Partial Assignment Research Articles

Hierarchical Graph Neural Network: A Lightweight Image Matching Model with Enhanced Message Passing of Local and Global Information in Hierarchical Graph Neural Networks

Graph Neural Networks (GNNs) have gained popularity in image matching methods, proving useful for various computer vision tasks like Structure from Motion (SfM) and 3D reconstruction. A well-known example is SuperGlue. Lightweight variants, such as LightGlue, have been developed with a focus on stacking fewer GNN layers compared to SuperGlue. This paper proposes the h-GNN, a lightweight image matching model, with improvements in the two processing modules, the GNN and matching modules. After image features are detected and described as keypoint nodes of a base graph, the GNN module, which primarily aims at increasing the h-GNN’s depth, creates successive hierarchies of compressed-size graphs from the base graph through a clustering technique termed SC+PCA. SC+PCA combines Principal Component Analysis (PCA) with Spectral Clustering (SC) to enrich nodes with local and global information during graph clustering. A dual non-contrastive clustering loss is used to optimize graph clustering. Additionally, four message-passing mechanisms have been proposed to only update node representations within a graph cluster at the same hierarchical level or to update node representations across graph clusters at different hierarchical levels. The matching module performs iterative pairwise matching on the enriched node representations to obtain a scoring matrix. This matrix comprises scores indicating potential correct matches between the image keypoint nodes. The score matrix is refined with a ‘dustbin’ to further suppress unmatched features. There is a reprojection loss used to optimize keypoint match positions. The Sinkhorn algorithm generates a final partial assignment from the refined score matrix. Experimental results demonstrate the performance of the proposed h-GNN against competing state-of-the-art (SOTA) GNN-based methods on several image matching tasks under homography, estimation, indoor and outdoor camera pose estimation, and 3D reconstruction on multiple datasets. Experiments also demonstrate improved computational memory and runtime, approximately 38.1% and 26.14% lower than SuperGlue, and an average of about 6.8% and 7.1% lower than LightGlue. Future research will explore the effects of integrating more recent simplicial message-passing mechanisms, which concurrently update both node and edge representations, into our proposed model.

Finding and exploring promising search space for The 0–1 Multidimensional Knapsack Problem

The 0–1, Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact algorithm to solve the 0–1 MKP. It maintains a set of solutions and utilizes the information from the population to extract good partial assignments. To find high-quality solutions, an exact algorithm is applied to explore the promising search space specified by the good partial assignments. The new solutions are used to update the population. Thus, the good partial assignments evolve towards a better direction with the improvement of the population. Extensive experimentation with commonly used benchmark sets shows that our algorithm outperforms the state-of-the-art heuristic algorithms, TPTEA and DQPSO, as well as the commercial solver CPlex. It finds better solutions than the existing algorithms and provides new lower bounds for 10 large and hard instances.

Alterations in methylation and SNPs of OPRM1 gene show lack of association with heroin (nyaope) consumption in South African males of African ancestry

Nyaope is a highly addictive heroin derivative that elicits its effects via the -opioid receptor. Gene mutations and (cytosine-phospho-guanosine) CpG methylation, alter the function of the -opioid receptor gene (OPRM1) and protein. The single nucleotide polymorphisms (SNPs) rs1799971 (118 A>G) and intronic rs3778150 (T>C) in the OPRM1 have previously been associated with heroin use. The SNP rs1799971 can influence methylation levels of OPRM1 and alter mRNA and protein expression. This study compared the degree of OPRM1 methylation and allele frequency of SNPs rs1799971 and rs3778150 in black South African male nyaope users (n=200) to age-and gender-matched controls (n=55).DNA was extracted from whole blood samples, and analysed by methylation-specific PCR and sequencing to determine methylation frequencies across 29 CpGs within the OPRM1promoter gene region. SNPsrs1799971 (118 A>G) and rs3778150 (T>C) were assessed using SNP genotyping Taqman assays.Using a positive methylation assignment method, most CpGs were significantly more unmethylated in nyaope users than in controls. Using a partial methylation assignment method, most CpGs displayed significantly higher percentages of partial methylation in nyaope users than in controls. The AG genotype frequency for SNP (118 A>G), was higher in controls than in nyaope users while other genotypes (AA & GG) for SNP rs1799971 and (TT, CT, CC) SNP rs3778150 were broadly similar in both groups. There was no correlation observed between nyaope consumption and the presence of SNP rs1799971 and/or rs3778150 in the study populations.This study provided evidence that methylation may not be associated with the intake of nyaope and that SNPs rs1799971 and rs3778150 did not alter the methylation status of the OPRM1 promoter gene or contribute to nyaope addiction in a black South African male population.

Backdoor DNFs

We introduce backdoor DNFs, as a tool to measure the theoretical hardness of CNF formulas. Like backdoor sets and backdoor trees, backdoor DNFs are defined relative to a tractable class of CNF formulas. Each conjunctive term of a backdoor DNF defines a partial assignment that moves the input CNF formula into the base class. Backdoor DNFs are more expressive and potentially smaller than their predecessors backdoor sets and backdoor trees. We establish the fixed-parameter tractability of the backdoor DNF detection problem. Our results hold for the fundamental base classes Horn and 2CNF, and their combination. We complement our theoretical findings by an empirical study. Our experiments show that backdoor DNFs provide a significant improvement over their predecessors.

Adaptive Optimal Terminal Sliding Mode Control for T-S Fuzzy-Based Nonlinear Systems

This study utilizes the Takagi–Sugeno fuzzy model to represent a subset of nonlinear systems and presents an innovative adaptive approach for optimal dynamic terminal sliding mode control (TSMC). The systems under consideration encompass bounded uncertainties in parameters and actuators, as well as susceptibility to external disturbances. Performance evaluation entails the design of an adaptive terminal sliding surface through a two-step process. Initially, a state feedback gain and controller are developed using Linear Matrix Inequality (LMI) techniques, grounded on H2-performance and partial eigenstructure assignment. Dynamic sliding gain is subsequently attained via convex optimization, leveraging the derived state feedback gain and the designed terminal sliding mode (TSM) controller. This approach diverges from conventional methods by incorporating control effort and estimating actuator uncertainty bounds, while also addressing sliding surface and TSM controller design intricacies. The TSM controller is redefined into a strict feedback form, rendering it suitable for addressing output-tracking challenges in nonlinear systems. Comparative simulations validate the effectiveness of the proposed TSM controller, emphasizing its practical applicability.

Partial Eigenvalues Assignment in Singular Systems Using Brauer and Rado Eigenvalue Embedding for Impulse Elimination

Abstract A partial infinite eigenvalues assignment for singular systems is proposed, inspired by the well-known Brauer theorem for eigenvalue embedding. Removal of infinite eigenvalues is a frequent practice in mechanical systems, for instance, to avoid impulsive acceleration and dangerous jerk of the system degrees-of-freedom with null or highly unbalanced mass. Recent efforts were delivered to extend the Brauer theorem to the generalized singular regular eigenvalue problem. However, removing infinite eigenvalues is treated as a particular example by taking the reciprocal pencil and removing its null eigenvalues. In this note, proof for partial infinite eigenvalues removal is made directly in the original regular singular pencil by updating the descriptor matrix, with no need to take the reciprocal pencil. Multi-step and single-step procedures for impulsive response elimination using Brauer’s and Rado’s type finite eigenvalues embedding are presented. The obtained results are effective, as illustrated in a numerical example.

Robust partial quadratic pole assignment of asymmetric systems using receptances

Robust partial quadratic pole assignment of asymmetric systems using receptances

Minimum norm partial eigenstructure assignment approach for vibration system with time delay

AbstractIn this paper, the minimum norm partial eigenstructure assignment problems (PESAPs) in vibration system with time delay is studied via acceleration‐velocity‐displacement active control. A new explicit solution is given for solving PESAPs using orthogonality relations of symmetric vibration system. A new constructive technique is presented to solve the PESAPs in vibration system with time delay by singular value decomposition method. An optimization algorithm is proposed to solve the minimum norm PESAPs by a quasi‐Newton optimization method. The proposed algorithm works without using the knowledge of receptance matrices and without solving the Sylvester equation. The effectiveness of the proposed algorithm is verified by the results of two numerical examples.

Partial quadratic eigenvalue assignment for vibration systems using receptances and system matrices

In this paper, we consider the partial quadratic eigenvalue assignment problem (PQEAP) for vibration system by active feedback control, such that some “troublesome” eigenpairs are replaced by some suitable chosen or newly measured ones, while the remaining unknown eigenpairs are kept unchanged. With the assumptions that the mass and stiffness matrices are nonsingular, we give a new proof of the spectral decomposition of quadratic symmetric pencil. And then we provide some necessary and sufficient conditions of the feedback matrices so that the closed-loop can preserve the no spill-over property. With these conditions, we characterize a set of parametric solutions to the PQEAP using receptances, system matrices and a few open-loop eigenpairs. Finally, we propose a gradient-based optimization method for solving the minimum norm solution to the PQEAP. Numerical experiments illustrate the effectiveness and robustness of the proposed algorithm.

A robust regional eigenvalue assignment problem using rank-one control for undamped gyroscopic systems

<abstract><p>Considering the advantages of economic benefit and cost reduction by using rank-one control, we investigated the problem of robust regional eigenvalue assignment using rank-one control for undamped gyroscopic systems. Based on the orthogonality relation, we presented a method for solving partial eigenvalue assignment problems to reassign partial undesired eigenvalues accurately. Since it is difficult to achieve robust control by assigning desired eigenvalues to precise positions with rank-one control, we assigned eigenvalues within specified regions to provide the necessary freedom. According to the sensitivity analysis theories, we derived the sensitivity of closed-loop eigenvalues to parameter perturbations to measure robustness and proposed a numerical algorithm for solving robust regional eigenvalue assignment problems so that the closed-loop eigenvalues were insensitive to parameter perturbations. Numerical experiments demonstrated the effectiveness of our method.</p></abstract>

Partial Singular Value Assignment for Large-Scale Systems

The partial singular value assignment problem stems from the development of observers for discrete-time descriptor systems and the resolution of ordinary differential equations. Conventional techniques mostly utilize singular value decomposition, which is unfeasible for large-scale systems owing to their relatively high complexity. By calculating the sparse basis of the null space associated with some orthogonal projections, the existence of the matrix in partial singular value assignment is proven and an algorithm is subsequently proposed for implementation, effectively avoiding the full singular value decomposition of the existing methods. Numerical examples exhibit the efficiency of the presented method.

MT-MAG: Accurate and interpretable machine learning for complete or partial taxonomic assignments of metagenomeassembled genomes.

We propose MT-MAG, a novel machine learning-based software tool for the complete or partial hierarchically-structured taxonomic classification of metagenome-assembled genomes (MAGs). MT-MAG is alignment-free, with k-mer frequencies being the only feature used to distinguish a DNA sequence from another (herein k = 7). MT-MAG is capable of classifying large and diverse metagenomic datasets: a total of 245.68 Gbp in the training sets, and 9.6 Gbp in the test sets analyzed in this study. In addition to complete classifications, MT-MAG offers a "partial classification" option, whereby a classification at a higher taxonomic level is provided for MAGs that cannot be classified to the Species level. MT-MAG outputs complete or partial classification paths, and interpretable numerical classification confidences of its classifications, at all taxonomic ranks. To assess the performance of MT-MAG, we define a "weighted classification accuracy," with a weighting scheme reflecting the fact that partial classifications at different ranks are not equally informative. For the two benchmarking datasets analyzed (genomes from human gut microbiome species, and bacterial and archaeal genomes assembled from cow rumen metagenomic sequences), MT-MAG achieves an average of 87.32% in weighted classification accuracy. At the Species level, MT-MAG outperforms DeepMicrobes, the only other comparable software tool, by an average of 34.79% in weighted classification accuracy. In addition, MT-MAG is able to completely classify an average of 67.70% of the sequences at the Species level, compared with DeepMicrobes which only classifies 47.45%. Moreover, MT-MAG provides additional information for sequences that it could not classify at the Species level, resulting in the partial or complete classification of 95.13%, of the genomes in the datasets analyzed. Lastly, unlike other taxonomic assignment tools (e.g., GDTB-Tk), MT-MAG is an alignment-free and genetic marker-free tool, able to provide additional bioinformatics analysis to confirm existing or tentative taxonomic assignments.

Robust and minimum norm dynamic compensator design for partial eigenvalues assignment problems in singular vibration systems

This paper considers robust and minimum norm dynamic compensator design for studying partial eigenvalues assignment problems in singular vibration systems. The new partial eigenvalues assignment methods are proposed by using dynamic compensator. The parametric dynamic compensator expressions are derived for solving partial eigenvalues assignment problems using the corresponding characteristic equations and no spill property. Quadrature rectangle decomposition method is adopted to design the dynamic compensator gains. The optimal energy consumption control problem is discussed by designing the minimum norm dynamic compensator in singular vibration systems. A new gradient-based optimization method is proposed to discuss the robust and minimum dynamic compensator design by establishing the gradient formulas of objective functions. Simulation examples are provided to verify the main results.

Partial Eigenstructure Assignment for Linear Time-Invariant Systems via Dynamic Compensator

This article studies the partial eigenstructure assignment (PEA) problem for a type of linear time-invariant (LTI) system. By introducing a dynamic output feedback controller, the closed-loop system is similar to a given arbitrary constant matrix, so the desired closed-loop eigenstructure can be obtained. Different from the normal eigenstructure assignment, only a part of the left and right generalized eigenvectors is assigned to the closed-loop system to remove complicated constraints, which reflects the partial eigenstructure assignment. Meanwhile, based on the solutions to the generalized Sylvester equations (GSEs), two arbitrary parameter matrices representing the degrees of freedom are presented to obtain the parametric form of the coefficient matrices of the dynamic compensator and the partial eigenvector matrices. Finally, an illustrative example and the simulation results prove the excellent effectiveness and feasibility of parametric method we proposed.

Finding Good Partial Assignments during Restart-Based Branch and Bound Search

Restart-based Branch-and-Bound Search (BBS) is a standard algorithm for solving Constraint Optimization Problems (COPs). In this paper, we propose an approach to find good partial assignments to jumpstart search at each restart for general COPs, which are identified by comparing different best solutions found in different restart runs. We consider information extracted from historical solutions to evaluate the quality of the partial assignments. Thus the good partial assignments are dynamically updated as the current best solution evolves. Our approach makes restart-based BBS explore different promising sub-search-spaces to find high-quality solutions. Experiments on the MiniZinc benchmark suite show how our approach brings significant improvements to a black-box COP solver equipped with the state of the art search techniques. Our method finds better solutions and proves optimality for more instances.

NMR resonance assignments of 18.5kDa complex of Arabidopsis thalianaDRB7.2:DRB4 interaction domains.

In higher eukaryotes, the dsRNA binding proteins (dsRBPs) assist the corresponding Dicer in the cleavage of dsRNA precursors to effect post-transcriptional gene regulation through RNA interference. In contrast, the DRB7.2:DRB4 complex in Arabidopsis thaliana acts as a potent inhibitor of Dicer-like 3 (DCL3) processing by sequestering endogenous inverted-repeat dsRNA precursors. DRB7.2 possesses a single dsRNA Binding Domain (dsRBD) flanked by unstructured N- and C-terminal regions. Whereas, DRB4 has two concatenated N-terminal dsRBDs and a long unstructured C-terminus harboring a small domain of unidentified function, D3. Here, we present near-complete backbone and partial side chain assignments of the interaction domains, DRB7.2M (i.e., DRB7.2 (71-162)) and DRB4D3 (i.e., DRB4 (294-355)) as a complex. Our findings establish the groundwork for future structural, dynamic, and functional research on DRB7.2 and DRB4, and provide clues for the endo-IR pathway in plants.

A Method for Robust Partial Quadratic Eigenvalue Assignment with Repeated Eigenvalues

Abstract A new method is proposed for robust partial quadratic eigenvalue assignment problem (RPQEAP) with repeated prescribed eigenvalues. We first derive a result on the solution of partial quadratic eigenvalue assignment problem, which leads to the partial Schur form of the close-loop system. Then by minimizing the normality departure of the partial Schur form of the close-loop system, we assign the prescribed eigenvalues step by step such that the close-loop system is as robust as possible. Our method allows the prescribed eigenvalues are repeated. Moreover, the proposed method does not use the unchanged eigenpairs of the open-loop system and avoids transforming the second-order control system to the first-order system. Numerical experiments show that the proposed method is efficient for solving the RPQEAP with repeated eigenvalues.

NMR sample optimization and backbone assignment of a stabilized neurotensin receptor

G protein-coupled receptors (GPCRs) are involved in a multitude of cellular signaling cascades and consequently are a prominent target for pharmaceutical drugs. In the past decades, a growing number of high-resolution structures of GPCRs has been solved, providing unprecedented insights into their mode of action. However, knowledge on the dynamical nature of GPCRs is equally important for a better functional understanding, which can be obtained by NMR spectroscopy. Here, we employed a combination of size exclusion chromatography, thermal stability measurements and 2D-NMR experiments for the NMR sample optimization of the stabilized neurotensin receptor type 1 (NTR1) variant HTGH4 bound to the agonist neurotensin. We identified the short-chain lipid di-heptanoyl-glycero-phosphocholine (DH7PC) as a promising membrane mimetic for high resolution NMR experiments and obtained a partial NMR backbone resonance assignment. However, internal membrane-incorporated parts of the protein were not visible due to lacking amide proton back-exchange. Nevertheless, NMR and hydrogen deuterium exchange (HDX) mass spectrometry experiments could be used to probe structural changes at the orthosteric ligand binding site in the agonist and antagonist bound states. To enhance amide proton exchange we partially unfolded HTGH4 and observed additional NMR signals in the transmembrane region. However, this procedure led to a higher sample heterogeneity, suggesting that other strategies need to be applied to obtain high-quality NMR spectra of the entire protein. In summary, the herein reported NMR characterization is an essential step toward a more complete resonance assignment of NTR1 and for probing its structural and dynamical features in different functional states.

Advances in the Specificity of Mass Spectrometry and Nuclear Magnetic Resonance Spectroscopy Based Structural Characterisation Methods for Synthetic Oligonucleotides

Identity testing is a critical part in the development of a therapeutic synthetic oligonucleotide. Tandem Mass Spectrometry (MS/MS) is commonly used for the analysis of oligonucleotides to obtain structural and sequence information, however there are challenges resulting from chemical modifications introduced to improve their pharmacokinetics and stability. For these structurally complex oligonucleotides, Nuclear Magnetic Resonance (NMR) Spectroscopy has found limited use for characterisation and identity testing, as only partial NMR resonance assignment for oligonucleotides is achieved without isotopic labelling methodologies. Regardless of the choice of method used for oligonucleotide analysis, the specificity is of critical importance. In this work, in-source dissociation mass spectrometry and proton (1H) and carbon (13C) NMR at high temperature were used to analyse danvatirsen, a 16 nucleotide phosphorothioate antisense oligonucleotide, and its closely related switch sequences. Both approaches have shown specificity to distinguish danvatirsen from these similar sequences.

Clarifying the Configuration of Pandamine by an Extensive Spectroscopic Reinvestigation of the Authentic 1964 Sample.

Since its partial configurational assignment in 1964, pandamine has not been isolated or obtained by total synthesis. For decades, different works representing the structure of pandamine for illustrative purposes have lent different configurations to this molecule, causing tenacious confusion about the structure of this ansapeptide. A comprehensive spectroscopic analysis of the authentic pandamine sample led to the complete and unambiguous assignment of its configuration, 59 years after its isolation. In addition to ascertaining and completing the initial structural deductions by a state-of-the-art set of analytical techniques, the purpose of this study is also to clarify the literature in a context in which various erroneous structures have been attributed to pandamine for half a century. While fully in agreement with Goutarel's conclusions, the specific example of pandamine should serve as a cautionary tale to any chemist interested in natural products, encouraging access to initial structural assignments rather than relying solely on subsequent, possibly erroneous, structure depictions of a natural product.