Multidimensional Sequences Research Articles

Exploring the energetic and conformational properties of the sequence space connecting naturally occurring RNA tetraloop receptor motifs.

Folded RNAs contain tertiary contact motifs whose structures and energetics are conserved across different RNAs. The transferable properties of RNA motifs simplify the RNA folding problem, but measuring energetic and conformational properties of many motifs remains a challenge. Here, we use a high-throughput thermodynamic approach to investigate how sequence changes alter the binding properties of naturally-occurring motifs, the GAAA tetraloop•tetraloop receptor (TLR) interactions. We measured the binding energies and conformational preferences of TLR sequences that span mutational pathways from the canonical 11ntR to two other natural TLRs, the IC3R and Vc2R. While the IC3R and Vc2R share highly similar energetic and conformational properties, the landscapes that map the sequence changes for their conversion from the 11ntR to changes in these properties differ dramatically. Differences in the energetic landscapes stem from the mutations needed to convert the 11ntR to the IC3R and Vc2R rather than a difference in the intrinsic energetic architectures of these TLRs. The conformational landscapes feature several non-native TLR variants with conformational preferences that differ from both the initial and final TLRs; these species represent potential branching points along the multidimensional sequence space to sequences with greater fitness in other RNA contexts with alternative conformational preferences. Our high-throughput, quantitative approach reveals the complex nature of sequence-fitness landscapes and leads to models for their molecular origins. Systematic and quantitative molecular approaches provide critical insights into understanding the evolution of natural RNAs as they traverse complex landscapes in response to selective pressures.

Correction: Hosvd-tmpe: an extrapolation method for multidimensional sequences

Correction: Hosvd-tmpe: an extrapolation method for multidimensional sequences

Parameter probabilistic prediction for satellite power system based on unsupervised multi-dimensional sequence segmentation

With the increasing operational autonomy and mission complexity of satellites, the power system, as one of the most critical subsystems in a satellite platform, needs to provide high-quality and fast-response power output under complex load requirements. State monitoring is valuable to ensure the power system's stable and safe operation. Monitoring and predicting the key parameters based on the satellite power system's telemetry data are meaningful in detecting potential anomalies. However, the multi-physical high-dimensional telemetry data of the satellite power system are oriented to the operating conditions. The dynamic operating conditions of the satellite power system make it difficult to establish the proper parameter prediction model with high adaptability. To address these challenging issues, this paper proposes a parameter probabilistic prediction based on unsupervised time series segmentation. Firstly, the telemetry data under dynamic operation conditions are divided based on the unsupervised dynamic factor model and K-Means algorithm. The dynamic factor model is used to extract the common factor sequences of the multidimensional telemetry data according to the dynamic relationship between different parameters, followed by the clustering operation using K-Means to classify the multidimensional telemetry data into different sub-sequences. Secondly, a probabilistic prediction method based on the spatio-temporal fusion of multi-physical parameters is proposed. The method utilizes a Bayesian neural network to learn the spatial relationship between parameters and applies Gaussian process regression to establish the temporal dependence of parameters. Afterward, a specific strategy is utilized to fuse the prediction results of the two, thus realizing the fusion of spatio-temporal information of satellite multi-dimensional telemetry data. The experimental results based on the real meteorological satellite power system telemetry data in 2010 show that the average absolute errors of the key parameter predictions after the division of the working conditions are all less than 0.25, which is improved by more than 37.08 % compared with the pre-division. This indicates that the proposed method can well recognize the dynamic operation modes and has a positive advancing effect on the parameter prediction task. Meanwhile, the average absolute error of the proposed prediction method is improved by at least 40.4 % compared with other single prediction models. It shows that the method proposed in this paper can realize high-precision prediction of parameters, and has good application prospects in condition monitoring and anomaly detection of satellite power systems.

Molecular insights into titin’s A-band

The thick filament-associated A-band region of titin is a highly repetitive component of the titin chain with important scaffolding properties that support thick filament assembly. It also has a demonstrated link to human disease. Despite its functional significance, it remains a largely uncharacterized part of the titin protein. Here, we have performed an analysis of sequence and structure conservation of A-band titin, with emphasis on poly-FnIII tandem components. Specifically, we have applied multi-dimensional sequence pairwise similarity analysis to FnIII domains and complemented this with the crystallographic elucidation of the 3D-structure of the FnIII-triplet A84-A86 from the fourth long super-repeat in the C-zone (C4). Structural models serve here as templates to map sequence conservation onto super-repeat C4, which we show is a prototypical representative of titin’s C-zone. This templating identifies positionally conserved residue clusters in C super-repeats with the potential of mediating interactions to thick-filament components. Conservation localizes to two super-repeat positions: Ig domains in position 1 and FnIII domains in position 7. The analysis also allows conclusions to be drawn on the conserved architecture of titin’s A-band, as well as revisiting and expanding the evolutionary model of titin’s A-band.

Reconstruction of multidimensional digital signals

We study the reconstruction of multidimensional digital signals in multirate digital signal processing. We show that the composition of sampling operator and interpolation operator forms the frame operator of multivariate discrete time wavelet (MDTW) system of scale matrix [Formula: see text]. By taking a collection of [Formula: see text] filters, we construct dual MDTW tight frames. Also, we discuss the existence and construction of MDTW Parseval frames in multidimensional sequence space. The necessary and sufficient condition for the existence of orthonormal basis of scale matrix [Formula: see text] is discussed. Using dual MDTW tight frame, we characterize biorthogonal pair of Riesz bases. Further, we define multivariate Parseval frame of weighted exponentials, dual multivariate tight frame of weighted exponentials of scale matrix [Formula: see text] in periodic space [Formula: see text]. Finally, we give the applications of MDTW frames in the theory of frames of weighted exponentials of scale matrix [Formula: see text] in periodic space [Formula: see text].

A Novel Method for AI-Assisted INS/GNSS Navigation System Based on CNN-GRU and CKF during GNSS Outage

In the fields of positioning and navigation, the integrated inertial navigation system (INS)/global navigation satellite systems (GNSS) are frequently employed. Currently, high-precision INS typically utilizes fiber optic gyroscopes (FOGs) and quartz flexural accelerometers (QFAs) rather than MEMS sensors. But when GNSS signals are not available, the errors of high-precision INS also disperse rapidly, similar to MEMS-INS when GNSS signals would be unavailable for a long time, leading to a serious degradation of the navigation accuracy. This paper presents a new AI-assisted method for the integrated high-precision INS/GNSS navigation system. The position increments during GNSS outage are predicted by the convolutional neural network-gated recurrent unit (CNN-GRU). In the process, the CNN is utilized to quickly extract the multi-dimensional sequence features, and GRU is used to model the time series. In addition, a new real-time training strategy is proposed for practical application scenarios, where the duration of the GNSS outage time and the motion state information of the vehicle are taken into account in the training strategy. The real road test results verify that the proposed algorithm has the advantages of high prediction accuracy and high training efficiency.

CRISPR-OTE: Prediction of CRISPR On-Target Efficiency Based on Multi-Dimensional Feature Fusion

ObjectiveClustered Regularly Interspaced Short Palindromic Repeats (CRISPR) is a powerful genome editing technology. Guide RNA (gRNA) plays an essential guiding role in the CRISPR system by complementary base pairing with target DNA. Since the CRISPR targeting mechanism problem has not yet been fully resolved, it remains a challenge to predict gRNA on-target efficiency. Current gRNA design tools often lack efficient information extraction and cannot learn the target efficiency patterns thoroughly. Material and methodsIn this study, CRISPR-OTE is proposed to consider both multi-dimensional sequence information and important complementary prior knowledge based on a simple but effective framework. CRISPR-OTE consists of the local-contextual information branch and the prior knowledge branch. The local-contextual information branch extracts multi-dimensional sequence features from the DNA primary sequence by a parallel framework of Convolutional Neural Networks (CNN) and bidirectional Long Short-Term Memory networks (biLSTM). The prior knowledge branch selects the optimal subset of physicochemical features to provide the neural network with complementary knowledge, such as complex secondary structures. A simple feature fusion strategy is also adopted to fully utilize multi-modal data from the two branches. ResultsThe experimental results show that the optimal subset of physicochemical features (RNA secondary structure and melting temperature of 34nt target) can effectively improve the prediction performance. Additionally, combining multi-dimensional sequence features and multi-modal features can extract information more comprehensively. Through transfer learning, CRISPR-OTE trained on the CRISPR-Cpf1 system can also be successfully applied to the CRISPR-Cas9 system. ConclusionThe performance of CRISPR-OTE is superior to other methods in different CRISPR systems and species. Therefore, CRISPR-OTE is a simple on-target efficiency prediction framework with better accuracy and generalization performance.

Mid- to Long-Term Electric Load Forecasting Based on the EMD–Isomap–Adaboost Model

Accurate load forecasting is an important issue for the reliable and efficient operation of a power system. In this study, a hybrid algorithm (EMDIA) that combines empirical mode decomposition (EMD), isometric mapping (Isomap), and Adaboost to construct a prediction mode for mid- to long-term load forecasting is developed. Based on full consideration of the meteorological and economic factors affecting the power load trend, the EMD method is used to decompose the load and its influencing factors into multiple intrinsic mode functions (IMF) and residuals. Through correlation analysis, the power load is divided into fluctuation term and trend term. Then, the key influencing factors of feature sequences are extracted by Isomap to eliminate the correlations and redundancy of the original multidimensional sequences and reduce the dimension of model input. Eventually, the Adaboost prediction method is adopted to realize the prediction of the electrical load. In comparison with the RF, LSTM, GRU, BP, and single Adaboost method, the prediction obtained by this proposed model has higher accuracy in the mean absolute percentage error (MAPE), mean absolute error (MAE), root mean square error (RMSE), and determination coefficient (R2). Compared with the single Adaboost algorithm, the EMDIA reduces MAE by 11.58, MAPE by 0.13%, and RMSE by 49.93 and increases R2 by 0.04.

Quantifying Uncertainty of Damage in Composites Using a Quasi Monte Carlo Technique

Abstract Property variations in a structure strongly impact the macroscopic mechanical performance as regions with lower strength will be prone to damage initiation or acceleration. Consideration of the variability in material property is critical for high-resolution simulations of damage initiation and propagation. While the recent progressive damage analyses consider randomness in property fields, accurately quantifying the uncertainty in damage measures remains computationally expensive. Stochastic damage analyses require extensive sampling of random property fields and numerous replications of the underlying nonlinear deterministic simulations. This paper demonstrates that a Quasi-Monte Carlo (QMC) method, which uses a multidimensional low discrepancy sobol sequence, is a computationally economical way to obtain the mean and standard deviations in cracks evolving in composites. An extended finite element method (XFEM) method with spatially random strength fields simulates the damage initiation and evolution in a model composite. We compared the number of simulations required for Monte Carlo (MC) and QMC techniques to measure the influence of input variability on the mean crack-length in an open-hole angle-ply tensile test. We conclude that the low discrepancy sampling and QMC technique converges substantially faster than traditional MC methods.

The algorithm of current prediction based on multi-dimensional Long Short Term Memory networks

Precisely predict the current on the node circuit in advance, which can facilitate the manager to manage and control the risk in advance. The current, voltage, residual current, cable temperature, ambient temperature, and ambient humidity on the circuit constitute a multi-dimensional sequence characteristic sequence data. This paper proposes an improved Long Short-Term Memory (LSTM) cyclic neural network method, which combines multi-dimensional Train the neural network in a specific way to obtain the LSTM current prediction model. The experiment is validated with the perception data in an intelligent building, and compared with the classic neural network and Recurrent Neural Network (RNN) prediction method. The experimental results show that, compared with the prediction methods such as BP neural network and RNN network, the multi-dimensional LSTM has a higher accuracy in predicting the current in the circuit, and the MSE index is as low as 0.5. And this method can detect potential electrical fire hazards and give early warning 1–2 time intervals in advance to avoid electrical fires.

A feature extraction- and ranking-based framework for electricity spot price forecasting using a hybrid deep neural network

In deregulated electricity markets, reliable electricity market price forecasting is the foundation for making the bidding strategy, operating dispatch control, and hedging volatility risk. However, electricity prices are high-volatile, nonstationary, multi-seasonal, making it difficult to estimate future trends. This paper proposes a hybrid model integrating a deep learning model, feature extraction and feature selection method to forecast short-term electricity prices. In the proposed framework, the ensemble empirical mode decomposition (EEMD) filter is utilized for multi-dimensional sequences, solving hidden characteristic extraction problems. The constructed feature space is identified and ranked under the max-dependency and min-redundancy (MRMR) criterion, improving the accuracy of feature selection. Finally, combining EEMD and MRMR with bidirectional long short-term memory (BiLSTM), a new hybrid framework is designed to improve the efficiency of short-term electricity price forecasting. Case studies on the PJM and New South Wales electricity markets confirm that our model outperforms alternatives on the forecasting accuracy. The average mean absolute percentage error (MAPE) of the proposed model is reduced by 4% to 21% compared to state-of-the-art models for 1-h and 24-h ahead forecasting. The proposed model has achieved relatively higher stability and adaptability in different forecasting steps and can better capture sophisticated fluctuations in electricity prices.

Utility Mining Across Multi-Dimensional Sequences

Knowledge extraction from database is the fundamental task in database and data mining community, which has been applied to a wide range of real-world applications and situations. Different from the support-based mining models, the utility-oriented mining framework integrates the utility theory to provide more informative and useful patterns. Time-dependent sequence data are commonly seen in real life. Sequence data have been widely utilized in many applications, such as analyzing sequential user behavior on the Web, influence maximization, route planning, and targeted marketing. Unfortunately, all the existing algorithms lose sight of the fact that the processed data not only contain rich features (e.g., occur quantity, risk, and profit), but also may be associated with multi-dimensional auxiliary information, e.g., transaction sequence can be associated with purchaser profile information. In this article, we first formulate the problem of utility mining across multi-dimensional sequences, and propose a novel framework named MDUS to extract <underline>M</underline>ulti-<underline>D</underline>imensional <underline>U</underline>tility-oriented <underline>S</underline>equential useful patterns. To the best of our knowledge, this is the first study that incorporates the time-dependent sequence-order, quantitative information, utility factor, and auxiliary dimension. Two algorithms respectively named MDUS EM and MDUS SD are presented to address the formulated problem. The former algorithm is based on database transformation, and the later one performs pattern joins and a searching method to identify desired patterns across multi-dimensional sequences. Extensive experiments are carried on six real-life datasets and one synthetic dataset to show that the proposed algorithms can effectively and efficiently discover the useful knowledge from multi-dimensional sequential databases. Moreover, the MDUS framework can provide better insight, and it is more adaptable to real-life situations than the current existing models.

Research on Grey Relational Clustering Model of Multiobjective Human Resources Based on Time Constraint

The existing grey relational clustering method has limitations in the application of multidimensional sequences and cannot directly calculate the grey correlation degree between unequal-length sequences. In this paper, by introducing the multidimensional dynamic DTW distance into the existing 3D grey relational model, a new grey relational analysis model that can be applied to multidimensional data is proposed, which is based on DTW distance. The model does not require one-to-one correspondence of data points but evaluates the similarity of its geometric curves by calculating the shortest distance between sequences. In addition, since the traditional grey correlation clustering method is implemented, the method first extracts the reference sequence from the observation sequence and then calculates the similarity between the observation objects by calculating the grey correlation degree between each sequence and the reference sequence, so each object only needs to be calculated once. The experimental results show that the multidimensional grey correlation degree based on DTW distance and the grey relational clustering model oriented to multidimensional data are more accurate than other existing methods. Finally, the grey relation clustering method of multidimensional data is used to analyze the multiobjective human resource grey relational clustering model under time constraints, and the validity of the model is verified.

The Rainfall and Meteorological Data Mining Model Based on Multi-Dimensional Precipitation Time Series

In order to study the relationship between rainfall and related meteorological elements in rainy weather, find out the changes of related meteorological elements before and after rainfall, a multi-dimensional time series data mining model is proposed. The model first performs dimension selection pre-processing on the time series of meteorological elements to remove irrelevant and redundant dimensions, then uses the proposed extreme slope piecewise linear fitting method to segment the time series, data compression and eigenvalue extraction, and finally uses k-means clustering algorithm to symbolize the processed multi-dimensional sequence, and uses rules to extract the rainfall weather model. Experimental results show that the model has good practical value.

Snow profile alignment and similarity assessment for aggregating, clustering, and evaluating snowpack model output for avalanche forecasting

Abstract. Snowpack models simulate the evolution of the snow stratigraphy based on meteorological inputs and have the potential to support avalanche risk management operations with complementary information relevant for their avalanche hazard assessment, especially in data-sparse regions or at times of unfavorable weather and hazard conditions. However, the adoption of snowpack models in operational avalanche forecasting has been limited, predominantly due to missing data processing algorithms and uncertainty around model validity. Thus, to enhance the usefulness of snowpack models for the avalanche industry, numerical methods are required that evaluate and summarize snowpack model output in accessible and relevant ways. We present algorithms that compare and assess generic snowpack data from both human observations and models, which consist of multidimensional sequences describing the snow characteristics of grain type, hardness, and age. Our approach exploits Dynamic Time Warping, a well-established method in the data sciences, to match layers between snow profiles and thereby align them. The similarity of the aligned profiles is then evaluated by our independent similarity measure based on characteristics relevant for avalanche hazard assessment. Since our methods provide the necessary quantitative link to data clustering and aggregating methods, we demonstrate how snowpack model output can be grouped and summarized according to similar hazard conditions. By emulating aspects of the human avalanche hazard assessment process, our methods aim to promote the operational application of snowpack models so that avalanche forecasters can begin to build an understanding of how to interpret and trust operational snowpack simulations.

Learning Meta-Distance for Sequences by Learning a Ground Metric via Virtual Sequence Regression.

Distance between sequences is structural by nature because it needs to establish the temporal alignments among the temporally correlated vectors in sequences with varying lengths. Generally, distances for sequences heavily depend on the ground metric between the vectors in sequences to infer the alignments and hence can be viewed as meta-distances upon the ground metric. Learning such meta-distance from multi-dimensional sequences is appealing but challenging. We propose to learn the meta-distance through learning a ground metric for the vectors in sequences. The learning samples are sequences of vectors for which how the ground metric between vectors induces the meta-distance is given. The objective is that the meta-distance induced by the learned ground metric produces large values for sequences from different classes and small values for those from the same class. We formulate the ground metric as a parameter of the meta-distance and regress each sequence to an associated pre-generated virtual sequence w.r.t. the meta-distance, where the virtual sequences for sequences of different classes are well-separated. We develop general iterative solutions to learn both the Mahalanobis metric and the deep metric induced by a neural network for any ground-metric-based sequence distance. Experiments on several sequence datasets demonstrate the effectiveness and efficiency of the proposed methods.

Stimulus-induced sequential activity in supervisely trained recurrent networks of firing rate neurons

In this work, we consider recurrent neural networks of firing rate neurons supervisely trained to generate multidimensional sequences of given configurations. We study dynamical objects in the network multidimensional phase space underlying successfully trained outputs and analyze spatiotemporal neural activity and its features in three cases. First, we consider autonomous generation of complex sequences by output units driven by a recurrent network. Second, we study how input pulses can trigger different output units. Third, we explore the case where input pulses allow us to switch between different sequential activities of output units.

MasterMovelets: discovering heterogeneous movelets for multiple aspect trajectory classification

In the last few years trajectory classification has been applied to many real problems, basically considering the dimensions of space and time or attributes inferred from these dimensions. However, with the explosion of social media data and the advances in the semantic enrichment of mobility data, a new type of trajectory data has emerged, and the trajectory spatio-temporal points have now multiple and heterogeneous semantic dimensions. By semantic dimensions we mean any type of information that is neither spatial nor temporal. As a consequence, new classification methods are needed to deal with this new type of data. The main challenge is how to automatically select and combine the data dimensions and to discover the subtrajectories that better discriminate the class. In this paper we propose MasterMovelets, a new parameter-free method for trajectory classification which finds the best trajectory partition and dimension combination for robust high dimensional trajectory classification. Experimental results show that our approach outperforms state-of-the-art methods by reducing the classification error up to $$63\%$$ , indicating that our proposal is very promising for multidimensional sequence data classification.

Modeling and forecasting the electricity clearing price: A novel BELM based pattern classification framework and a comparative analytic study on multi-layer BELM and LSTM

With the deregulation of power market and the increasing penetration of renewable energy, the core role of demand side management (DSM) has become even more prominent. In this sense, there is an urgent need for all market participants to identify the pivotal aspects of electricity market price fluctuation effectively and anticipate its future trend. For certain applications such as DSM, considering the high volatility and nonlinear of real-time electricity price, we can approximate the interval prediction to achieve the multi-classification that relies on critical pattern recognition of entire category of the price sequence. Therefore, this paper presents a study on the utilization of a novel electricity price classification framework which consists of Bayesian extreme learning machine (BELM) model, minimum redundancy maximum relevance (MRMR) algorithm, and multivariate sequence segmentation (MSS). Considering many advantages of deep learning structure in capturing the hierarchical and sophisticated characteristics of multidimensional sequence, the multi-layer BELM (ML-BELM) model is also extended and utilized to the modeling. To demonstrate the potential of the pattern classification framework, the proposed approaches are evaluated using hourly clearing price cases from Canada Ontario and New York electricity market. In particular, we investigate the performance of different classifiers regarding the 3 multi-classification and higher dimensional classification modes with respect to various scenarios in terms of precision, recall, AUC (Area Under roc Curve) score, and F1-measure indicators. The findings suggest that the proposed pattern classification framework can obtain satisfactory forecasting results provided that suitable scheme is utilized to the pattern segmentation and feature ranking process.

Equidistribution of Farey sequences on horospheres in covers of and applications

We establish the limiting distribution of certain subsets of Farey sequences, i.e., sequences of primitive rational points, on expanding horospheres in covers $\unicode[STIX]{x1D6E5}\backslash \text{SL}(n+1,\mathbb{R})$ of $\text{SL}(n+1,\mathbb{Z})\backslash \text{SL}(n+1,\mathbb{R})$, where $\unicode[STIX]{x1D6E5}$ is a finite-index subgroup of $\text{SL}(n+1,\mathbb{Z})$. These subsets can be obtained by projecting to the hyperplane $\{(x_{1},\ldots ,x_{n+1})\in \mathbb{R}^{n+1}:x_{n+1}=1\}$ sets of the form $\mathbf{A}=\bigcup _{j=1}^{J}\mathbf{a}_{j}\unicode[STIX]{x1D6E5}$, where for all $j$, $\mathbf{a}_{j}$ is a primitive lattice point in $\mathbb{Z}^{n+1}$. Our method involves applying the equidistribution of expanding horospheres in quotients of $\text{SL}(n+1,\mathbb{R})$ developed by Marklof and Strömbergsson, and more precisely understanding how the full Farey sequence distributes in $\unicode[STIX]{x1D6E5}\backslash \text{SL}(n+1,\mathbb{R})$ when embedded on expanding horospheres as done in previous work by Marklof. For each of the Farey sequence subsets, we extend the statistical results by Marklof regarding the full multidimensional Farey sequences, and solutions by Athreya and Ghosh to Diophantine approximation problems of Erdős–Szüsz–Turán and Kesten. We also prove that Marklof’s result on the asymptotic distribution of Frobenius numbers holds for sets of primitive lattice points of the form $\mathbf{A}$.