Tree Decomposition Research Articles

Morphometry and genetic diversity pattern of Cysticercus tenuicollis, an important food-borne taeniid metacestode in goats in Bangladesh.

Cysticercus tenuicollis is a larval stage of Taenia hydatigena resulting in cysticercosis, and responsible for enormous economic loses, especially in livestock production. Here, we planned to determine the prevalence and explore genetic variation of C. tenuicollis isolated from goats based on small subunit ribosomal RNA (rrnS) and cytochrome oxidase subunit 1 (cox1). To do this, samples were collected from different slaughter houses of municipal areas such as Bramhapalli slaughterhouse, Jubileeghat slaughterhouse and Mesuabazar slaughterhouse at Mymensingh sadar, and tentatively identified by morphological and morphometrical analysis. To study genetic variation, DNA was extracted from C. tenuicollis, and amplified rrnS and cox1 genes using specific primers, and were sequenced. Among 1372 examined animals, 177 (12.9%) were infected with C. tenuicollis. Cysts were recovered from peritoneum (7.9%), liver (4.4%) and urinary bladder (0.6%) of the infected animals. Females (18.9%) and adults (20.7%) were significantly more susceptible than male (8.8%) and young (9.3%), respectively. Genetic analysis defined 8 distinct rrnS genotypes and 9 unique cox1 haplotypes among 20 C. tenuicollis isolates. The nucleotide diversities were 0.00283 and 0.00434 for rrnS and cox1 genes, respectively. Neighbor joining (NJ) trees of rrnS and cox1 gene were constructed and the studied sequences were clustered with reference sequences of T. hydatigena with strong nodal support (100%). To compare Bangladeshi isolates, a median joining network was constructed with the population from other geographical regions and hosts. This led to a clustering pattern, but the clusters were not built with unique geographical regions or hosts. In conclusion, this is the first study that describes the genetic variation of T. hydatigena population and suggests the existence of host-specific variants. Therefore, it is fundamental to dispose infected viscera, restrict dog movement and proper management of slaughter house for the prevention and control of cysticercosis.

Systematic engineering design approach for improvement of oil-free twin-screw compressors

Twin-screw compressors are widely used in industry, especially in compressed air, refrigeration, air-conditioning and process gas which consume a significant part of the world’s energy. Nowadays, oil-injected compressors represent the majority of twin-screw compressors in the market due to their high efficiency and reliability. The oil-free compressor is potentially a better solution in the context of the net-zero CO2 target in 2050. However, due to its high thermal deformation and small clearances, this technology still suffers from reliability issues. To remedy this problem disruptive innovative solutions are required. In this purpose, the present study uses a systematic engineering design process to develop new concepts for the improvement of the oil-free twin-screw compressor. The paper is focused on the first two phases of the design process which are the definition of problem and the conceptual design. In the problem definition, main objectives are expressed and are divided into sub-objectives and weighed using an objective tree decomposition. Moreover, a thorough functional model of the oil-free compressor is detailed with a focus on the leakage paths and heat transfers. For the conceptual design, engineering characteristics extracted from the functional analysis have been assessed against the most important objectives using Quality Function Deployment matrices (QFD). Based on the developed problem definition, new concepts have been generated and three distinct concept categories have been further explored: Secondary flow; Surface features; Clearance control and monitoring. The evaluation, embodiment and detailed designs of the concepts, using experimental and numerical analyses will follow.

From modular decomposition trees to level-1 networks: Pseudo-cographs, polar-cats and prime polar-cats

The modular decomposition of a graph G is a natural construction to capture key features of G in terms of a labeled tree ( T , t ) whose vertices are labeled as “series” (1), “parallel” (0) or “prime”. However, full information of G is provided by its modular decomposition tree ( T , t ) only, if G does not contain prime modules. In this case, ( T , t ) explains G , i.e., { x , y } ∈ E ( G ) if and only if the lowest common ancestor lca T ( x , y ) of x and y has label “1”. This information, however, gets lost whenever ( T , t ) contains vertices with label “prime”. In this contribution, we aim at replacing “prime” vertices in ( T , t ) by simple 0/1-labeled cycles, which leads to the concept of rooted labeled level-1 networks ( N , t ) . We characterize graphs that can be explained by such level-1 networks ( N , t ) , which generalizes the concept of graphs that can be explained by labeled trees, that is, cographs. We provide three novel graph classes: polar-cats are a proper subclass of pseudo-cographs which forms a proper subclass of prime polar-cats . In particular, every cograph is a pseudo-cograph and prime polar-cats are precisely those graphs that can be explained by a labeled level-1 network. The class of prime polar-cats is defined in terms of the modular decomposition of graphs and the property that all prime modules “induce” polar-cats. We provide a plethora of structural results and characterizations for graphs of these new classes. In particular, Polar-cats are precisely those graphs that can be explained by an elementary level-1 network ( N , t ) , i.e., ( N , t ) contains exactly one cycle C that is rooted at the root ρ N of N and where ρ N has exactly two children while every vertex distinct from ρ N has a unique child that is not located in C . Pseudo-cographs are less restrictive and those graphs that can be explained by particular level-1 networks ( N , t ) that contain at most one cycle. These findings, eventually, help us to characterize the class of all graphs that can be explained by labeled level-1 networks, namely prime polar-cats. Moreover, we show under which conditions there is a unique least-resolved labeled level-1 network that explains a given graph. In addition, we provide linear-time algorithms to recognize all these types of graphs and to construct level-1 networks to explain them.

Solving Projected Model Counting by Utilizing Treewidth and its Limits

In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projection variables, where multiple solutions that are identical when restricted to the projection variables count as only one solution. Inspired by the observation that the so-called “treewidth” is one of the most prominent structural parameters, our algorithm utilizes small treewidth of the primal graph of the input instance. More precisely, it runs in time O(22k+4n2) where k is the treewidth and n is the input size of the instance. In other words, we obtain that the problem PMC is fixed-parameter tractable when parameterized by treewidth. Further, we take the exponential time hypothesis (ETH) into consideration and establish lower bounds of bounded treewidth algorithms for PMC, yielding asymptotically tight runtime bounds of our algorithm.While the algorithm above serves as a first theoretical upper bound and although it might be quite appealing for small values of k, unsurprisingly a naive implementation adhering to this runtime bound suffers already from instances of relatively small width. Therefore, we turn our attention to several measures in order to resolve this issue towards exploiting treewidth in practice: We present a technique called nested dynamic programming, where different levels of abstractions of the primal graph are used to (recursively) compute and refine tree decompositions of a given instance. Further, we integrate the concept of hybrid solving, where subproblems hidden by the abstraction are solved by classical search-based solvers, which leads to an interleaving of parameterized and classical solving. Finally, we provide a nested dynamic programming algorithm and an implementation that relies on database technology for PMC and a prominent special case of PMC, namely model counting (#Sat). Experiments indicate that the advancements are promising, allowing us to solve instances of treewidth upper bounds beyond 200.

Hierarchical and modularly-minimal vertex colorings

Cographs are exactly the hereditarily well-colored graphs, i.e., the graphs for which a greedy vertex coloring of every induced subgraph uses only the minimally necessary number of colors χ(G). Greedy colorings are shown to be a subclass of hierarchical vertex colorings that naturally appear in phylogenetic combinatorics. The hierarchical colorings of cographs form a special class of minimal colorings. The fact that cotrees are the modular decomposition trees of cographs suggests a natural generalization: A coloring σ is modularly-minimal if |σ(M)| = χ(M) for every strong module M of G. We show that every graph admits a modularly minimal coloring. On cographs, furthermore, the modularly minimal colorings coincide with the hierarchical colorings. For certain hereditary graph classes efficient algorithms can be designed to compute modularly-minimal colorings.

Cloud-native alternating directions solver for isogeometric analysis

Computer simulations with isogeometric analysis (IGA) have multiple applications, from phase-field modeling to tumor-growth simulations. We focus on the alternating-directions solver (ADS) algorithm, in which the matrix equation representing a computational problem is decomposed into parallel tasks following the binary and balanced structure of an elimination tree. In this paper, we explore the possibility of running large-scale IGA simulations using linear computational cost alternating direction solvers on top of modern data-parallel cloud computing frameworks. To this end, we propose a new way of decomposition of the elimination tree which makes the IGA alternating-direction solver effectively a large graph problem suitable for modern cloud-computing frameworks. On this basis, we propose a new algorithm for isogeometric analysis alternating-directions solver based on the Pregel computational model, used for large-scale graph-processing in the cloud. We implement a cloud-native solver using this algorithm in the Apache Giraph framework, and show that it can be applied for solution of challenging higher-order PDEs. We evaluate the solver in terms of various scalability models and run configurations. The results indicate linear scalability of the proposed algorithm with respect to the number of elements in the mesh.

A New Voltage Based Fault Detection Technique for Distribution Network Connected to Photovoltaic Sources Using Variational Mode Decomposition Integrated Ensemble Bagged Trees Approach

The increasing integration of renewable sources into distributed networks results in multiple protection challenges that would be insufficient for conventional protection strategies to tackle because of the characteristics and functionality of distributed generation. These challenges include changes in fault current throughout various operating modes, different distribution network topologies, and high-impedance faults. Therefore, the protection and reliability of a photovoltaic distributed network relies heavily on accurate and adequate fault detection. The proposed strategy utilizes the Variational Mode Decomposition (VMD) and ensemble bagged trees method to tackle these problems in distributed networks. Primarily, VMD is used to extract intrinsic mode functions from zero-, positive-, and negative-sequence components of a three-phase voltage signal. Next, the acquired intrinsic mode functions are supplied into the ensemble bagged trees mechanism for detecting fault events in a distributed network. Under both radial and mesh-soft normally open-point (SNOP) topologies, the outcomes are investigated and compared in the customarily connected and the island modes. Compared to four machine learning mechanisms, including linear discriminant, linear support vector mechanism (SVM), cubic SVM and ensemble boosted tree, the ensemble bagged trees mechanism (EBTM) has superior accuracy. Furthermore, the suggested method relies mainly on local variables and has no communication latency requirements. Therefore, fault detection using the proposed strategy is reasonable. The simulation outcomes show that the proposed strategy provides 100 percent accurate symmetrical and asymmetrical fault diagnosis within 1.25 ms. Moreover, this approach accurately identifies high- and low-impedance faults.

Gapped Indexing for Consecutive Occurrences

The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting queries (return all positions where the pattern occurs), and counting queries (return the number of occurrences of the pattern). In this paper we consider a variant of string indexing, where the goal is to compactly represent the string such that given two patterns \(P_1\) and \(P_2\) and a gap range \({[}\alpha , \beta ]\) we can quickly find the consecutive occurrences of \(P_1\) and \(P_2\) with distance in \({[}\alpha , \beta ]\), i.e., pairs of subsequent occurrences with distance within the range. We present data structures that use linear space and query time \({\widetilde{O}}(|P_1|+|P_2|+n^{2/3})\) for existence and counting and \({\widetilde{O}}(|P_1|+|P_2|+n^{2/3}\hbox {occ}^{1/3})\) for reporting. We complement this with a conditional lower bound based on the set intersection problem showing that any solution using \({\widetilde{O}}(n)\) space must use \({\widetilde{\Omega }}(|P_1| + |P_2| + \sqrt{n})\) query time. To obtain our results we develop new techniques and ideas of independent interest including a new suffix tree decomposition and hardness of a variant of the set intersection problem.

Chordal graphs through clique trees

Here we present a part of the work in collaboration with Jayme Luiz Szwarcfiter and Marisa Gutierrez, during the development of the thesis of Silvia Tondato at Facultad de Ciencias Exactas (UNLP), "Grafos Cordales: árboles cliques y representaciones canónicas'', finished in 2009.

A review of challenges and solutions in the design and implementation of deep graph neural networks

The study of graph neural networks has revealed that they can unleash new applications in a variety of disciplines using such a basic process that we cannot imagine in the context of other deep learning designs. Many limitations limit their expressiveness, and researchers are working to overcome them to fully exploit the power of graph data. There are a number of publications that explore graph neural networks (GNNs) restrictions and bottlenecks, but the common thread that runs through them all is that they can all be traced back to message passing, which is the key technique we use to train our graph models. We outline the general GNN design pipeline in this study as well as discuss solutions to the over-smoothing problem, categorize the solutions, and identify open challenges for further research. Abbreviations: CGNN: Continuous Graph Neural Networks; CNN: Convolution NeuralNetwork; DeGNN: Decomposition Graph Neural Network; DGN: Directional GraphNetworks; DGN: Differentiable Group Normalization; DL: Deep Learning; EGAI:Enhancing GNNs by a High-quality Aggregation of Beneficial Information; GAT: GraphAttention Network; GCN: Graph Convolutional Network; GDC: Graph Drop Connect; GDR: Group Distance Ratio; GNN: Graph Neural Network; GRAND: GraphRandom Neural Networks; IIG: Instance Information Gain; MAD: Man AverageDistance; PDE-GCN: Partial Differential Equations-GCN; PTDNet: ParameterizedTopological Denoising network; TDGNN: Tree Decomposition Graph NeuralNetwork;

Detecting Feedback Vertex Sets of Size k in O ⋆ (2.7 k ) Time

In the Feedback Vertex Set (FVS) problem, one is given an undirected graph G and an integer k , and one needs to determine whether there exists a set of k vertices that intersects all cycles of G (a so-called feedback vertex set). Feedback Vertex Set is one of the most central problems in parameterized complexity: It served as an excellent testbed for many important algorithmic techniques in the field such as Iterative Compression [Guo et al. (JCSS’06)], Randomized Branching [Becker et al. (J. Artif. Intell. Res’00)] and Cut&Count [Cygan et al. (FOCS’11)]. In particular, there has been a long race for the smallest dependence f(k) in run times of the type O ⋆ (f(k)) , where the O ⋆ notation omits factors polynomial in n . This race seemed to have reached a conclusion in 2011, when a randomized O ⋆ (3 k ) time algorithm based on Cut&Count was introduced. In this work, we show the contrary and give a O ⋆ (2.7 k ) time randomized algorithm. Our algorithm combines all mentioned techniques with substantial new ideas: First, we show that, given a feedback vertex set of size k of bounded average degree, a tree decomposition of width (1-Ω (1))k can be found in polynomial time. Second, we give a randomized branching strategy inspired by the one from [Becker et al. (J. Artif. Intell. Res’00)] to reduce to the aforementioned bounded average degree setting. Third, we obtain significant run time improvements by employing fast matrix multiplication.

Genetic Diversity and Population Structure of Hemiculter leucisculus (Basilesky, 1855) in Xinjiang Tarim River.

Hemiculter leucisculus is an invasive fish and widely distributed in the Xinjiang Tarim River. In this study, RAD-seq was used to explore the genetic diversity and population subgroup structure of H. leucisculus in the Tarim River and develop relevant Simple Sequence Repeat (SSR) markers. The study collected 40 samples distributed at four different sites of the Tarim River. A total of 7,291,260 single nucleotide polymorphisms (SNPs) were obtained. The genetic diversity results showed that the population genetic diversity level of H. leucisculus was low. The population pairwise FST values ranged from 0.231 to 0.258, indicating that there was moderate genetic differentiation among these populations. AMOVA showed that the genetic variation within populations accounted for 92.31% of the total variation. The principal component analysis (PCA) and neighbor joining (NJ) tree revealed that the four populations could be separated into two clusters (upper-middle and downstream populations) and the individuals from Taitema Lake (TTMH) showed differences and had a bigger geographic distance than the others. There is the probability that the H. leucisculus from Bosten Lake entered Taitema Lake to breed and then expanded into the Tarim River due to the water diversion projects in location. In addition, 147,705 SSRs loci were detected and 22,651 SSR primer pairs were developed. This study will contribute to providing valuable molecular data for the management of wild populations, marker-assisted selection and resource exploitation of H. leucisculus.

Automating Global Threat-Maps Generation via Advancements of News Sensors and AI

Negative events are prevalent all over the globe round the clock. People demonstrate psychological affinity to negative events, and they incline to stay away from troubled locations. This paper proposes an automated geospatial imagery application that would allow a user to remotely extract knowledge of troubled locations. The autonomous application uses thousands of connected news sensors to obtain real-time news pertaining to all global troubles. From the captured news, the proposed application uses artificial intelligence-based services and algorithms like sentiment analysis, entity detection, geolocation decoder, news fidelity analysis, and decomposition tree analysis to reconstruct global threat maps representing troubled locations interactively. The fully deployed system was evaluated for full three months of summer 2021, during which the autonomous system processed above 22 k news from 2397 connected news sources involving BBC, CNN, NY Times, Government websites of 192 countries, and all possible major social media sites. The study revealed 11,668 troubled locations classified successfully with outstanding precision, recall, and F1-score, all evaluated in ubiquitous environment covering mobile, tablet, desktop, and cloud platforms. The system generated interesting global threat maps for robust scenario set of 3.71 times {10}^{29}, to be reported as original fully autonomous remote sensing application of this kind. The research discloses attractive news and global threat-maps with trusted overall classification accuracy.

Delineating species boundary through DNA barcodes ofsome fishes inhabiting river Murti in the foothills of Darjeeling Himalayas

The aim of the present study was to establish a global bioidentification system in the form of a reference sequencelibrary where fish species inhabiting river Murti were delineated by a particular sequence denoted as genetic‘barcode’.40 species representing 27 genera, 16 families and 5 orders were collected along different altitudinal gradients if river Murti. Mitochondrial DNA was isolated from the samples followed by amplification of COI gene, alignment by CLUSTAL W and submission to GenBank. The average nucleotide frequencies were calculated whereall the fishes showed relatively higher GC content at second codon position. Haplotypes showed gradually decreasinggenetic distance within orders, families, genera with very low genetic distance within species indicating markedgenetic divergence beyond species boundaries. The average transitional pairs were found more frequent than averagetransversional pairs. The Neighbour Joining tree revealed distinct clusters formed by members of order Cypriniformes, Siluriformes, Perciformes, Synbranchiformes and Beloniformes, where the conspecific individualswere always found to cluster under the same node supported by high bootstrap value, while dissimilar species wereclustered under separate nodes, ensuring unambiguous identification of species. The research work suggests that COI barcoding can be taken up as a sensible approach to eliminate obscurity in the identification of the fish fauna withapplications in its management and conservation of the species inhabiting in specific microhabitats. Keywords: COI gene, DNA Barcode, sequence library, unambiguous identification, conservation.

Sequential sampling of junction trees for decomposable graphs

The junction-tree representation provides an attractive structural property for organising a decomposable graph. In this study, we present two novel stochastic algorithms, referred to as the junction-tree expander and junction-tree collapser, for sequential sampling of junction trees for decomposable graphs. We show that recursive application of the junction-tree expander, which expands incrementally the underlying graph with one vertex at a time, has full support on the space of junction trees for any given number of underlying vertices. On the other hand, the junction-tree collapser provides a complementary operation for removing vertices in the underlying decomposable graph of a junction tree, while maintaining the junction tree property. A direct application of the proposed algorithms is demonstrated in the setting of sequential Monte Carlo methods, designed for sampling from distributions on spaces of decomposable graphs. Numerical studies illustrate the utility of the proposed algorithms for combinatorial computations on decomposable graphs and junction trees. All the methods proposed in the paper are implemented in the Python library trilearn.

A stochastic dual dynamic integer programming based approach for remanufacturing planning under uncertainty

ABSTRACT We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent the uncertain information structure. We introduce a new dynamic programming formulation that relies on a partial nested decomposition of the scenario tree. We then propose a new approximate stochastic dual dynamic integer programming algorithm based on this partial decomposition. Our numerical results show that the proposed solution approach is able to provide near-optimal solutions for large-size instances with a reasonable computational effort.

Induced subgraphs and tree decompositions III. Three-path-configurations and logarithmic treewidth

A _theta_ is a graph consisting of two non-adjacent vertices and three internally disjoint paths between them, each of length at least two. For a family $\mathcal{H}$ of graphs, we say a graph $G$ is $\mathcal{H}$-_free_ if no induced subgraph of $G$ is isomorphic to a member of $\mathcal{H}$. We prove a conjecture of Sintiari and Trotignon, that there exists an absolute constant $c$ for which every (theta, triangle)-free graph $G$ has treewidth at most $c\log (|V(G)|)$. A construction by Sintiari and Trotignon shows that this bound is asymptotically best possible, and (theta, triangle)-free graphs comprise the first known hereditary class of graphs with arbitrarily large yet logarithmic treewidth. Our main result is in fact a generalization of the above conjecture, that treewidth is at most logarithmic in $|V(G)|$ for every graph $G$ excluding the so-called _three-path-configurations_ as well as a fixed complete graph. It follows that several NP-hard problems such as Stable Set, Vertex Cover, Dominating Set and $k$-Coloring (for fixed $k$) admit polynomial time algorithms in graphs excluding the three-path-configurations and a fixed complete graph.

RJT-RL: De novo molecular design using a Reversible Junction Tree and Reinforcement Learning

RJT-RL: De novo molecular design using a Reversible Junction Tree and Reinforcement Learning

Treewidth-based algorithms for the small parsimony problem on networks

BackgroundPhylogenetic reconstruction is one of the paramount challenges of contemporary bioinformatics. A subtask of existing tree reconstruction algorithms is modeled by the Small Parsimony problem: given a tree T and an assignment of character-states to its leaves, assign states to the internal nodes of T such as to minimize the parsimony score, that is, the number of edges of T connecting nodes with different states. While this problem is polynomial-time solvable on trees, the matter is more complicated if T contains reticulate events such as hybridizations or recombinations, i.e. when T is a network. Indeed, three different versions of the parsimony score on networks have been proposed and each of them is NP-hard to decide. Existing parameterized algorithms focus on combining the number c of possible character-states with the number of reticulate events (per biconnected component).ResultsWe consider the parameter treewidth t of the underlying undirected graph of the input network, presenting dynamic programming algorithms for (slight generalizations of) all three versions of the parsimony problem on size-n networks running in times c^t {n^{O(1)}}, (3c)^t {n^{O(1)}}, and 6^{tc}n^{O(1)}, respectively. Our algorithms use a formulation of the treewidth that may facilitate formalizing treewidth-based dynamic programming algorithms on phylogenetic networks for other problems.ConclusionsOur algorithms allow the computation of the three popular parsimony scores, modeling the evolutionary development of a (multistate) character on a given phylogenetic network of low treewidth. Our results subsume and improve previously known algorithm for all three variants. While our results rely on being given a “good” tree-decomposition of the input, encouraging theoretical results as well as practical implementations producing them are publicly available. We present a reformulation of tree decompositions in terms of “agreeing trees” on the same set of nodes. As this formulation may come more natural to researchers and engineers developing algorithms for phylogenetic networks, we hope to render exploiting the input network’s treewidth as parameter more accessible to this audience.

Molecular Design Method Using a Reversible Tree Representation of Chemical Compounds and Deep Reinforcement Learning.

Automatic design of molecules with specific chemical and biochemical properties is an important process in material informatics and computational drug discovery. In this study, we designed a novel coarse-grained tree representation of molecules (Reversible Junction Tree; “RJT”) for the aforementioned purposes, which is reversely convertible to the original molecule without external information. By leveraging this representation, we further formulated the molecular design and optimization problem as a tree-structure construction using deep reinforcement learning (“RJT-RL”). In this method, all of the intermediate and final states of reinforcement learning are convertible to valid molecules, which could efficiently guide the optimization process in simple benchmark tasks. We further examined the multiobjective optimization and fine-tuning of the reinforcement learning models using RJT-RL, demonstrating the applicability of our method to more realistic tasks in drug discovery.