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The classical extremal function for a graph H , ex (K n , H) is the largest number of edges in a subgraph of K n that contains no subgraph isomorphic to H. Note that defining ex (K n , H − ind) by forbidding induced subgraphs isomorphic to H is not very meaningful for a non-complete H since one can avoid it by considering a clique. For graphs F and H , let ex (K n , { F , H − ind }) be the largest number of edges in an n -vertex graph that contains no subgraph isomorphic to F and no induced subgraph isomorphic to H. Determining this function asymptotically reduces to finding either ex (K n , F) or ex (K n , H) , unless H is a biclique or both F and H are bipartite. Here, we consider the bipartite setting, ex (K n , n , { F , H − ind }) when K n is replaced with K n , n , F is a biclique, and H is a bipartite graph. Our main result, a strengthening of a result by Sudakov and Tomon, implies that for any d ≥ 2 and any K d , d -free bipartite graph H with each vertex in one part of degree either at most d or a full degree, so that there are at most d − 2 full degree vertices in that part, one has ex (K n , n , { K t , t , H − ind }) = o (n 2 − 1 / d). This provides an upper bound on the induced Turán number for a wide class of bipartite graphs and implies in particular an extremal result for bipartite graphs of bounded VC-dimension by Janzer and Pohoata. [ABSTRACT FROM AUTHOR]

ABSTRACT Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition into disjoint colourings, we speak of a packing. However, even for complete bipartite graphs, the list chromatic number can be arbitrarily large, and its exact determination is generally difficult. For the packing variant, this question becomes even harder. In this paper, we study the correspondence‐ and list‐packing numbers of (asymmetric) complete bipartite graphs. In the most asymmetric cases, Latin squares come into play. Our results show that every z ∈ Z + \{ 3 } $z\in {{\mathbb{Z}}}^{+}\backslash \{3\}$ can be equal to the correspondence packing number of a graph. We disprove a recent conjecture that relates the list packing number and the list flexibility number. Additionally, we improve the threshold functions for the correspondence packing variant. [ABSTRACT FROM AUTHOR]

In this paper, we first give some sufficient criteria for normality of monomial ideals. As applications, we show that closed neighborhood ideals of complete bipartite graphs are normal, and hence satisfy the (strong) persistence property. We also prove that dominating ideals of complete bipartite graphs are nearly normally torsion-free. In addition, we show that dominating ideals of h -wheel graphs, under certain condition, are normal. [ABSTRACT FROM AUTHOR]

An edge-coloured path is monochromatic if all of its edges have the same colour. For a k -connected graph G , the monochromatic k -connection number of G , denoted by m c k (G) , is the maximum number of colours in an edge-colouring of G such that, any two vertices are connected by k internally vertex-disjoint monochromatic paths. In this paper, we shall study the parameter m c k (G). We obtain bounds for m c k (G) , for general graphs G. We also compute m c k (G) exactly when k is small, and G is a graph on n vertices, with a spanning k -connected subgraph having the minimum possible number of edges, namely ⌈ k n 2 ⌉. We prove a similar result when G is a bipartite graph. [ABSTRACT FROM AUTHOR]

A bipartite graph G is two-disjoint-cycle-cover edge [ r 1 , r 2 ] -bipancyclic if, for any vertex-disjoint edges u v and x y in G and any even integer ℓ satisfying r 1 ⩽ ℓ ⩽ r 2 , there exist vertex-disjoint cycles C 1 and C 2 such that | V (C 1) | = ℓ , | V (C 2) | = | V (G) | − ℓ , u v ∈ E (C 1) and x y ∈ E (C 2). In this paper, we prove that the n -star graph S n is two-disjoint-cycle-cover edge [ 6 , n ! 2 ] -bipancyclic for n ⩾ 5 , and thus it is two-disjoint-cycle-cover vertex [ 6 , n ! 2 ] -bipancyclic for n ⩾ 5. Additionally, it is examined that S n is two-disjoint-cycle-cover [ 6 , n ! 2 ] -bipancyclic for n ⩾ 4. [ABSTRACT FROM AUTHOR]

For f:R2→R, let ΓR(f) be a two‐dimensional algebraically defined graph, that is, a bipartite graph where each partite set is a copy of R2 and two vertices (a,a2) and [x,x2] are adjacent if and only if a2+x2=f(a,x). It is known that ΓR(XY) has girth 6 and can be extended to the point‐line incidence graph of the classical real projective plane. However, it was unknown whether there exists f∈R[X,Y] such that ΓR(f) has girth 6 and is nonisomorphic to ΓR(XY). This paper answers this question affirmatively and thus provides a construction of a nonclassical real projective plane. This paper also studies the diameter and girth of ΓR(f) for families of bivariate functions f. [ABSTRACT FROM AUTHOR]

We prove that in a connected graph, the distances between non-cut vertices are odd if and only if it is the line graph of a strong unique independence tree. We then show that any such tree can be inductively constructed from stars using a simple operation. Further, we study the connected graphs in which the distances between non-cut vertices are even (shortly, NCE-graphs). Our main results on NCE-graphs are the following: we give a criterion of NCE-graphs, show that any bipartite graph is an induced subgraph of an NCE-graph, characterize NCE-graphs with exactly two leaves, characterize graphs that can be subdivided to NCE-graphs, and provide a characterization for NCE-graphs which are maximal with respect to the edge addition operation. [ABSTRACT FROM AUTHOR]

Statistical analysis of bipartite networks frequently requires randomly sampling from the set of all bipartite networks with the same degree sequence as an observed network. Trade algorithms offer an efficient way to generate samples of bipartite networks by incrementally 'trading' the positions of some of their edges. However, it is difficult to know how many such trades are required to ensure that the sample is random. I propose a stopping rule that focuses on the distance between sampled networks and the observed network, and stops performing trades when this distribution stabilizes. Analyses demonstrate that, for over 650 different degree sequences, using this stopping rule ensures a random sample with a high probability, and that it is practical for use in empirical applications. • Statistical analysis of bipartite networks requires randomly sampling. • It is difficult to determine whether a sample of bipartite networks is random. • The proposed stopping rule yields a random sample over 85% of the time. [ABSTRACT FROM AUTHOR]

An edge e of a matching covered graph G is removable if G−e is also matching covered. The notion of removable edge arises in connection with ear decompositions of matching covered graphs introduced by Lovász and Plummer. A nonbipartite matching covered graph G is a brick if it is free of nontrivial tight cuts. Carvalho, Lucchesi and Murty proved that every brick other than K4 and C6¯ has at least Δ−2 removable edges. A brick G is near‐bipartite if it has a pair of edges {e1,e2} such that G−{e1,e2} is a bipartite matching covered graph. In this paper, we show that in a near‐bipartite brick G with at least six vertices, every vertex of G, except at most six vertices of degree three contained in two disjoint triangles, is incident with at most two nonremovable edges; consequently, G has at least |V(G)|−62 removable edges. Moreover, all graphs attaining this lower bound are characterized. [ABSTRACT FROM AUTHOR]

Geography is a combinatorial game in which two players take turns moving a token along edges of a directed graph and deleting the vertex they came from. We expand upon work by Fox and Geissler, who classified the computational complexity of determining the winner of various Geography variants given a graph. In particular, we show NP-hardness for undirected partizan Geography with free deletion on bipartite graphs and directed partizan Geography with free deletion on acyclic graphs. In addition, we study Kotzig's Nim, a special case of Geography where the vertices are labeled and moves correspond to additions by fixed amounts. We partially resolve a conjecture by Tan and Ward about games with a certain move set. [ABSTRACT FROM AUTHOR]

We correct an error in Theorem 13 in our published article Barik et al. [1]. [ABSTRACT FROM AUTHOR]

A bisection of a graph is a bipartition of its vertex set in which the two parts differ in size by at most 1, and its size is the number of edges which across the two parts. Let G be a graph with n vertices, m edges and degree sequence d 1 , d 2 , ... , d n . Motivated by a few classical results on Max-Cut of graphs, Lin and Zeng proved that if G is { C 4 , C 6 } -free and has a perfect matching, then G has a bisection of size at least m / 2 + Ω (∑ i = 1 n d i ) , and conjectured the same bound holds for C 4 -free graphs with perfect matchings. In this paper, we confirm the conjecture under the additional condition that G is C 5 -free. [ABSTRACT FROM AUTHOR]

For a given graph H , its subdivisions carry the same topological structure. The existence of H -subdivisions within a graph G has deep connections with topological, structural and extremal properties of G. One prominent example of such a connection, due to Bollobás and Thomason and independently Komlós and Szemerédi, asserts that the average degree of G being d ensures a K Ω (d) -subdivision in G. Although this square-root bound is best possible, various results showed that much larger clique subdivisions can be found in a graph for many natural classes. We investigate the connection between crux, a notion capturing the essential order of a graph, and the existence of large clique subdivisions. This reveals the unifying cause underpinning all those improvements for various classes of graphs studied. Roughly speaking, when embedding subdivisions, natural space constraints arise; and such space constraints can be measured via crux. Our main result gives an asymptotically optimal bound on the size of a largest clique subdivision in a generic graph G , which is determined by both its average degree and its crux size. As corollaries, we obtain • a characterization of extremal graphs for which the square-root bound above is tight: they are essentially disjoint unions of graphs having crux size linear in d ; • a unifying approach to find a clique subdivision of almost optimal size in graphs which do not contain a fixed bipartite graph as a subgraph; • and that the clique subdivision size in random graphs G (n , p) witnesses a dichotomy: when p = ω (n − 1 / 2) , the barrier is the space, while when p = o (n − 1 / 2) , the bottleneck is the density. [ABSTRACT FROM AUTHOR]

Characterizing the graph having the maximum or minimum spectral radius in a given class of graphs is a classical problem in spectral extremal graph theory, originally proposed by Brualdi and Solheid. Given a graph G , a vertex subset S is called a maximum generalized 4-independent set of G if the induced subgraph G [ S ] dose not contain a 4-tree as its subgraph, and the subset S has maximum cardinality. The cardinality of a maximum generalized 4-independent set is called the generalized 4-independence number of G. In this paper, we firstly determine the connected graph (resp. bipartite graph, tree) having the largest spectral radius over all connected graphs (resp. bipartite graphs, trees) with fixed order and generalized 4-independence number, in addition, we establish a lower bound on the generalized 4-independence number of a tree with fixed order. Secondly, we describe the structure of all the n -vertex graphs having the minimum spectral radius with generalized 4-independence number ψ , where ψ ⩾ ⌈ 3 n / 4 ⌉. Finally, we identify all the connected n -vertex graphs with generalized 4-independence number ψ ∈ { 3 , ⌈ 3 n / 4 ⌉ , n − 1 , n − 2 } having the minimum spectral radius. • Characterize the extremal graphs having the maximum spectral radius in some given class of graphs. • Establish a sharp lower bound on the generalized 4-independence number of a tree with fixed order. • Describe the structure of connected graphs in terms of generalized 4-independence numbers and spectral radii. [ABSTRACT FROM AUTHOR]

We consider the classic budgeted maximum weight independent set (BMWIS) problem. The input is a graph G = (V , E) , where each vertex v ∈ V has a weight w (v) and a cost c (v) , and a budget B. The goal is to find an independent set S ⊆ V in G such that ∑ v ∈ S c (v) ≤ B , which maximizes the total weight ∑ v ∈ S w (v). Since the problem on general graphs cannot be approximated within ratio | V | 1 − ɛ for any ɛ > 0 , BMWIS has attracted significant attention on graph families for which a maximum weight independent set can be computed in polynomial time. Two notable such graph families are bipartite and perfect graphs. BMWIS is known to be NP-hard on both of these graph families; however, prior to this work, the best possible approximation guarantees for these graphs were wide open. In this paper, we give a tight 2-approximation for BMWIS on perfect graphs and bipartite graphs. In particular, we give a (2 − ɛ) lower bound for BMWIS on bipartite graphs, already for the special case where the budget is replaced by a cardinality constraint, based on the Small Set Expansion Hypothesis (SSEH). For the upper bound, we design a 2-approximation for BMWIS on perfect graphs using a Lagrangian relaxation based technique. Finally, we obtain a tight lower bound for the capacitated maximum weight independent set (CMWIS) problem, the special case of BMWIS where w (v) = c (v) ∀ v ∈ V. We show that CMWIS on bipartite and perfect graphs is unlikely to admit an efficient polynomial-time approximation scheme (EPTAS). Thus, the existing PTAS for CMWIS is essentially the best we can expect. [ABSTRACT FROM AUTHOR]

We present an algorithm that finds a maximum cardinality \(f\) -matching of a simple graph in time \(O(n^{2/3}m)\). Here, \(f:V\to\mathbb{N}\) is a given function and an \(f\) -matching is a subgraph wherein each vertex \(v\in V\) has degree \(\leq f(v)\). This result generalizes a string of algorithms that concentrate on simple bipartite graphs. The bipartite case is based on the notion of level graph, introduced by Dinic for network flow. In general graphs this notion breaks down: Vertices no longer have unique levels, and there are too many levels to analyze the corresponding level graph like bipartite graphs (\(\Theta(n^{2})\) vs. \(n\)). We use "natural" levels to prove properties of shortest augmenting trails (e.g., formulas for trail length). We use "shortened" levels to derive the algorithm's time bound. The algorithm, unmodified, is also efficient on multigraphs, achieving time \(O(\min\{\sqrt{f(V)},n\} m)\) for \(f(V)=\sum_{v}f(v)\). The special case \(f\equiv 1\) shows the algorithm duplicates the classic time bound for maximum cardinality matching, \(O(\sqrt{n} m)\). [ABSTRACT FROM AUTHOR]

Graph neural networks (GNNs) have gained prominence as an effective technique for representation learning and have found wide application in tag recommendation tasks. Existing approaches aim to encode the hidden collaborative information among entities into embedding representations by propagating node information between connected nodes. However, in sparse observable graph structures, a significant number of connections are missing, leading to incomplete and biased propagation. To address these issues, we propose a novel model called Low-frequency Spectral Graph Convolution Networks with one-hop connections information for Personalized Tag Recommendation (LSGCNT). This model utilizes graph convolution in the spectral domain and incorporates a graph structure comprising two bipartite graphs, the user–tag interaction graph and the item–tag interaction graph. Our model aims to reduce information loss caused by propagation by utilizing graph convolution networks with trainable convolution kernels to recover preference information. In order to preserve useful low-frequency signals, we couple graph convolution with low-pass filters in the frequency domain. Through reconstructing the true rating tensor and ranking the tag scores within the tensor, we can achieve top-N recommendations. Furthermore, to preserve the one-hop connection information of the bipartite graphs, we treat the observed two bipartite graphs as two homogeneous graphs, where both users and tags contribute to the convolution of a node in the user–tag graph, and both items and tags contribute to the convolution of a node in the item–tag graph. Lastly, we analyze the impact of different internal components, pooling methods, parameter choices, and prediction approaches of LSGCNT on recommendation performance. Experimental results on two real-world datasets demonstrate that LSGCNT achieves superior recommendation performance compared with eight other state-of-the-art recommendation models. [ABSTRACT FROM AUTHOR]

In order to alleviate the issue of data sparsity, knowledge graphs are introduced into recommender systems because they contain diverse information about items. The existing knowledge graph enhanced recommender systems utilize both user–item interaction data and knowledge graph, but those methods ignore the semantic difference between interaction data and knowledge graph. On the other hand, for the item representations obtained from two kinds of graph structure data respectively, the existing methods of fusing representations only consider the item representations themselves, without considering the personalized preference of users. In order to overcome the limitations mentioned above, we present a recommendation method named Interaction-Knowledge Semantic Alignment for Recommendation (IKSAR). By introducing a semantic alignment module, the semantic difference between the interaction bipartite graph and the knowledge graph is reduced. The representation of user is integrated during the fusion of representations of item, which improves the quality of the fused representation of item. To validate the efficacy of the proposed approach, we perform comprehensive experiments on three datasets. The experimental results demonstrate that the IKSAR is superior to the existing methods, showcasing notable improvement. [ABSTRACT FROM AUTHOR]

Given a graph G , a subset of vertices is called a maximum dissociation set of G if it induces a subgraph with vertex degree at most 1, and the subset has maximum cardinality. The cardinality of a maximum dissociation set is called the dissociation number of G. The adjacency matrix and the degree diagonal matrix of G are denoted by A (G) and D (G) , respectively. In 2017, Nikiforov proposed the A α -matrix: A α (G) = α D (G) + (1 − α) A (G) , where α ∈ [ 0 , 1 ]. The largest eigenvalue of this novel matrix is called the A α -index of G. In this paper, we firstly determine the connected graph (resp. bipartite graph, tree) having the largest A α -index over all connected graphs (resp. bipartite graphs, trees) with fixed order and dissociation number. Secondly, we describe the structure of all the n -vertex graphs having the minimum A α -index with dissociation number τ , where τ ⩾ ⌈ 2 3 n ⌉. Finally, we identify all the connected n -vertex graphs with dissociation number τ ∈ { 2 , ⌈ 2 3 n ⌉ , n − 1 , n − 2 } having the minimum A α -index. [ABSTRACT FROM AUTHOR]

A subset S ⊆ V (G) , where V(G) is the vertex set of a graph G, is a disjunctive total dominating set of G if each vertex has a neighbour in S or has at least two vertices in S at distance two from it. The minimum cardinality of such a set is the disjunctive total domination number. There are some graph modifications on the edge or vertex of a graph, one of which is subdividing an edge. The disjunctive total domination subdivision number of G is the minimum number of edges which must be subdivided (each edge in G can be subdivided exactly once) to increase the disjunctive total domination number. Firstly, we prove that the disjunctive total domination subdivision problem is NP-complete in bipartite graphs. We next establish some bounds on disjunctive total domination subdivision. [ABSTRACT FROM AUTHOR]

Multi-view clustering is widely applied in engineering and scientific research. It helps reveal the underlying structures and correlations behind complex multi-view data. Graph-based multi-view clustering stands as a prominent research frontier within the multi-view clustering field, yet faces persistent challenges. Firstly, typically constructed initial input graphs for each view yields sparse clustering structure, hindering clustering performance. Secondly, as data sources proliferate, algorithms encounter escalating time complexities, notably in methods relying on n × n fully connected graphs. Thirdly, prevailing graph fusion strategies struggle to mitigate the impact of low-quality graphs, impeding overall efficacy. In this paper, we present a novel Multi-View Clustering method based on High-Order Bipartite Graph fusion (MCHBG). For the first two challenges, the introduced high-order bipartite graphs in MCHBG reveal richer clustering structures, effectively alleviating sparse clustering structure of the input graph, while keeping the overall algorithm's computational complexity controlled within O (n). For the third challenge, our graph fusion mechanism selectively integrates high-order bipartite graphs, and implicitly weights the selected bipartite graphs to mitigate the impact of low-quality bipartite graphs. MCHBG learns a structured fusion bipartite graph under the Laplacian rank constraint, which directly indicates the clusters of data. Extensive experimental results demonstrate the effectiveness and superiority of MCHBG. Code available: https://anonymous.4open.science/r/MCHBG. • Multi-view High-order Bipartite Graph Fusion for Enhanced Clustering. • Adaptive Fusion with Truncation Selection and Implicit Weighting • Computational Efficiency and Superiority in Multi-View Clustering. [ABSTRACT FROM AUTHOR]

Topological indices are mathematical descriptors used in the field of chemistry to characterize the topological structure of chemical compounds. The Randić index (R), the geometric–arithmetic index (G A), and the arithmetic–geometric index (A G) represent three widely recognized topological indices. In most scenarios, the properties of A G and G A exhibit opposing tendencies. Furthermore, it is observed that, A G (G) > R (G) and G A (G) > R (G) for any given graph G. Our focus is thus directed towards investigating the gaps between A G and R , as well as G A and R. We find that the invariants A G − R and G A − R correlate well with some molecular properties. Numerous upper and lower bounds for the quantities A G − R and G A − R are computed for general graphs, bipartite graphs, chemical graphs, trees, and chemical trees, in terms of graph order, with an emphasis on characterizing extremal graphs. [ABSTRACT FROM AUTHOR]

Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite topologies, associative algebras, subgroups of matrix groups, ideals in polynomial rings, and classes of bipartite graphs. [ABSTRACT FROM AUTHOR]

Predicting postoperative prognosis is vital for clinical decision making in patients undergoing adrenalectomy (ADX). This study introduced GAPPA, a novel GNN-based approach, to predict post-ADX outcomes in patients with unilateral primary aldosteronism (UPA). The objective was to leverage the intricate dependencies between clinico-biochemical features and clinical outcomes using GNNs integrated into a bipartite graph structure to enhance prognostic prediction accuracy. We conceptualized prognostic prediction as a link prediction task on a bipartite graph, with nodes representing patients, clinico-biochemical features, and clinical outcomes, and edges denoting the connections between them. GAPPA utilizes GNNs to capture these dependencies and seamlessly integrates the outcome predictions into a graph structure. This approach was evaluated using a dataset of 640 patients with UPA who underwent unilateral ADX (uADX) between 1990 and 2022. We conducted a comparative analysis using repeated stratified five-fold cross-validation and paired t -tests to evaluate the performance of GAPPA against conventional machine learning methods and previous studies across various metrics. GAPPA significantly outperformed conventional machine learning methods and previous studies (p < 0.05) across various metrics. It achieved F1-score, accuracy, sensitivity, and specificity of 71.3 % ± 3.1 %, 71.1 % ± 3.4 %, 69.9 % ± 4.3 %, and 72.4 % ± 7.2 %, respectively, with an AUC of 0.775 ± 0.030. We also investigated the impact of different initialization schemes on GAPPA outcome-edge embeddings, highlighting their robustness and stability. GAPPA aids in preoperative prognosis assessment and facilitates patient counseling, contributing to prognostic prediction and advancing the applications of GNNs in the biomedical domain. [Display omitted] • We are the first to apply GNNs to improve prognostic prediction of UPA patients. • We introduce GAPPA for post-adrenalectomy prognostic outcome prediction. • GAPPA innovates by integrating outcome prediction into the graph structure. • GAPPA surpasses machine learning methods and prior research (p < 0.05). [ABSTRACT FROM AUTHOR]

Let i be a positive integer, an i -star denoted by S i is a complete bipartite graph K 1 , i. An { S 2 , S 3 } -packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum { S 2 , S 3 } -packing problem is to find an { S 2 , S 3 } -packing of a given graph containing the maximum number of vertices. The { S 2 , S 3 } -factor problem is to answer whether there is an { S 2 , S 3 } -packing containing all vertices of the given graph. The { S 2 , S 3 } -factor problem is NP-complete in cubic graphs. In this paper we design a quadratic-time algorithm for finding an { S 2 , S 3 } -packing of G that covers at least thirteen-sixteenths of its vertices with only a few exceptions. We also present some (2 , 3) -regular graphs with their maximum { S 2 , S 3 } -packings covering exactly thirteen-sixteenths of their vertices. [ABSTRACT FROM AUTHOR]

Small molecule machine learning aims to predict chemical, biochemical, or biological properties from molecular structures, with applications such as toxicity prediction, ligand binding, and pharmacokinetics. A recent trend is developing end-to-end models that avoid explicit domain knowledge. These models assume no coverage bias in training and evaluation data, meaning the data are representative of the true distribution. However, the domain of applicability is rarely considered in such models. Here, we investigate how well large-scale datasets cover the space of known biomolecular structures. For doing so, we propose a distance measure based on solving the Maximum Common Edge Subgraph (MCES) problem, which aligns well with chemical similarity. Although this method is computationally hard, we introduce an efficient approach combining Integer Linear Programming and heuristic bounds. Our findings reveal that many widely-used datasets lack uniform coverage of biomolecular structures, limiting the predictive power of models trained on them. We propose two additional methods to assess whether training datasets diverge from known molecular distributions, potentially guiding future dataset creation to improve model performance. Small molecule machine learning aims to predict properties from molecular structures. Here, the authors introduce the myopic MCES distance and show that frequently used datasets fail to uniformly cover biomolecular structures, limiting resulting models. [ABSTRACT FROM AUTHOR]

Prediction of trust and distrust in nodes in signed network analysis is an important task with diverse applications. However, the presence of imbalanced and incomplete rankings in signed networks makes prediction of node-level trust values using machine learning (ML) methods a very challenging task. To overcome these challenges, we introduce DATIS, an innovative approach employing generative adversarial networks (GANs) for data augmentation in node-level trust prediction tasks in signed networks. DATIS addresses imbalances in both sign and value of rankings, handling missing rankings by training on nodes' local and global network features without explicit information on edge rankings assigned to nodes. Unlike existing methods, we consider the trust prediction problem as a regression task to imply the strength of trust a node gained in a network. Our experimental evaluation shows that DATIS can significantly improve the accuracy of node-level trust intensity prediction on real-world datasets. [ABSTRACT FROM AUTHOR]

In response to the problem of low prediction accuracy in ultra short-term prediction of photovoltaic power, this study combines Hungarian clustering analysis and particle swarm optimization variational mode decomposition algorithm to construct a photovoltaic power ultra short-term forecasting model, to analyze data in depth and improve prediction accuracy. The experiment outcomes show that the Hungarian algorithm performs well in integrating single clustering results and effectively improves the problem of atypical classification. In addition, the clustering ensemble model shows significant improvement compared to other models on the Calinski-Harabasz index, and effectively reduces the overlap between clusters on the Davies-Bouldin index, improving the overall quality of clustering. Under different weather conditions, the convergence accuracy and speed of the multiverse optimization support vector machine, multiverse optimization support vector machine, and particle swarm optimization variational mode decomposition algorithms each have their own advantages, but the particle swarm optimization variational mode decomposition algorithm performs better. In addition, the Hungarian clustering model has high stability in predicting errors, with average absolute error and average relative error lower than BP and RBF models. The maximum absolute error and maximum relative error are reduced, indicating the effectiveness and predictive advantage of the proposed Hungarian clustering ensemble model in predicting photovoltaic power. [ABSTRACT FROM AUTHOR]

Alzheimer's disease (AD), a progressive neurodegenerative condition, notably impacts cognitive functions and daily activity. One method of detecting dementia involves a task where participants describe a given picture, and extensive research has been conducted using the participants' speech and transcribed text. However, very few studies have explored the modality of the image itself. In this work, we propose a method that predicts dementia automatically by representing the relationship between images and texts as a graph. First, we transcribe the participants' speech into text using an automatic speech recognition system. Then, we employ a vision language model to represent the relationship between the parts of the image and the corresponding descriptive sentences as a bipartite graph. Finally, we use a graph convolutional network (GCN), considering each subject as an individual graph, to classify AD patients through a graph-level classification task. In experiments conducted on the ADReSSo Challenge datasets, our model surpassed the existing state-of-the-art performance by achieving an accuracy of 88.73%. Additionally, ablation studies that removed the relationship between images and texts demonstrated the critical role of graphs in improving performance. Furthermore, by utilizing the sentence representations learned through the GCN, we identified the sentences and keywords critical for AD classification. [ABSTRACT FROM AUTHOR]