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Understanding how the traits of lineages are related to diversification is key for elucidating the origin of variation in species richness. Here, we test whether traits are related to species richness among lineages of trees from all major biogeographical settings of the lowland wet tropics. We explore whether variation in mortality rate, breeding system and maximum diameter are related to species richness, either directly or via associations with range size, among 463 genera that contain wet tropical forest trees. For Amazonian genera, we also explore whether traits are related to species richness via variation among genera in mean species-level range size. Lineages with higher mortality rates—faster life-history strategies—have larger ranges in all biogeographic settings and have higher mean species-level range sizes in Amazonia. These lineages also have smaller maximum diameters and, in the Americas, contain dioecious species. In turn, lineages with greater overall range size have higher species richness. Our results show that fast life-history strategies influence species richness in all biogeographic settings because lineages with these ecological strategies have greater range sizes. These links suggest that dispersal has been a key process in the evolution of the tropical forest flora. [ABSTRACT FROM AUTHOR]

One major problem in the study of numerical semigroups is determining the growth of the semigroup tree. We study infinite chains of numerical semigroups in the semigroup tree, firstly introduced by Bras-Amorós and Bulygin (Semigroup Forum, 79:561-574, 2009). Computational results show that these chains are rare, but without them the tree would not be infinite. It is proved that for each genus g ≥ 5 there are more semigroups of that genus not belonging to infinite chains than semigroups belonging. Bras-Amorós and Bulygin (Semigroup Forum, 79:561-574, 2009) presented a characterization of the semigroups that belong to infinite chains in terms of the coprimality of the left elements of the semigroup as well as a result on the cardinality of the set of infinite chains to which a numerical semigroup belongs in terms of the primality of the greatest common divisor of these left elements. We revisit these results and fix an imprecision on the cardinality of the set of infinite chains to which a semigroup belongs in the case when the greatest common divisor of the left elements is a prime number. We then look at infinite chains in subtrees with fixed multiplicity. When the multiplicity is a prime number there is only one infinite chain in the tree of semigroups with such multiplicity. When the multiplicity is 4 or 6 we prove a self-replication behavior in the subtree and provide a formula for the number of semigroups in infinite chains of a given genus and multiplicity 4 and 6, respectively. [ABSTRACT FROM AUTHOR]

The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or lateral gene transfer events between lineages, and so the history of life is more accurately described by a rooted phylogenetic network. Nevertheless, phylogenetic networks may be complex and difficult to interpret, so biologists sometimes prefer a tree that summarises the central tree-like trend of evolution. In this paper, we formally investigate methods for transforming an arbitrary phylogenetic network into a tree (on the same set of leaves) and ask which ones (if any) satisfy a simple consistency condition. This consistency condition states that if we add additional species into a phylogenetic network (without otherwise changing this original network) then transforming this enlarged network into a rooted phylogenetic tree induces the same tree on the original set of species as transforming the original network. We show that the LSA (lowest stable ancestor) tree method satisfies this consistency property, whereas several other commonly used methods (and a new one we introduce) do not. We also briefly consider transformations that convert arbitrary phylogenetic networks to another simpler class, namely normal networks. [ABSTRACT FROM AUTHOR]

Let G be a graph with n vertices and let d i be the degree of vertex i of G. The ABC matrix of G is a square matrix of order n whose (i, j) entry is d i + d j - 2 d i d j if the vertices v i and v j are connected in G and zero otherwise. A generalized Bethe tree is a rooted tree of k levels where the root vertex at level 1 has degree d k , for i = 2 , .... k - 1 , the vertices at level i have a constant degree and the vertices at level k are pendant vertices. In this paper, for a certain family of generalized Bethe trees we characterize those with the largest ABC spectral radius and we apply this characterization to improve an upper bound for the largest ABC eigenvalue of the mentioned trees. We also study the ABC energy of generalized Bethe trees. [ABSTRACT FROM AUTHOR]

The first inverse Nirmala index is a novel degree-based topological descriptor that was introduced in 2021. Preliminary QSPR investigations suggest that this index deserves further consideration because of its unusually good predictive potential. This paper investigates the relations between this index with some elementary graph quantities and some related degree-based topological index. Further, the computational analysis will reveal extremal graphs among trees, molecular trees, all connected graphs, and their molecular counterparts. [ABSTRACT FROM AUTHOR]

We consider a scattering problem generated by the Sturm–Liouville equation on a tree formed by an equilateral compact subtree with a lead (half-infinite edge) attached to this compact subtree. It is assumed that the potential on the lead is identically equal to zero and the potentials on finite edges are real L2-functions. It is shown how to determine the shape of the tree by using the S-function and the eigenvalues of the scattering problem. [ABSTRACT FROM AUTHOR]

In the general AntiFactor problem, a graph G and, for every vertex v of G, a set X v ⊆ N of forbidden degrees is given. The task is to find a set S of edges such that the degree of v in S is not in the set X v . Standard techniques (dynamic programming plus fast convolution) can be used to show that if M is the largest forbidden degree, then the problem can be solved in time (M + 2) tw · n O (1) if a tree decomposition of width tw is given. However, significantly faster algorithms are possible if the sets X v are sparse: our main algorithmic result shows that if every vertex has at most x forbidden degrees (we call this special case AntiFactorx), then the problem can be solved in time (x + 1) O (tw) · n O (1) . That is, AntiFactorx is fixed-parameter tractable parameterized by treewidth tw and the maximum number x of excluded degrees. Our algorithm uses the technique of representative sets, which can be generalized to the optimization version, but (as expected) not to the counting version of the problem. In fact, we show that #AntiFactor1 is already # W [ 1 ] -hard parameterized by the width of the given decomposition. Moreover, we show that, unlike for the decision version, the standard dynamic programming algorithm is essentially optimal for the counting version. Formally, for a fixed nonempty set X , we denote by X -AntiFactor the special case where every vertex v has the same set X v = X of forbidden degrees. We show the following lower bound for every fixed set X : if there is an ϵ > 0 such that # X -AntiFactor can be solved in time (max X + 2 - ϵ) tw · n O (1) given a tree decomposition of width tw , then the counting strong exponential-time hypothesis (#SETH) fails. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) is evolving rapidly, increasing demand for safeguarding data against routing attacks. While achieving complete security for RPL protocols remains an ongoing challenge, this paper introduces an innovative hybrid autoencoder–decision tree framework (HADTF) designed to detect four types of RPL attacks: decreased rank, version number, DIS flooding, and blackhole attacks. The HADTF comprises three key components: enhanced feature extraction, feature selection, and a hybrid autoencoder–decision tree classifier. The enhanced feature extraction module identifies the most pertinent features from the raw data collected, while the feature selection component carefully curates' optimal features to reduce dimensionality. The hybrid autoencoder–decision tree classifier synergizes the strengths of both techniques, resulting in high accuracy and detection rates while effectively minimizing false positives and false negatives. To assess the effectiveness of the HADTF, we conducted evaluations using a self-generated dataset. The results demonstrate impressive performance with an accuracy of 97.41%, precision of 97%, recall of 97%, and F1-score of 97%. These findings underscore the potential of the HADTF as a promising solution for detecting RPL attacks within IoT networks. [ABSTRACT FROM AUTHOR]

A graph in which all minimal zero forcing sets are in fact minimum zero forcing sets is called a well-forced graph. The main result of this paper is to characterize well-forced trees and based on this characterization present an algorithm for determining which trees are well-forced. As part of this characterization, certain subgraphs are identified as being forbidden in a well-forced graph. Additionally it is shown whether some common families of graphs are well-forced or not. Understanding well-forced graphs turns out to be closely related to the question of which vertices of a graph are in a minimal zero forcing set. A vertex of G that is in no minimal zero forcing set of G is called an irrelevant vertex. For any graph, a sufficient condition for a vertex to be irrelevant is established. In addition, it is proved that this condition is a characterization of irrelevant vertices in trees. [ABSTRACT FROM AUTHOR]

The idempotent semigroups (bands) that give rise to partial orders by defining a ≤ b ⟺ a · b = a are the right-regular bands (RRB), which are axiomatized by x · y · x = y · x . In this work we consider the class of associative posets, which comprises all partial orders underlying right-regular bands, and study to what extent the ordering determines the possible "compatible" band structures and their canonicity. We show that the class of associative posets in the signature { ≤ } is not first-order axiomatizable. We also show that the Axiom of Choice is equivalent over ZF to the fact that every tree with finite branches is associative. We study the smaller class of "normal" posets (corresponding to right-normal bands) and give a structural characterization. [ABSTRACT FROM AUTHOR]

The linear-size suffix tries (LSTries) (Crochemore et al. in Theor Comput Sci 638:171–178, 2016) are a version of suffix trees in which the edge labels are single characters, yet are able to perform pattern matching queries in optimal time. Instead of explicitly storing the input text, LSTries have some extra non-branching internal nodes called type-2 nodes. The extended techniques are then used in the linear-size compact directed acyclic word graphs (LCDAWGs) (Takagi et al., in: SPIRE 2017, pp. 304–316, 2017), which can be stored with O (el (T) + er (T)) space (i.e. without the text), where el (T) and er (T) are the numbers of left- and right-extensions of the maximal repeats in the input text string T, respectively. In this paper, we present simpler alternatives to the aforementioned indexing structures, called the simplified LSTries (simLSTries) and the simplified LCDAWGs (simLCDAWGs), in which most of the type-2 nodes are removed. In particular, our simLCDAWGs require only O (er (T)) space and work in a weaker model of computation (i.e. the pointer machine model). This contrasts the O (er (T)) -space CDAWG representation of Belazzougui and Cunial (in: Proceedings of the 24th international symposium on string processing and information retrieval, pp. 161–175, 2017), which works on the word RAM model. [ABSTRACT FROM AUTHOR]

We present an analysis of the lepton-flavor violating decay of the Higgs boson mediated by an ultralight gauge boson, χ . Our analysis matches a model generating the lepton flavor-violating interaction ℓ ¯ i ℓ j χ at tree level with an effective field theory, safeguarding a physical massless χ -boson limit of the observables. By utilizing the upper bounds on H → ℓ i ℓ ¯ j decays from CMS and ATLAS Collaborations, we establish an indirect upper limit on the nonstandard decay H → ℓ i ℓ ¯ j χ . The analysis encompasses various observables such as the lepton energy spectrum, Dalitz plot distribution, and Lepton Charge and Forward-Backward Asymmetries. [ABSTRACT FROM AUTHOR]

Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such a route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due to limited energy resources of the searcher). The objective is to cover all the edges of a tree T using the minimum number of routes, each starting and ending at the root and each being of length at most B. To this end, we analyze the following natural greedy tree traversal process that is based on decomposing a depth first search traversal into a sequence of limited length routes. Given any arbitrary depth first search traversal R of the tree T, we cover R with routes R 1 , ... , R l , each of length at most B such that: R i starts at the root, reaches directly the farthest point of R visited by R i - 1 , then R i continues along the path R as far as possible, and finally R i returns to the root. We call the above algorithm piecemeal-DFS and we prove that it achieves the asymptotically minimal number of routes l, regardless of the choice of R. Our analysis also shows that the total length of the traversal (and thus the traversal time) of piecemeal-DFS is asymptotically minimum over all energy-constrained exploration strategies. The fact that R can be chosen arbitrarily means that the exploration strategy can be constructed in an online fashion when the input tree T is not known in advance. Each route R i can be constructed without any knowledge of the yet unvisited part of T. Surprisingly, our results show that depth first search is efficient for energy constrained exploration of trees, even though it is known that the same does not hold for energy constrained exploration of arbitrary graphs. [ABSTRACT FROM AUTHOR]

We show that for a large class of Artin groups with Dynkin diagrams being a tree, the K (π , 1) -conjecture holds. We also establish the K (π , 1) -conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which applies to some Artin groups whose Dynkin diagrams are of hyperbolic type. This is based on a new approach to the K (π , 1) -conjecture for Artin groups. [ABSTRACT FROM AUTHOR]

To any tree on n vertices we associate an n-dimensional Lotka–Volterra system with 3 n - 2 parameters and, for generic values of the parameters, prove it is superintegrable, i.e. it admits n - 1 functionally independent integrals. We also show how each system can be reduced to an ( n - 1 )-dimensional system which is superintegrable and solvable by quadratures. [ABSTRACT FROM AUTHOR]

We provide a characterization of Carleson measures on locally finite trees. This characterization establishes the connection between Carleson measures and the boundedness of a suitable Poisson integral between L p -spaces. Additionally, when the tree has bounded degree, we investigate the relationship between Carleson measures and BMO functions defined on the boundary of the tree. [ABSTRACT FROM AUTHOR]

Science educators report that students struggle with understanding, using, and evaluating the evidence underpinning scientific knowledge. However, there are not many studies focused on helping instructors address those difficulties. Here, we report on a laboratory instructor's scaffolding of students' evidentiary reasoning with and about evidence for evolutionary trees with guidance from the Conceptual Analysis of Disciplinary Evidence (CADE) framework, which links biological knowledge with epistemic considerations. To consider both domain-general and discipline-specific aspects of evidence, CADE was implemented to inform scaffolds in two ways: (1) generic evidence scaffolds (GES) reminded students of general epistemic considerations; (2) disciplinary evidence scaffolds (DES) explicitly reminded students of the disciplinary knowledge of relevance for considering biological evidence. An instructor's lab discussions were compared before and after they had a workshop with CADE. CADE helped the lab instructor facilitate students' evidentiary reasoning about evolutionary trees. In comparison to baseline, both GES and DES discussions covered more aspects and relationships among types of evidence for evolutionary tree-thinking and the instructor prompted more kinds of general epistemic considerations and biological knowledge. DES discussions emphasized the importance of disciplinary knowledge for research design. The CADE framework guided planning and implementation of intentional scaffolding aimed at guiding evidentiary reasoning. [ABSTRACT FROM AUTHOR]

In the field of autonomous mobile robots, sampling-based motion planning methods have demonstrated their efficiency in complex environments. Although the Rapidly-exploring Random Tree (RRT) algorithm and its variants have achieved significant success in known static environment, it is still challenging in achieving optimal motion planning in unknown dynamic environments. To address this issue, this paper proposes a novel motion planning algorithm Bi-HS-RRT X , which facilitates asymptotically optimal real-time planning in continuously changing unknown environments. The algorithm swiftly determines an initial feasible path by employing the bidirectional search. When dynamic obstacles render the planned path infeasible, the bidirectional search is reactivated promptly to reconstruct the search tree in a local area, thereby significantly reducing the search planning time. Additionally, this paper adopts a hybrid heuristic sampling strategy to optimize the planned path quality and search efficiency. The convergence of the proposed algorithm is accelerated by merging local biased sampling with nominal path and global heuristic sampling in hyper-ellipsoid region. To verify the effectiveness and efficiency of the proposed algorithm in unknown dynamic environments, numerous comparative experiments with existing algorithms were conducted. The experimental results indicate that the proposed planning algorithm has significant advantages in planned path length and planning time. [ABSTRACT FROM AUTHOR]

Mangrove forests enhance Small Island Developing States' resilience to climate change, yet in 2020, a mangrove dieback impacted ~ 25% of mangrove-containing islands in the Maldives. Using remote sensing, dendrology and sediment geochemistry, we document a significant decrease in mangrove health post-2020 (NDVI: 0.75 ± 0.09) compared to pre-2020 (0.85 ± 0.04; P < 0.0001). Dead trees showed reduced stomatal conductance (δ13C: − 26.21 ± 0.11 ‰) relative to living ones (− 27.66 ± 0.14 ‰), indicating salinity stress. Critically, sea-level rise (30.50 ± 23.30 mm/year) outpaced mangrove sediment accretion (6.40 ± 0.69 mm/year) five-fold between 2017 and 2020. We attribute this dieback to salinity stress driven by record-high sea levels in 2020, linked to an extreme positive Indian Ocean Dipole event. These findings reveal the vulnerability of mangrove ecosystems to rapid sea-level rise and highlights the urgent need for adaptive conservation strategies in Small Island Developing States. [ABSTRACT FROM AUTHOR]

Traditional LSM-tree-based key-value storage systems face significant read amplification issues due to the multi-level structure of LSM-tree, the unordered SSTable files in Level 0, and the lack of an in-memory index structure for key-value pairs. We observed that, under the influence of workloads with locality features, key-value pairs exhibit a range-specific access intensity. Addressing the three reasons for LSM-tree read amplification, we have utilized the range-specific access intensity of workload to propose a multi-tree structure consisting of a B+ tree, a single-level hot tree, and an LSM-tree with partition-based Level 0. This aims to enhance the read performance of LSM-tree-based key-value storage systems. We designed the prototype, MTDB, based on LevelDB. The experimental results show that MTDB's read performance is 1.62× to 2.02× that of LevelDB, and it approaches or exceeds the read performance of KVell and Bourbon while reducing memory overhead by 58.85%–86%. [ABSTRACT FROM AUTHOR]

Let k ≥ 2 be an integer. A tree T is called a k-tree if d T (v) ≤ k for each v ∈ V (T) ; that is, the maximum degree of a k-tree is at most k. A k-tree T is a spanning k-tree if T is a spanning subgraph of a connected graph G. Let λ 1 (D (G)) denote the distance spectral radius in G, where D(G) denotes the distance matrix of G. In this paper, we verify an upper bound for λ 1 (D (G)) in a connected graph G to guarantee the existence of a spanning k-tree in G. [ABSTRACT FROM AUTHOR]

We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str 0 -trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing—rather than locally basing or EM-basing—str-trees on s-trees and str 0 -trees on str-trees. As an application we show that a thick positive theory has k- TP 2 iff it has 2- TP 2 [ABSTRACT FROM AUTHOR]

We study two families of lattices whose number of elements are given by the numbers in even (respectively odd) positions in the Fibonacci sequence. The even Fibonacci lattice arises as the lattice of simple elements of a Garside monoid partially ordered by left-divisibility, and the odd Fibonacci lattice is an order ideal in the even one. We give a combinatorial proof of the lattice property, relying on a description of words for the Garside element in terms of Schröder trees, and on a recursive description of the even Fibonacci lattice. This yields an explicit formula to calculate meets and joins in the lattice. As a byproduct we also obtain that the number of words for the Garside element is given by a little Schröder number. [ABSTRACT FROM AUTHOR]

Tillandsia recurvata is an epiphytic plant commonly found in tropical regions and colonizes tree trunks, fences, and power wires. This plant plays an important role in interacting with trees, sharing microorganisms, and performing specific functions in the process of tree colonization. The objective of this study was to evaluate and compare the microbiomes of T. recurvata collected from two different locations (trees and fences) and two plant tissues (leaves and roots). The hypothesis of this study was that the microbiome of T. recurvata is composed of microorganisms that would provide nutritional support to compensate for the lack of nutrients in a particular growth support. The results showed significant differences in microbial diversity between trees and fences, with trees exhibiting higher richness and more complex microbial networks. Proteobacteria was the most prevalent bacterial phylum, with Actinobacteria and Sphingomonas also playing key roles in nitrogen fixation and plant growth. Fungal communities were similar across locations, with Ascomycota and Basidiomycota being predominant, but Paraconiothyrium and Nigrospora showed significant differences in abundance between trees and fences. Functional analysis indicated similar metabolic profiles across leaf and root samples, with key functions for T. recurvata including carbohydrate and amino acid metabolism, stress control, and biofertilization. [ABSTRACT FROM AUTHOR]

This paper studies the robust vertex centdian location problem on tree networks with interval edge lengths. To obtain a robust solution, we use the minmax regret criterion. First, we obtain atmost n worst case scenario for each pair of vertices on tree networks. Then we reduce this number to log n . Finally, the total time for obtaining a robust solution is equal to O (n 4) . This time is reduced to O (n 3 log n) by using the property of binary search tree and weighted centroid. [ABSTRACT FROM AUTHOR]

Background: Trees in natural forests are a major contributor to atmospheric methane (CH4), yet these emissions have never been investigated in reclaimed forests. Our study aimed to assess the magnitude, seasonality, drivers, and contributions of tree CH4 emissions to ecosystem CH4 flux in the reclaimed forests. We measured CH4 emissions from different emission pathways, including the stems of trees (Populus euramericana, Metasequoia glyptostroboides, and Camphora officinarum), shoots of herbs (Carex breviculmis and Carex dispalata), and soils in the two reclaimed forests with reclamation periods of 12 and 5 years. We identified factors controlling seasonal tree CH4 emissions and measured tree morphological variables (diameter at breast height, wood density, and lenticel density) to determine species differences in emissions. Results: CH4 emissions from trees in the 12-year-old reclaimed forest were significantly higher than those in the 5-year-old forest. Seasonal variations in tree CH4 emissions were primarily driven by growth stage and soil parameters, including soil CH4 flux, temperature, and moisture. Conclusion: In the reclaimed forests, tree-mediated CH4 emissions could be an important contributor to ecosystem CH4 flux, with contributions varying by season. As these forests mature and become ecologically restored, they may significantly impact regional and global CH4 emissions. [ABSTRACT FROM AUTHOR]

The article proposes a new exact algorithm of quadratic complexity that solves the problem of the shortest transformation ("alignment") of one weighted tree into another, taking into account arbitrary costs of operations on trees. Three operations are considered: adding vertex deletions to an edge or root of a tree and shifting a subtree with deletions. [ABSTRACT FROM AUTHOR]

Access control is a fundamental component of any data management system, ensuring the prevention of unauthorized data access. Within the realm of data streams, it plays a crucial role in query processing by facilitating authorized access to them. This paper introduces the StreamFilter framework, which focuses on securely processing queries with range filters over streaming data. Leveraging the Role-Based Access Control model, the StreamFilter framework enables the specification of fine-grained access policies at various levels of granularity, such as tuples and attributes, through the utilization of a bit string structure. To enhance the search operation during data stream query processing, the framework employs a distributed indexing method, constructing a set of smaller B + Tree indices rather than a single large B + Tree index. Furthermore, it seamlessly integrates access authorization evaluation with query processing, efficiently filtering unauthorized parts from the query results. The experimental results demonstrate an approximately 50% increase in efficiency for processing queries with range filters compared to the post-filtering strategy. This improvement is observed across all types of data distribution, including uniform, skew, and hyper skew. [ABSTRACT FROM AUTHOR]

Galton–Watson trees formed by a critical branching process are considered. The distribution of the number of offspring of the particles in the process has infinite variance. The limit distribution of the number of vertices in the lower layers of a tree is found as the number of vertices approaches infinity. [ABSTRACT FROM AUTHOR]

The amortized step complexity of an implementation measures its performance as a whole, rather than the performance of individual operations. Specifically, the amortized step complexity of an implementation is the average number of steps performed by invoked operations, in the worst case, taken over all possible executions. The point contention of an execution, denoted by c ˙ , measures the maximal number of precesses simultaneously active in the execution. Ruppert (2016) showed that the amortized step complexity of known lock-free implementations for many shared data structures includes an additive factor linear in the point contention c ˙ . This paper shows that there is no lock-free implementation with o (min { c ˙ , log log n }) amortized RMR complexity of queues, stacks or heaps from reads, writes, comparison primitives (such as compare &swap) and LL/SC, where n is the total number of the processes in the system. In addition, the paper shows a Ω (min { c ˙ , log log n }) lower bound on the amortized step complexity for shared linked lists, skip lists, search trees and other pointer-based data structures. These lower bounds mean that the additive factor linear in c ˙ is inherent for these implementations, provided that the point contention is small compared to the number of processes in the system (i.e. c ˙ ∈ O (log log n) or c ˙ ∈ O (log log n) ). [ABSTRACT FROM AUTHOR]

In connectivity augmentation problems we are given a graph G = (V , E G) and an edge set E on V, and seek a min-size edge set J ⊆ E such that G ∪ J has larger connectivity than G. In the 1-Connectivity Augmentation ( 1 -CA) problem G is connected and G ∪ J should be 2-connected. In the Leaf to Leaf 1 -CA every edge in E connects two leaves in the block-tree of G. For this version we give a simple combinatorial 5/3-approximation algorithm, improving the 1.892 approximation that applies for the general case. We will also show by a simple proof that if the Steiner Tree problem admits approximation ratio α then 1 -CA admits approximation ratio 1 + ln (4 - x) + ϵ , where x is the solution to the equation 1 + ln (4 - x) = α + (α - 1) x . For the currently best value of α = ln 4 + ϵ this gives approximation ratio 1.942. This is worse than the best known ratio 1.892, but has the advantage of using Steiner Tree approximation as a "black box". In the Element Connectivity Augmentation problem we are given a graph G = (V , E) , S ⊆ V , and connectivity requirements { r (u , v) : u , v ∈ S } . The goal is to find a min-size set J of new edges on S such that for all u , v ∈ S the graph G ∪ J contains r(u, v) uv-paths such that no two of them have an edge or a node in V \ S in common. The problem is NP-hard even when r max = max u , v ∈ S r (u , v) = 2 . We obtain approximation ratio 3/2, improving the previous best ratio 7/4. For the case of degree bounds on S we obtain the same ratio with just + 1 degree violation, which is tight, since deciding whether there exists a feasible solution is NP-hard even when r max = 2 . [ABSTRACT FROM AUTHOR]

We consider the problem of finding the initial vertex (Adam) in a Barabási–Albert tree process (T (n) : n ≥ 1) at large times. More precisely, given ε > 0 , one wants to output a subset P ε (n) of vertices of T (n) so that the initial vertex belongs to P ε (n) with probability at least 1 - ε when n is large. It has been shown by Bubeck, Devroye and Lugosi, refined later by Banerjee and Huang, that one needs to output at least ε - 1 + o (1) and at most ε - 2 + o (1) vertices to succeed. We prove that the exponent in the lower bound is sharp and the key idea is that Adam is either a "large degree" vertex or is a neighbor of a "large degree" vertex (Eve). [ABSTRACT FROM AUTHOR]

The spectral radius ρ (G) of a graph G is the largest eigenvalue of the adjacency matrix of G. For a graph G with maximum degree Δ (G) , it is known that ρ (G) ≤ Δ (G) with equality when G is connected if and only if G is regular. So the quantity β (G) = Δ (G) - ρ (G) is a spectral measure of irregularity of G. In this paper, we identify the trees of order n ≥ 12 with the first 15 largest β -values, the unicyclic graphs of order n ≥ 17 with the first 16 largest β -values, as well as the bicyclic graphs of order n ≥ 30 with the first 11 largest β -values. We also determine the graphs with the largest β -values among all connected graphs with given order and clique number. [ABSTRACT FROM AUTHOR]

Aimed at sufficiently utilizing available data and prior distribution information, we introduce a data-driven Bayesian-type approach to solve multi-stage convex stochastic optimization, which can easily cope with the uncertainty about data process's distributions and their inter-stage dependence. To unravel the properties of the proposed multi-stage Bayesian expectation optimization (BEO) problem, we establish the consistency of optimal value functions and solutions. Two kinds of algorithms are designed for the numerical solution of single-stage and multi-stage BEO problems, respectively. A queuing system and a multi-stage inventory problem are adopted to numerically demonstrate the advantages and practicality of the new framework and corresponding solution methods, compared with the usual formulations and solution methods for stochastic optimization problems. [ABSTRACT FROM AUTHOR]

We investigate location problems where the optimal solution is found within the tropical convex hull of the given input points. Our initial focus is on geodesically star-convex sets, using the asymmetric tropical distance. We introduce the concept of tropically quasiconvex functions, which have sub-level sets with this shape, and are closely related to monotonic functions. Our findings demonstrate that location problems using tropically quasiconvex functions as distance measures will result in an optimal solution within the tropical convex hull of the input points. We also extend this result to cases where the input points are replaced with tropically convex sets. Finally, we explore the applications of our research in phylogenetics, highlighting the properties of consensus methods that arise from our class of location problems. [ABSTRACT FROM AUTHOR]

Commonsense Question Answering (CQA) aims to select the correct answers to common knowledge questions. Most existing approaches focus on integrating external knowledge graph (KG) representations with question context representations to facilitate reasoning. However, the approaches cannot effectively select the correct answer due to (i) the incomplete reasoning chains when using knowledge graphs as external knowledge, and (ii) the insufficient understanding of semantic information of the question during the reasoning process. Here we propose a novel model, KA-AGN. First, we utilize a joint representation of dependency parse trees and language models to describe QA pairs. Next, we introduce question semantic information as nodes into a knowledge subgraph and compute the correlations between nodes using adaptive graph networks. Finally, bidirectional attention and graph pruning are employed to update the question representation and the knowledge subgraph representation. To evaluate the performance of our method, we conducted experiments on two widely used benchmark datasets: CommonsenseQA and OpenBookQA. The ablation experiment results demonstrate the effectiveness of the adaptive graph network in enhancing reasoning chains, while showing the ability of the joint representation of dependency parse trees and language models to correctly understand question semantics. Our code is publicly available at https://github.com/agfsghfdhg/KAAGN-main. [ABSTRACT FROM AUTHOR]

Perennial vegetation in farmlands can mitigate anthropogenic greenhouse gases (GHG) by capturing atmospheric carbon and storing it in the soil for extended periods. The objective of this study was to quantify soil organic carbon (SOC) concentrations and stocks under tree buffer (TB), grass buffer (GB), grass waterways (WW) and crop field (CS, corn-soybean rotation) to evaluate the significance of conservation measures in C sequestration projects. Soil samples were collected up to 1 m depth at upper, middle, and lower landscape positions from 26-year-old TB, GB, and WW in a watershed. The SOC concentration decreased with increasing soil depth for all four land uses. However, as expected, bulk density increased with increasing soil depth for all four land uses. It was highest for the CS land use. In 2023, for the depth of 0–10 cm, SOC increased by +0.63, +1.06, +1.37 and +1.63% in CS, GB, TB, and WW, respectively, since the land uses were established 26 years ago. Land uses had greater impacts on SOC stock in the top 50 cm depth, with WW (113.5 ± 12.9 Mg ha−1), TB (106 ± 14.5 Mg ha−1), and GB (102.4 ± 11.6 Mg ha−1) compared to CS (90.9 ± 10.2 Mg ha−1). However, at watershed level, with ~ 10% cover by TB or GB areas and the rest under CS, SOC stock up to 50 cm depth was respectively 91.6 and 91.2 Mg ha−1 compared to 90 Mg ha−1 by CS alone—1.3 to 1.8% increase. This is a significant increase in soil organic carbon across the landscape, which was realized with the conservation practices and agroforestry, while also playing a crucial role in protecting surface runoff in the landscape. Future studies may consider valuation of the overall ecosystem services due to the land uses (conservation measures) and the trees by considering optimization of incorporating such technologies in the farming systems to reduce negative trade-offs. [ABSTRACT FROM AUTHOR]

Given a graph H, we prove that every (theta, prism)-free graph of sufficiently large treewidth contains either a large clique or an induced subgraph isomorphic to H, if and only if H is a forest. [ABSTRACT FROM AUTHOR]

Vehicular ad hoc networks (VANETs) are recent advancements that permit vehicles to communicate with infrastructure and other vehicles, improving road safety and traffic efficiency. One of the difficulties in constructing and maintaining VANETs deals with the consequences of blockage, it may occur when buildings, trees, or other obstructions block radio signals between vehicles. However, the presence of vehicles as obstacles can severely impact the performance of VANETs. In this paper, an efficient machine learning (ML) model is developed to identify the impact of vehicle obstacles in VANETs. The proposed optimizable tree ML model showed better results in comparison to the other existing models. The results of the proposed model are superior as compared with other existing models in terms of nine performance measures namely, recall, specificity, balanced accuracy, accuracy, error rate, precision, F1 score, FNR and FPR. The values of these nine performance matrices for the proposed optimizable tree ML model are 0.99, 0.99, 0.99, 0.99, 0.01, 0.99, 0.99, 0.01, and 0.01 respectively. [ABSTRACT FROM AUTHOR]

Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798–811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity. [ABSTRACT FROM AUTHOR]

Existing research extensively incorporates syntactic information, especially dependency trees, to enhance the performance of relation extraction tasks. However, relying solely on dependency information may not fully exploit the rich semantic and syntactic information contained in sentences, and not all information in dependency trees is substantively helpful for relation extraction. Therefore, this paper proposes the Dependent-Position Relation Graph Convolutional network with Hierarchical Attention (DPR-GHA) for relation extraction, a method that integrates dependency relations and position relations into a hierarchical attention mechanism to effectively capture the relations between entities in text. The method aims to capture rich semantic information and enhance the performance of relation extraction. Specifically, we introduce the dependency relations of sentences and position relations of words to model global dependencies and local features, respectively. Subsequently, a novel hierarchical attention mechanism is introduced into the Graph Convolutional Network (GCN), dynamically adjusting the weights between nodes based on the input of the graph convolutional layer. This adaptive information aggregation enables each node to aggregate information adaptively according to its context and the importance of neighboring nodes. The research results on the SemEval-2010 Task 8 and KBP37 datasets thoroughly validate the effectiveness of the proposed model, demonstrating its significant performance advantage in relation extraction tasks. [ABSTRACT FROM AUTHOR]

The parametrization of the oblique corrections through S, T, and U – later extended by V, W and X – is a convenient way of comparing the predictions for various electroweak observables at the one-loop level between the Standard Model and its extensions. That parametrization assumes that the extensions under consideration have S U (2) × U (1) gauge symmetry and the tree-level relation m W = m Z cos θ W between the Weinberg angle and the gauge-boson masses. In models where that relation does not hold at the Lagrangian level, the parameter T is not ultraviolet-finite, making the parametrization inadequate. We present expressions that parametrize the difference of the various predictions of two models with m W ≠ m Z cos θ W in terms of oblique parameters. The parameter T does not play a role in those expressions. Conveniently, they may be reached from the ones that were derived for models with tree-level m W = m Z cos θ W , by performing a simple substitution for T. We also discuss the difficulties in using oblique parameters when comparing a model with m W ≠ m Z cos θ W to the Standard Model. Finally, we compute the relevant five oblique parameters S, U, V, W and X in the SM extended by both, hypercharge Y = 0 and Y = 1 , triplet scalars. [ABSTRACT FROM AUTHOR]

The Connectivity Augmentation Problem (CAP) together with a well-known special case thereof known as the Tree Augmentation Problem (TAP) are among the most basic Network Design problems. There has been a surge of interest recently to find approximation algorithms with guarantees below 2 for both TAP and CAP, culminating in the currently best approximation factor for both problems of 1.393 through quite sophisticated techniques. We present a new and arguably simple matching-based method for the well-known special case of leaf-to-leaf instances. Combining our work with prior techniques, we readily obtain a (4 / 3 + ε) -approximation for Leaf-to-Leaf CAP by returning the better of our solution and one of an existing method. Prior to our work, a 4 / 3 -guarantee was only known for Leaf-to-Leaf TAP instances on trees of height 2. Moreover, when combining our technique with a recently introduced stack analysis approach, which is part of the above-mentioned 1.393-approximation, we can further improve the approximation factor to 1.29, obtaining for the first time a factor below 4 3 for a nontrivial class of TAP/CAP instances. [ABSTRACT FROM AUTHOR]

Red–black (RB) trees are one of the most efficient variants of balanced binary search trees. However, they have often been criticized for being too complicated, hard to explain, and unsuitable for pedagogical purposes, particularly their delete operation. Sedgewick (in: Dagstuhl Workshop on Data Structures, 2008. https://sedgewick.io/wp-content/themes/sedgewick/papers/2008LLRB.pdf) identified the length of code as the root of the problems and introduced left-leaning red–black (LLRB) trees. The delete operation of LLRB trees has a compact recursive code. Unfortunately, it may perform many unnecessary operations. The crux of the deletion algorithm is dealing with a "deficient" subtree, that is one whose black-height has become one less than that of its sibling subtree. In this paper, we revisit 2–3 red–black trees and propose a parity-seeking delete algorithm with the basic idea of making a deficient subtree on a par with its sibling: either by fixing the deficient subtree or by turning the sibling deficient as well, ascending deficiency to the parent node. Interestingly, the proposed parity-seeking delete algorithm also works for 2–3–4 RB trees. Our experiments show that the proposed parity-seeking delete algorithm is as efficient as the best preceding RB trees. The proposed parity-seeking delete algorithm is easily understandable and suitable for pedagogical and practical purposes. [ABSTRACT FROM AUTHOR]

The goal of aspect-based sentiment analysis is to recognize the aspect information in the text and the corresponding sentiment polarity. A variety of robust methods, including attention mechanisms and convolutional neural networks, have been extensively utilized to tackle this complex task. Better experimental results are obtained by using graph convolutional networks (GCN) based on semantic dependency trees in previous studies. Therefore, abundant methods begin to use sentence structure information to complete this task. However, only the loose connection between aspect words and contexts is realized in some practices due to sentences may contain complex relations. To solve this problem, Twain-Syntax graph convolutional network model is proposed, which can utilize multiple syntactic structure information simultaneously. Guided by the constituent tree and dependency tree, rich syntactic information is fully used in the model to build the sentiment-aware context for each aspect. In special, the multilayer attention mechanism and GCN are employed for learning to capture the correlation between words. By integrating syntactic information, this approach significantly refines the model's technical performance. Extensive testing on four benchmark datasets shows that the model delineated in this paper exhibits high levels of efficiency, comparable to several cutting-edge models. [ABSTRACT FROM AUTHOR]

Studies show that homogeneity among trees interferes with stand productivity, however, this information has not been incorporated into stand-level growth and yield models to assist forest managers. This paper presents a new format for basal area growth modeling, that includes the effect of homogeneity on stand productivity and was developed for unthinned and thinned Pinus taeda stands. The database came from a 3 × 3 factorial experiment with the factors of initial density (2500, 1250, and 625 trees ha−1), and thinning (without thinning, moderate thinning, and heavy thinning). The diameter distribution represented by the percentile method was used to represent stand homogeneity. The diameters (located in the 10th and 63rd percentiles) were inserted into the basal area growth model, which greatly increased the precision of the estimated predictions and projections. A simultaneous basal area growth model, compatible in prediction and projection, with the inclusion of stand homogeneity, is recommended for estimating the basal area growth of Pinus taeda stands in southern Brazil. [ABSTRACT FROM AUTHOR]

The projected northwards shift in the distribution suggests an expansion of European beech (Fagus sylvatica L.) into the Baltics and an increase of its commercial potential there. Furthermore, recent studies have shown good long-term survival of underplanted, yet non-rereleased beech under the presumedly limiting climate of the eastern part of Latvia, thus supporting the advance of the thermophilic species. Hence, the estimation of the responses of the underplanted beech to shelterwood removal is a logical step in the assessment of the specie's growth potential. To analyse the effect of conventionally managed mature coniferous shelterwood thinning on the growth of underplanted European beech, six thinning treatments (100, 75, and 50% of canopy, second canopy storey, second canopy storey with understorey removed, and the control) were tested in the 33-year-old northeasternmost experimental plantation in Europe. Growth responses were evaluated five years after the treatment, when beech was 38 years old. The survival and growth responses to shelterwood thinning and local characteristics at the tree and stand level were estimated using linear models. The post-treatment survival/mortality was independent, yet the dimensions of beech, particularly stem diameter, were significantly affected by shelterwood thinning intensity (positively). Regarding tree height, the response was somewhat weaker compared to that of stem diameter, while being disproportional to thinning intensity, with moderate thinning having the strongest positive effect. The estimated positive responsiveness of beech to shelterwood thinning suggested increasing growth potential of the species and expansion in the Baltics. Though the responses of beech were moderate probably due to the age and harsher climate. [ABSTRACT FROM AUTHOR]

Recently, finding extremal structures of graphs on Sombor index has received a lot of attention. The Sombor (SO) index of a graph G is defined by the sum of weights d e g G (u) 2 + d e g G (v) 2 over all edges uv of G, where d e g G (u) stands for the degree of vertex u in G. In this article, we obtain a lower bound on Sombor index of trees with a given order and total domination number, and characterize the trees achieving the bound. [ABSTRACT FROM AUTHOR]

In tropical forests, deciduous and evergreen leaf habits represent contrasting tree adaptations to precipitation seasonality. Both rainfall seasonality and interannual variation in rainfall are determinants of forest deciduousness, but their relative influence is not well understood. In this study, we evaluate the extent of deciduous-evergreen coexistence in tropical forests and develop a simple model of competition for water between leaf habits. Using this model, we formalize two mechanisms representing rainfall variability across time scales that may explain their stable coexistence: the temporal storage effect via interannual variability in rainfall vs. rainfall partitioning via evergreen access to dry-season rainfall. In our model, both mechanisms resulted in coexistence, but coexistence was more robust via resource partitioning. Empirically, remotely sensed deciduousness increased with precipitation seasonality, but effects of interannual rainfall variability on deciduousness were minor. We hypothesize that dry-season rainfall may prove a stronger influence on coexistence between leaf habits, and that changes in rainfall seasonality will have a greater impact on forest deciduousness than changes in the interannual variability of rainfall. [ABSTRACT FROM AUTHOR]

The widespread deployment of deep nets in practical applications has lead to a growing desire to understand how and why such black-box methods perform prediction. Much work has focused on understanding what part of the input pattern (an image, say) is responsible for a particular class being predicted, and how the input may be manipulated to predict a different class. We focus instead on understanding which of the internal features computed by the neural net are responsible for a particular class. We achieve this by mimicking part of the neural net with an oblique decision tree having sparse weight vectors at the decision nodes. Using the recently proposed Tree Alternating Optimization (TAO) algorithm, we are able to learn trees that are both highly accurate and interpretable. Such trees can faithfully mimic the part of the neural net they replaced, and hence they can provide insights into the deep net black box. Further, we show we can easily manipulate the neural net features in order to make the net predict, or not predict, a given class, thus showing that it is possible to carry out adversarial attacks at the level of the features. These insights and manipulations apply globally to the entire training and test set, not just at a local (single-instance) level. We demonstrate this robustly in the MNIST and ImageNet datasets with LeNet5 and VGG networks. [ABSTRACT FROM AUTHOR]