of mean computation in finite dimensional sequence spaces with mixed LpN norms. We determine the n-th minimal errors in the randomized adaptive and non-adaptive settings. It turns out that among the problems considered there are examples where adaptive and non-adaptive n-th minimal errors deviate by a power of n. The gap can be (up to log factors) of the order n1/4. We also show how to turn such results into infinite dimensional examples with suitable deviation for all n simultaneously.

Prediction problem for continuous time stochastic processes with periodically correlated increments observed with noise

We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of this process with periodically stationary noise. To solve the problem, we transform the processes to the sequences of stochastic functions which form an infinite dimensional vector stationary sequences. In the case of known spectral densities of these sequences, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas determining the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where the sets of admissible spectral densities are given.

Theoretical investigation of bidirectional and unidirectional dual-band absorption in one dimensional Octonacci sequences controlled by Dirac semimetal and Vanadium dioxide

The dual-band absorption properties of one-dimensional ternary Octonacci sequences, comprising dielectric, Dirac semimetal (DS), and Vanadium dioxide (VO2), are investigated theoretically and numerically using transfer matrix method, full-wave simulations, and impedance match theory. The photonic quasi-periodic multilayers exhibit bidirectional dual-band high absorption properties, attributed to strong electric field localization. Interestingly, this dual-band absorption can be spectrally tuned to the desired frequencies by adjusting the Fermi energy of the DS, changing the structure's parameters, the choice of dielectric, and the angle of incidence. Furthermore, the addition of a VO2 layer at the bottom of the Octonacci sequence enables the realization of dynamically tunable bidirectional and unidirectional dual-band absorption by modulating the conductivity of VO2. Remarkably, the absorption response remains insensitive to the polarization of the incident wave. These unique properties, together with the ease of manufacturing, make our proposed structures a promising candidate for wide applications in tunable optical devices.

Time dimension feature extraction and classification of high-dimensional large data streams based on unsupervised learning

In order to solve the problem of low accuracy of time dimension feature extraction and classification of high-dimensional large data streams, this paper proposes a time dimension feature extraction and classification algorithm of high-dimensional large data streams based on unsupervised learning. Analyze the trend of high-dimensional data flow changes under machine learning, and achieve dimensionality reduction of high-dimensional large traffic time dimensional data through local save projection. Analyze the spatial relationship between feature attributes and feature space, segment and fit high-dimensional big data streams and time dimensional feature data streams, further segment time dimensional sequences using sliding windows, and complete feature extraction through discrete dyadic wavelet transform. According to the clustering algorithm, cluster the time dimension feature data stream, calculate the cosine similarity of the feature data, model the time dimension feature stream of training samples, use the feature classification function to minimize the classification loss, and use unsupervised learning to achieve the final classification task. The test results show that this method can improve the temporal feature extraction and classification accuracy streams.

Enhanced stock price forecasting through a regularized ensemble framework with graph convolutional networks

Stock prediction is a prominent and challenging topic of interest for both investors and researchers. With the introduction of Graph Convolutional Networks (GCNs) to financial data analysis, many researchers have attempted to use GCNs to exploit the interrelationships among stock data. However, a notable research gap remains in the application of GCNs to establish associations among transaction data, which inherently exhibit more stable and well-defined correlations. Hence, this study proposes a regularized ensemble framework with graph convolutional networks for stock price prediction. The framework employs multiple multi-graph convolutional networks to construct an ensemble graph convolutional network, elucidating spatiotemporal relationships within transaction data across various time scales. Additionally, the Variational Modal Decomposition (VMD) method is utilized to extract features from each dimensional sequence of the transaction data, enabling the capture of features across different time scales and mitigating non-stationarity and noise in the data. Furthermore, a regularization term incorporating trend accuracy is introduced to strike a balance between numerical precision and trend accuracy, thereby enhancing the overall model performance. Finally, this study presents a specialized investment strategy designed for stock price prediction. Our approach yields substantial improvements on SSE and DJIA datasets, with ACC and R2 improving by over 15% and 10%, respectively, accompanied by reductions of more than 40% in RMSE, MAE, and MAPE compared to the baseline. These results underscore the effectiveness, robustness, and adaptability of our proposed methodology. Our codes and data can be accessed at https://github.com/WonderNothing/REGCN/.

Two dimensional parallel sequence spread spectrum for wireless communications

A novel two-dimensional parallel sequence spread spectrum (2D-PSSS) structure for the physical layer of wireless communication systems is introduced. The proposed 2D-PSSS system partitions a data block into two groups of bits, representing the two dimensions. The first dimension represents the selected code from a predefined set of Gold codes. While the second dimension determines a shift value applied to the chosen code. The shifted Gold code will represent the data block. By design, the 2D-PSSS system overcomes the challenge of inter-code interference encountered in conventional PSSS systems without introducing additional computational complexity. Moreover, the 2D-PSSS system offers reduced encoder computational complexity compared to PSSS systems, enhancing its suitability for a wide range of wireless communication applications. The performance of the 2D-PSSS system in terms of bit error rate has been evaluated in additive white Gaussian noise (AWGN) channel and under different fading channel conditions.

Inferring single-cell copy number profiles through cross-cell segmentation of read counts

BackgroundCopy number alteration (CNA) is one of the major genomic variations that frequently occur in cancers, and accurate inference of CNAs is essential for unmasking intra-tumor heterogeneity (ITH) and tumor evolutionary history. Single-cell DNA sequencing (scDNA-seq) makes it convenient to profile CNAs at single-cell resolution, and thus aids in better characterization of ITH. Despite that several computational methods have been proposed to decipher single-cell CNAs, their performance is limited in either breakpoint detection or copy number estimation due to the high dimensionality and noisy nature of read counts data.ResultsBy treating breakpoint detection as a process to segment high dimensional read count sequence, we develop a novel method called DeepCNA for cross-cell segmentation of read count sequence and per-cell inference of CNAs. To cope with the difficulty of segmentation, an autoencoder (AE) network is employed in DeepCNA to project the original data into a low-dimensional space, where the breakpoints can be efficiently detected along each latent dimension and further merged to obtain the final breakpoints. Unlike the existing methods that manually calculate certain statistics of read counts to find breakpoints, the AE model makes it convenient to automatically learn the representations. Based on the inferred breakpoints, we employ a mixture model to predict copy numbers of segments for each cell, and leverage expectation–maximization algorithm to efficiently estimate cell ploidy by exploring the most abundant copy number state. Benchmarking results on simulated and real data demonstrate our method is able to accurately infer breakpoints as well as absolute copy numbers and surpasses the existing methods under different test conditions. DeepCNA can be accessed at: https://github.com/zhyu-lab/deepcna.ConclusionsProfiling single-cell CNAs based on deep learning is becoming a new paradigm of scDNA-seq data analysis, and DeepCNA is an enhancement to the current arsenal of computational methods for investigating cancer genomics.

Post -contrast Three -dimensional MP RAGE T1WI Sequence Compared to Brain MRV Sequence for Diagnosing Brain Sinus Venous Thrombosis.

Dural sinus thrombosis is considered as a one of the clinical and radiological emergencies that require special attention and high index of suspicion and needs combined effort of both the treating physician and the radiologist to obtain proper diagnosis and subsequently proper management. The aim of this article was to compare the accuracy of MRV TOF and post contrast MP-RAGE sequences in diagnosis of cerebral sinus venous thrombosis. After all informed consents were obtained and upon ethical committee approval from the ethical committee in Joradanian Royal medical services in Amman we perform this study as a retrospective study done on 50 patients with cerebral sinus venous thrombosis with 50 pateints control group done at king Hussein medical center in Amman Jordan. The guidelines and regulations of studies conducted in Royal medical services were followed. 68 females and 32 males with age range between 19 and 52 years. All patients underwent brain MRI for evaluation of cerebral sinus thrombosis, all studies were done on seimens skyra 3 Tesla machine with standardized protocol including 2 D TOF MRV, axial T2WI, axial FLAIR, Axial T1, SWI and diffusion weighted images along with 3D MP-RAGE post contrast. Images were reviewed by two well experienced neuroradiologists (Maysoon and Qamar) in separate sessions, each MRI sequence was reported separately without knowing patients name or clinical history. Conclusion: The results for T2 WI, SWI, MRV TOF and MP-RAGE post contrast were reported. We used a confidence level score to standardize the results. Then the results were analyzed using simple statistical methods.

Significance of Sequence Features in Classification of Protein-Protein Interactions Using Machine Learning.

Protein-protein interactions are crucial for the entry of viruses into the cell. Understanding the mechanism of interactions is essential in studying human-virus association, developing new biologics and drug candidates, as well as viral infections and antiviral responses. Experimental methods to analyze human-virus protein-protein interactions based on protein sequence data are time-consuming and labor-intensive, so machine learning models are being developed to predict interactions and determine large-scale interactomes between species. The present work highlights the importance of sequence features in classifying interacting and non-interacting proteins from the protein sequence data. Higher dimensional amino acid sequence features such as Amino Acid Composition (AAC), Dipeptide Composition (DPC), Grouped Amino Acid Composition (GAAC), Pseudo-Amino Acid Composition (PAAC) etc., are extracted. Following feature extraction, three datasets were created: Dataset 1 contains all of the extracted features. While Datasets 2 and 3 contain the most relevant features obtained through dimensionality reduction. To analyze the importance of high-dimensional features and their participation in protein-protein interactions, a random forest classifier is trained on three datasets. With dimensionality reduction, the model exhibited exceptional accuracy, indicating that dimensionality reduction fails to capture the complexity of interactions and the underlying relationships between human and viral proteins. As a result of retaining high-dimensional features, it is possible to capture all the characteristics of protein-protein interactions that resemble host-pathogen associations, leading to the development of biologically meaningful models. Our proposed approach is a more realistic and comprehensive classification model, leading to deeper insights and better applications in virology and drug development.

Semi-Supervised Representation Learning for Segmentation on Medical Volumes and Sequences.

Benefiting from the massive labeled samples, deep learning-based segmentation methods have achieved great success for two dimensional natural images. However, it is still a challenging task to segment high dimensional medical volumes and sequences, due to the considerable efforts for clinical expertise to make large scale annotations. Self/semi-supervised learning methods have been shown to improve the performance by exploiting unlabeled data. However, they are still lack of mining local semantic discrimination and exploitation of volume/sequence structures. In this work, we propose a semi-supervised representation learning method with two novel modules to enhance the features in the encoder and decoder, respectively. For the encoder, based on the continuity between slices/frames and the common spatial layout of organs across subjects, we propose an asymmetric network with an attention-guided predictor to enable prediction between feature maps of different slices of unlabeled data. For the decoder, based on the semantic consistency between labeled data and unlabeled data, we introduce a novel semantic contrastive learning to regularize the feature maps in the decoder. The two parts are trained jointly with both labeled and unlabeled volumes/sequences in a semi-supervised manner. When evaluated on three benchmark datasets of medical volumes and sequences, our model outperforms existing methods with a large margin of 7.3% DSC on ACDC, 6.5% on Prostate, and 3.2% on CAMUS when only a few labeled data is available. Further, results on the M&M dataset show that the proposed method yields improvement without using any domain adaption techniques for data from unknown domain. Intensive evaluations reveal the effectiveness of representation mining, and superiority on performance of our method. The code is available at https://github.com/CcchenzJ/BootstrapRepresentation.

Comparison of Contrast-Enhanced 3D Imaging with 2D Imaging in the Evaluation of Perianal Fistula at 3T: A Prospective Observational Study.

Introduction Perianal fistula and its recurrence is a challenging entity for surgeons. It is a well-establi1shed fact that magnetic resonance imaging (MRI) findings influence surgical procedures and reduce the rate of recurrence. In this study, we assessed the contrast-enhanced (CE) three dimensional T1 sequences [sampling perfection with application optimized contrast using different flip angle evolution (SPACE) and volumetric interpolated breath-hold examination (VIBE)] in a 3T MRI system to evaluate perianal fistulas and compared them with two-dimensional (2D) sequences. Materials and Methods Forty-four patients (mean age, 38.8 ± 15.3 [standard deviation]; 32 males, 12 females) with perianal fistula were included in this prospective study. The patients underwent conventional noncontrast, 2D sequences, diffusion-weighted imaging, followed by postcontrast, 2D T1 images in both axial and coronal planes, and 3D sequences at 3T. Acquisition times were recorded for each sequence. Each postcontrast sequence was evaluated in terms of image quality, presence of artifacts, fistula type, presence of an abscess, visibility, and number of internal orifices. The surgical findings were considered the gold standard. The imaging findings were compared with the surgical findings. Results In all three sequences, the fistula type and abscess were identified correctly in all patients. The sensitivity value for identification of ramifications utilizing CE 3D T1 VIBE sequence, CE 3D T1 SPACE, and CE 2D T1 images was 100, 86, and 36%, respectively. The number of internal orifices was identified by the CE 3D T1 VIBE and CE 3D T1 SPACE sequences in 100 and 92% of patients, respectively. CE 2D T1 images correctly identified internal orifices in 80% of patients. The overall scan time for each 3D sequence was shorter than for the combined postcontrast 2D sequences. Conclusion CE 3D T1 SPACE and CE 3D T1 VIBE sequences outperformed conventional CE 2D sequences in the evaluation of perianal fistulas in terms of visibility and the number of internal orifices with a shorter scanning time. Among the 3D sequences, CE 3D T1 VIBE is slightly superior to CE 3D T1 SPACE sequence.

Infant formula containing large, milk phospholipid-coated lipid droplets and dairy lipids affects cognitive performance at school age.

Breastfeeding has been positively associated with infant and child neurocognitive development and function. Contributing to this effect may be differences between human milk and infant formula in the milk lipid composition and milk fat globule structure. To evaluate the effects of an infant formula mimicking human milk lipid composition and milk fat globule structure on childhood cognitive performance. In a randomized, controlled trial, healthy term infants received until 4 months of age either a Standard infant formula (n = 108) or a Concept infant formula (n = 115) with large, milk phospholipid coated lipid droplets and containing dairy lipids. A breastfed reference group (n = 88) was included. Erythrocyte fatty acid composition was determined at 3 months of age. Neurocognitive function was assessed as exploratory follow-up outcome at 3, 4, and 5 years of age using the Flanker test, Dimensional Change Card Sort (DCCS) test and Picture Sequence Memory test from the National Institutes of Health Toolbox Cognition Battery. Mann-Whitney U test and Fisher exact test were used to compare groups. Erythrocyte omega-6 to -3 long-chain polyunsaturated fatty acid ratio appeared to be lower in the Concept compared to the Standard group (P = 0.025). At age 5, only the Concept group was comparable to the Breastfed group in the highest reached levels on the Flanker test, and the DCCS computed score was higher in the Concept compared to the Standard group (P = 0.021). These outcomes suggest that exposure to an infant formula mimicking human milk lipid composition and milk fat globule structure positively affects child neurocognitive development. Underlying mechanisms may include a different omega-3 fatty acid status during the first months of life. https://onderzoekmetmensen.nl/en/trial/28614, identifier NTR3683 and NTR5538.

On higher dimensional Poissonian pair correlation

In this article we study the pair correlation statistic for higher dimensional sequences. We show that for any d≥2, strictly increasing sequences (an(1)),…,(an(d)) of natural numbers have metric Poissonian pair correlation with respect to sup-norm if their joint additive energy is O(N3−δ) for any δ>0. Further, in dimension two, we establish an analogous result with respect to the 2-norm. As a consequence, it follows that ({nα},{n2β}) and ({nα},{[nlogA⁡n]β}) (A∈[1,2]) have Poissonian pair correlation for almost all (α,β)∈R2 with respect to sup-norm and 2-norm. This gives a negative answer to the question raised by Hofer and Kaltenböck [15]. The proof uses estimates for ‘Generalized’ GCD-sums.

Identification of transcriptional programs using dense vector representations defined by mutual information with GeneVector

Deciphering individual cell phenotypes from cell-specific transcriptional processes requires high dimensional single cell RNA sequencing. However, current dimensionality reduction methods aggregate sparse gene information across cells, without directly measuring the relationships that exist between genes. By performing dimensionality reduction with respect to gene co-expression, low-dimensional features can model these gene-specific relationships and leverage shared signal to overcome sparsity. We describe GeneVector, a scalable framework for dimensionality reduction implemented as a vector space model using mutual information between gene expression. Unlike other methods, including principal component analysis and variational autoencoders, GeneVector uses latent space arithmetic in a lower dimensional gene embedding to identify transcriptional programs and classify cell types. In this work, we show in four single cell RNA-seq datasets that GeneVector was able to capture phenotype-specific pathways, perform batch effect correction, interactively annotate cell types, and identify pathway variation with treatment over time.

Estimation problem for continuous time stochastic processes with periodically correlated increments

We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve the problem, we construct a corresponding to the process sequence of stochastic functions which forms an infinite dimensional vector stationary increment sequence. In the case of known spectral density of the stationary increment sequence, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas determining the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where the sets of admissible spectral densities are given.

Two dimensional Gaussian Pell sequences

"In this study firstly we carried out the Pell sequence to the complex plane, then we defined the sequence into two dimensions. We called this generalized sequence two dimensional gaussian Pell sequence. We investigated the Binet formula, generating function, sum formula, explicit closed formula, and some relations between Pell sequences. Also, we get a matrix equality for obtaining elements of the two-dimensional gaussian Pell sequence. "

On Structured Random Matrices Defined by Matrix Substitutions

The structure of the random matrices introduced in this work is given by deterministic matrices—the skeletons of the random matrices—built with an algorithm of matrix substitutions with entries in a finite field of integers modulo some prime number, akin to the algorithm of one dimensional automatic sequences. A random matrix has the structure of a given skeleton if to the same number of an entry of the skeleton, in the finite field, it corresponds a random variable having, at least, as its expected value the correspondent value of the number in the finite field. Affine matrix substitutions are introduced and fixed point theorems are proven that allow the consideration of steady states of the structure which are essential for an efficient observation. For some more restricted classes of structured random matrices the parameter estimation of the entries is addressed, as well as the convergence in law and also some aspects of the spectral analysis of the random operators associated with the random matrix. Finally, aiming at possible applications, it is shown that there is a procedure to associate a canonical random surface to every random structured matrix of a certain class.

CD25 targeting with the afucosylated human IgG1 antibody RG6292 eliminates regulatory T cells and CD25+ blasts in acute myeloid leukemia.

Acute Myeloid leukemia is a heterogeneous disease that requires novel targeted treatment options tailored to the patients' specific microenvironment and blast phenotype. We characterized bone marrow and/or blood samples of 37 AML patients and healthy donors by high dimensional flow cytometry and RNA sequencing using computational analysis. In addition, we performed ex vivo ADCC assays using allogeneic NK cells isolated from healthy donors and AML patient material to test the cytotoxic potential of CD25 Mab (also referred to as RG6292 and RO7296682) or isotype control antibody on regulatory T cells and CD25+ AML cells. Bone marrow composition, in particular the abundance of regulatory T cells and CD25 expressing AML cells, correlated strongly with that of the blood in patients with time-matched samples. In addition, we observed a strong enrichment in the prevalence of CD25 expressing AML cells in patients bearing a FLT3-ITD mutation or treated with a hypomethylating agent in combination with venetoclax. We adopted a patient-centric approach to study AML clusters with CD25 expression and found it most highly expressed on immature phenotypes. Ex vivo treatment of primary AML patient samples with CD25 Mab, a human CD25 specific glycoengineered IgG1 antibody led to the specific killing of two different cell types, CD25+ AML cells and regulatory T cells, by allogeneic Natural Killer cells. The in-depth characterization of patient samples by proteomic and genomic analyses supported the identification of a patient population that may benefit most by harnessing CD25 Mab's dual mode of action. In this pre-selected patient population, CD25 Mab could lead to the specific depletion of regulatory T cells, in addition to leukemic stem cells and progenitor-like AML cells that are responsible for disease progression or relapse.