Induced subgraphs and tree decompositions XVI. Complete bipartite induced minors

A bstract The time-ordered multilayer integrals have long been cited as major challenges in the analytical study of cosmological correlators and wavefunction coefficients. The recently proposed family tree decomposition technique solved these time integrals in terms of canonical objects called family trees, which are multivariate hypergeometric functions with energies as variables and twists as parameters. In this work, we provide a systematic study of the analytical properties of family trees. By exploiting the great flexibility of Mellin representations of family trees, we identify and characterize all their singularities in both variables and parameters and find their exact series representations around all singularities with finite convergent domains. These series automatically generate analytical continuation of arbitrary family trees over many distinct regions in the energy space. As a corollary, we show the factorization of family trees at zero partial-energy singularities to all orders. Our findings offer essential analytical data for further understanding and computing cosmological correlators.

We describe the implementation of the Giudici–Green Metropolis sampling method for decomposable graphs using a variety of structures to represent the graph and maintain decomposability. These comprise the graph itself, the junction tree, the Almond tree and the Ibarra clique-separator graph. For each structure, we describe the process for ascertaining whether adding or deleting a specific edge results in a new graph that is also decomposable, and the updates that need to be made to the structure if the edge perturbation is made. We find that using the graph itself is generally competitive in terms of computational efficiency for a variety of graph distributions, but note that the other structures may allow and suggest samplers using different perturbations with lower rejection rates and/or better mixing properties. The sampler has applications in estimating graphical models for systems of multivariate Gaussian or Multinomial variables.

A Canonical Tree Decomposition for Order Types, and Some Applications

PurposeThis study assessed the effectiveness of treatments using intense pulsed light (IPL) in reducing vascular lesions of the facial skin, such as erythema and telangiectasia.Patients and MethodsThe study involved 38 subjects aged 20 to 61 who underwent a series of 3 IPL procedures. In order to quantitatively assess the effects of therapy, advanced clinical photography techniques involving cross-polarized light and dedicated image analysis algorithms, ie GLCM (Gray-Level Co-occurrence Matrix) and QTDCOMP (Quadratic Tree Decomposition), were used.ResultsThe results indicate a significant reduction in vascular lesions after a series of treatments, which was confirmed by a statistically significant reduction in GLCM contrast and an increase in image homogeneity. Additionally, the use of quadratic tree decomposition allowed for the quantitative determination of skin homogeneity after therapy.ConclusionThe study has shown that image registration in cross-polarized light as well as GLCM and QTDCOMP analysis are effective tools for the objective and quantitative assessment of vascular skin lesions. These methods can be widely used in clinical practice to optimize the therapy of vascular lesions and monitor the effectiveness of IPL procedures.

The increasing integration of engineering systems has led to heightened system complexity, significantly elevating functional failure risks. As a core strategy to enhance anti-interference capabilities and ensure long-term operational stability, resilience design must advance beyond traditional experience-driven functional analysis paradigms. This study proposes a Bayesian network-based method integrating functional coupling analysis with resilience design. First, a functional coupling network is constructed through functional decomposition trees and structural analysis, supplemented by a confounding factor analysis strategy. Subsequently, patent databases are analyzed to identify inter-functional coupling relationships, with Bayesian network backwards inference and sensitivity analysis pinpointing crucial functions and failure propagation paths, thereby overcoming empirical limitations. Finally, system functional cycle reconfiguration and resilience evaluation are implemented to strengthen conceptual design robustness. Through functional coupling analysis and resilience design of wind turbines under extreme operating conditions, the method’s efficacy in identifying crucial functions and guiding resilient product conceptual design is demonstrated.

Abstract In phylogenetics, reconstructing rooted trees from distances between taxa is a common task. Böcker and Dress generalized this concept by introducing symbolic dating maps $$\delta :X \times X \rightarrow \Upsilon $$ δ : X × X → Υ , where distances are replaced by symbols, and showed that there is a one-to-one correspondence between symbolic ultrametrics and labeled rooted phylogenetic trees. Many combinatorial structures fall under the umbrella of symbolic dating maps, such as 2-dissimilarities, symmetric labeled 2-structures, or edge-colored complete graphs, and are here referred to as strudigrams. Strudigrams have a unique decomposition into non-overlapping modules, which can be represented by a modular decomposition tree (MDT). In the absence of prime modules, strudigrams are equivalent to symbolic ultrametrics, and the MDT fully captures the relationships $$\delta (x,y)$$ δ ( x , y ) between pairs of vertices $$x,y \in X$$ x , y ∈ X through the label of their least common ancestor in the MDT. However, in the presence of prime modules, appearing as prime vertices in the MDT, this information is generally hidden. To provide this missing structural information, we aim to locally replace the prime vertices in the MDT to obtain networks that capture full information about the strudigrams. While starting with the general framework of prime-vertex replacement networks, we then focus on a specific type of such networks obtained by replacing prime vertices with so-called galls, resulting in labeled galled-trees. We introduce the concept of galled-tree explainable (GaTEx) strudigrams, provide their characterization, and demonstrate that recognizing these structures and reconstructing the labeled networks that explain them can be achieved in polynomial time.

Gray leaf spot (GLS) is a damaging disease of perennial ryegrass, tall fescue, and St. Augustinegrass (Harmon, 2023). Zoysiagrass samples exhibiting GLS-like symptoms were collected from ‘Zenith’ zoysiagrass in Raleigh (KL027603) and from an experimental line of zoysiagrass in Rolesville, NC (KL027571) in late July 2022. Symptoms included oval or round lesions, tan color, and a dark brown border (Fig. 1A). Over time, the affected leaves exhibited dieback from the tip, and significant damage was observed. Temperatures in the Raleigh area averaged 26°C in July 2022 and local precipitation was greater than average. Zoysiagrass is an important turfgrass for golf course fairways and home lawns in the transition zone and Southeastern US. Thus, knowledge of a new host for a devastating disease such as GLS is critical. Following incubation of affected zoysiagrass in a humid environment at 23°C for 24 hours, portions of leaves with typical GLS symptoms were viewed microscopically, where numerous three-celled, pear-shaped conidia were observed (Fig. 1B). Symptomatic leaves were placed onto antibiotic-amended potato dextrose agar (PDA) containing 0.05 g L-1 of chloramphenicol, streptomycin, and tetracycline. After subculturing, 95% of all samples plated yielded colonies that matched colony descriptions for P. oryzae (Harmon, 2023, Ma and Uddin, 2009, and Nanayakkara, U. N. et al., 2008). Once pure cultures were obtained, actively growing isolates were transferred to oatmeal agar and grown at 22°C for 5 days. After 5 days, sterilized alfalfa stems were placed in the cultures to induce sporulation. Cultures were incubated at 26°C under consistent fluorescent light for 10 to 12 days. Spores were harvested by flooding the plates with 15 mL of distilled water, and conidia were scraped from the surface of the plates from ten isolates with a sterilized needle (Ma and Uddin, 2009, and Nanayakkara, U. N. et al., 2008). Five spores per isolate were measured using a micrometer embedded in a Zeiss AX10 Imager A1 compound microscope. Conidia were hyaline, pyriform in shape, two-septate, and averaged 8.5 ± 1.2 (wide) x 27.3 ± 6.3 (length) μm, consistent with the descriptions presented in Harmon (2023). The ITS1, 5.8S, and ITS2 region along with the actin gene from two zoysiagrass isolates were amplified by polymerase chain reaction using fungal ITS5/4 primers (KL027603 / KL027571 - 509 bp) and ACT-512F/ACT-783R (KL027603 - 240 bp / KL027571 - 249 bp)(Couch and Kohn 2002, and White et. al 1990). These sequences were uploaded to NCBI GenBank under accession numbers (KL027603 rRNA: PV477962, KL027603 ACT: PV495209; KL027571 rRNA: PV477982, KL027571 ACT: PV495208). Nucleotide blasting resulted in ≥99% sequence identity to Pyricularia oryzae Cavara accession CBS:365.52. (ITS1,5.8S,ITS2: Genbank accession MH857082.1)(ACT: Genbank accession KM485191.1). The rRNA region and actin gene were concatenated, and a clustal omega alignment was performed. A Kamura-Nei neighbor joining tree with 1,000 bootstraps was generated and visualized in Geneious Prime (Kamura et al 2004) (Fig. 2). KL027603 and KL027571 clustered with P. oryzae with 100% bootstrap support, providing more evidence that these isolates are P. oryzae. Koch’s postulates were performed on ‘Zenith’ zoysiagrass plants established from seed. Pots containing sterilized potting mix were seeded with ‘Zenith’ zoysiagrass and allowed to grow and develop for 7 weeks prior to inoculation. All ten isolates of P. oryzae were plated onto PDA and allowed to grow at 26°C for three days. After 3 days of growth, agar plugs from the edge of the colonies were transferred into sterilized rye grain to produce inoculum. Five infested rye grains were placed in the canopy of ‘Zenith’ zoysiagrass and kept moist by putting them in a clear plastic bin in the greenhouse, where temperatures ranged from 23-28°C. Symptoms developed 5 to 7 days after inoculation and were consistent with those described above and those attributed to GLS on other turfgrasses. We successfully isolated P. oryzae from the affected tissue in the pathogenicity tests. To our knowledge, this is the first report of GLS disease on zoysiagrass in the United States.

The aim of the study is to improve the accuracy of machine learning of the electromyographic signal (EMG) recognition system for controlling a hand prosthesis with a non-invasive biosignal reading system.The information-extreme machine learning method is proposed, which is developed within the framework of the func-tional approach to modelling cognitive processes of building and making classification decisions by natural intelligence. This makes the method flexible when retraining the system in the case of expanding the alphabet of recognition classes. To solve the multidimensionality problem of the recognition class alphabet, a hierarchical information-extreme machine learning algorithm based on the decursive data structure was developed and implemented. This data structure allows switching from multi-class machine learning to two-class machine learning for each stratum of the binary decursive tree when the number of recognition classes increases. Construction of highly accurate decision rules for the recognition classes of each stratum of the binary decomposition tree is carried out by optimising the machine learning parameters, the number of which determines the level of machine learning depth. As the criterion for optimising machine learning parameters, the authors use the Kullback information measure modified by the authors in the form of a functional of the accuracy characteristics.Due to computer modelling, error-free decision rules for the alphabet with eight recognition classes, which characterise the EMG signals of the corresponding hand and finger movements, have been built using the training matrix.Conclusions: It has been experimentally proved that when the number of recognition classes exceeds two, it is necessary to switch from a linear data structure to a hierarchical one in the form of a binary decursive tree.

Fine woody debris (FWD; deadwood < 10cm diameter) is a crucial but often overlooked component of forest ecosystems. It provides habitat for microbial communities and enhances soil fertility through nutrient cycling. This role is especially important in managed forests, which typically have limited deadwood stocks. Climate change is increasing forest disturbances and expanding early successional forests with low canopy cover, yet the effects on microbial communities and related processes remain poorly understood. In a ten-year canopy manipulation experiment, we examined the decomposition of FWD of Fagus sylvatica and Abies alba. Increased canopy openness significantly decreased bacterial diversity in decomposing FWD and altered the community composition in surrounding soil. Decomposition time was the main factor shaping bacterial community structure in FWD, with tree species and canopy cover also contributing. We identified bacterial groups involved in carbohydrate degradation, fungal biomass breakdown, and nitrogen fixation. Importantly, bacterial communities in fully decomposed FWD remained distinct from soil communities. Deadwood decomposition and nutrient cycling are driven by complex ecological interactions. Microbial community dynamics are influenced by the interplay of FWD decomposition stage, tree species, and microclimatic conditions. Bacterial communities, although less frequently studied in this context, appear more stable over time than previously studied fungi. This stability may help sustain decomposition processes and nutrient turnover under the environmental variability associated with global change.

We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets \(\sigma,\rho\) of non-negative integers, a \((\sigma,\rho)\) -set of a graph G is a set S of vertices such that \(|N(u)\cap S|\in\sigma\) for every \(u\in S\) , and \(|N(\!\textit{v})\cap S|\in\rho\) for every \(\textit{v}\not\in S\) . The problem of finding a \((\sigma,\rho)\) -set (of a certain size) unifies standard problems, such as Independent Set , Dominating Set , Independent Dominating Set , and many others. For all pairs of finite or cofinite sets \((\sigma,\rho)\) , we determine (under standard complexity assumptions) the best possible value \(c_{\sigma,\rho}\) such that there is an algorithm that counts \((\sigma,\rho)\) -sets in time \(c_{\sigma,\rho}^{\textsf{tw}}\cdot n^{O(1)}\) (if a tree decomposition of width \(\textsf{tw}\) is given in the input). Let \(s_{{\rm top}}\) denote the largest element of \(\sigma\) if \(\sigma\) is finite, or the largest missing integer \(+1\) if \(\sigma\) is cofinite; \(r_{{\rm top}}\) is defined analogously for \(\rho\) . Surprisingly, \(c_{\sigma,\rho}\) is often significantly smaller than the natural bound \(s_{{\rm top}}+r_{{\rm top}}+2\) achieved by existing algorithms. Toward defining \(c_{\sigma,\rho}\) , we say that \((\sigma,\rho)\) is \({\mathrm{m}}\) -structured if there is a pair \((\alpha,\beta)\) such that every integer in \(\sigma\) equals \(\alpha\) mod \({\mathrm{m}}\) , and every integer in \(\rho\) equals \(\beta\) mod \({\mathrm{m}}\) . Then, setting — \(c_{\sigma,\rho}=s_{{\rm top}}+r_{{\rm top}}+2\) if \((\sigma,\rho)\) is not \({\mathrm{m}}\) -structured for any \({\mathrm{m}}\geq 2\) , — \(c_{\sigma,\rho}=\max\{s_{{\rm top}},r_{{\rm top}}\}+2\) if \((\sigma,\rho)\) is 2-structured, but not \({\mathrm{m}}\) -structured for any \({\mathrm{m}}\geq 3\) , and \(s_{{\rm top}}=r_{{\rm top}}\) is even, and we count the number of edges between — \(c_{\sigma,\rho}=\max\{s_{{\rm top}},r_{{\rm top}}\}+1\) , otherwise, we provide algorithms counting \((\sigma,\rho)\) -sets in time \(c_{\sigma,\rho}^{\textsf{tw}}\cdot n^{O(1)}\) . For example, for the Exact Independent Dominating Set problem (also known as Perfect Code ) corresponding to \(\sigma=\{0\}\) and \(\rho=\{1\}\) , this improves the \(3^{\textsf{tw}}\cdot n^{O(1)}\) algorithm of van Rooij to \(2^{\textsf{tw}}\cdot n^{O(1)}\) . Despite the unusually delicate definition of \(c_{\sigma,\rho}\) , an accompanying paper shows that our algorithms are most likely optimal, that is, for any pair \((\sigma,\rho)\) of finite or cofinite sets where the problem is non-trivial, and any \(\varepsilon &gt; 0\) , a \((c_{\sigma,\rho}-\varepsilon)^{\textsf{tw}}\cdot n^{O(1)}\) -algorithm counting the number of \((\sigma,\rho)\) -sets would violate the Counting Strong Exponential-Time Hypothesis (#SETH). For finite sets \(\sigma\) and \(\rho\) , these lower bounds also extend to the decision version, and hence, our algorithms are optimal in this setting as well. In contrast, for many cofinite sets, we show that further significant improvements for the decision and optimization versions are possible using the technique of representative sets.

In this article, we investigate space-time tradeoffs for answering conjunctive queries with access patterns (CQAPs). The goal is to create a space-efficient data structure in an initial preprocessing phase and use it for answering (multiple) queries in an online phase. Previous work has developed data structures that trades off space usage for answering time for queries of practical interest, such as the path and triangle query. However, these approaches lack a comprehensive framework and are not generalizable. Our main contribution is a general algorithmic framework for obtaining space-time tradeoffs for any CQAP. Our framework builds upon the PANDA algorithm and tree decomposition techniques. We demonstrate that our framework captures all state-of-the-art tradeoffs that were independently produced for various queries. Furthermore, we show surprising improvements over the state-of-the-art tradeoffs known in the existing literature for reachability queries.

Abstract In the ΛCDM universe, structure formation is generally not a self-similar process, while some self-similarity remains in certain statistics, which can greatly simplify our description and understanding of the cosmic structures. In this work, we show that the merger tree of dark matter halos is approximately self-similar by investigating the universality of the subhalo peak mass function (PMF) describing the mass distribution of progenitor halos. Using a set of cosmological simulations and identifying subhalos of different merger levels with hbt+, we verify that the level-1 subhalo PMF is close to universal across halo mass, redshift, and cosmology. This approximate self-similarity allows us to analytically derive the subhalo PMF for subhalos accreted at any level (i.e., for sub-subhalos) through self-convolutions of the level-1 PMF, and the resulting model shows good agreement with simulation measurements. We further derive a number of analytical properties of the hierarchical origin of subhalos. We show that higher-level subhalos dominate at progressively lower peak mass in the PMF and are more likely to originate from major mergers than lower-level ones. At a given merger mass ratio, the subhalo accretion rates at each level track the growth rate of the host halo. At a fixed final mass ratio, however, subhalos of higher-level, higher-mass-ratio, and in more massive haloes tend to be accreted more recently. Matching subhalo peak mass to galaxy mass, these results have direct implications on the hierarchical origin of satellite galaxies.

Abstract Machine learning (ML) has shown promise in screening organic molecular additives for planar perovskite photovoltaics, but is often hindered by predictive biases due to small datasets and reliance on predefined descriptors. Here, Co‐Pilot for Perovskite Additive Screener (Co‐PAS) is introduced, an ML‐driven framework designed to accelerate additive (or passivator) screening for perovskite solar cells (PSCs). Co‐PAS integrates the Molecular Scaffold Classifier (MSC) for scaffold‐based pre‐screening and utilizes Junction Tree Variational Autoencoder (JTVAE) to achieve data‐driven molecular structure representation, significantly enhancing the accuracy of power conversion efficiency (PCE) predictions. By applying Co‐PAS to screen 250 000 molecules randomly drawn from PubChem, candidates are prioritized based on predicted PCE values and key molecular properties, including donor number, dipole moment, and hydrogen bond acceptor count. This workflow helps narrow down to 76 promising candidates, including Boc‐L‐threonine N‐hydroxysuccinimide ester (BTN), a previously unexplored additive in PSCs. The solar cell with BTN achieves a device PCE of 25.20%. These results underscore the potential of Co‐PAS in advancing additive discovery for high‐performance PSCs.

Risk-averse decision strategies for influence diagrams using rooted junction trees

Video-based adaptive vibration modal identification via binary decomposition tree

Alzheimer’s disease (AD) is marked by the pathological accumulation of amyloid beta-42 (Aβ42), contributing to synaptic dysfunction and neurodegeneration. While extracellular amyloid plaques are well-studied, increasing evidence highlights intracellular Aβ42 as an early and toxic driver of disease progression. In this study, we present a novel, Generative AI–based drug design approach to promote targeted degradation of Aβ42 via the ubiquitin–proteasome system (UPS), using E3 ligase–directed molecular glues. We systematically evaluated the ternary complex formation potential of Aβ42 with three E3 ligases (CRBN, VHL, and MDM2) through structure-based modeling, ADMET screening, and docking. We then developed a Ligase-Conditioned Junction Tree Variational Autoencoder (LC-JT-VAE) to generate ligase-specific small molecules, incorporating protein sequence embeddings and torsional angle-aware molecular graphs. Our results demonstrate that this generative model can produce chemically valid, novel, and target-specific molecular glues capable of facilitating Aβ42 degradation. This integrated approach offers a promising framework for designing UPS-targeted therapies for neurodegenerative diseases.

One of the most celebrated results of computing join-aggregate queries defined over commutative semi-rings is the classic Yannakakis algorithm proposed in 1981. It is known that the runtime of the Yannakakis algorithm is O(N + OUT) for any free-connex query, where N is the input size of the database and ØUT is the output size of the query result. This is already output-optimal. However, only an upper bound O(N • OUT) on the runtime is known for the large remaining class of acyclic but non-free-connex queries. Alternatively, one can convert a non-free-connex query into a free-connex one using tree decomposition techniques and then run the Yannakakis algorithm. This approach takes O(N #fn-subw + OUT) time, where #fn-subw is the free-connex sub-modular width of the query. But, none of these results is known to be output-optimal. In this paper, we show a matching lower and upper bound Θ(N • OUT 1 - 1/(fn-fhtw) + OUT) for computing general acyclic join-aggregate queries by semiring algorithms, where fn-fhtw is the free-connex fractional hypertree width of the query. For example, fn-fhtw = 1 for free-connex queries, fn-fhtw = 2 for line queries (a.k.a. chain matrix multiplication), and fn-fhtw = k for star queries (a.k.a. star matrix multiplication) with k relations. Although free-connex fractional hypertree width is a natural and well-established measure of how far a join-aggregate query is from being free-connex, we demonstrate that it precisely captures the output-optimal complexity of these queries. To our knowledge, this has been the first polynomial improvement over the Yannakakis algorithm in the last 40 years and completely resolves the open question of computing acyclic join-aggregate queries in an output-optimal way. As a by-product, our output-optimal algorithm for acyclic queries also yields new output-sensitive algorithms for cyclic queries via tree decomposition techniques.

Hypertree decompositions provide a way to evaluate Conjunctive Queries (CQs) in polynomial time, where the exponent of this polynomial is determined by the width of the decomposition. In theory, the goal of efficient CQ evaluation therefore has to be a minimisation of the width. However, in practical settings, it turns out that there are also other properties of a decomposition that influence the performance of query evaluation. It is therefore of interest to restrict the computation of decompositions by constraints and to guide this computation by preferences. To this end, we propose a novel framework based on candidate tree decompositions, which allows us to introduce soft hypertree width (shw). This width measure is a relaxation of hypertree width (hw); it is never greater than hw and, in some cases, shw may actually be lower than hw. Most importantly, shw preserves the tractability of deciding if a given CQ is below some fixed bound, while offering more algorithmic flexibility. In particular, it provides a natural way to incorporate preferences and constraints into the computation of decompositions. A prototype implementation and preliminary experiments confirm that this novel framework can indeed have a practical impact on query evaluation.

On the maximum spectral radius of clique trees with a given zero forcing number