Binary Tree Research Articles

Integrated dynamic scheduling of shipyard blocks considering adaptive adjustment in stockyard layout

The scarcity of space resources and backward scheduling management in block assembly yards have become constraints on shipyard logistics owing to demands in shipbuilding technology and scheduling efficiency. This article proposes a novel integrated dynamic scheduling method for shipyard blocks considering adaptive adjustment in stockyard layout. First, an optimization model is established to minimize the interference block moves. Then, dynamic adaptive layout prioritization rules and multi-strategy block movement policies are introduced for different cases. A heap field dynamic layout method based on a binary search tree and deep reinforcement learning algorithms is integrated to seek optimal scheduling. The proposed algorithm is validated with 50 sets of actual block data, four road types and four stockyard types. The results indicate that the proposed method effectively utilizes stockyard layout while reducing interference blocks during the movement process by 56%. A stockyard aspect ratio of approximately 3.2 yields optimal block scheduling effectiveness.

PyLOM: A HPC open source reduced order model suite for fluid dynamics applications

pyLOM: A HPC open source reduced order model suite for fluid dynamics applications

Tight Bounds on the Spooky Pebble Game: Recycling Qubits with Measurements

Pebble games are popular models for analyzing time-space trade-offs. In particular, reversible pebble game strategies are frequently applied in quantum algorithms like Grover's search to efficiently simulate classical computation on inputs in superposition, as unitary operations are fundamentally reversible. However, the reversible pebble game cannot harness the additional computational power granted by intermediate measurements, which are irreversible. The spooky pebble game, which models interleaved Hadamard basis measurements and adaptive phase corrections, reduces the number of qubits beyond what purely reversible approaches can achieve. While the spooky pebble game does not reduce the total space (bits plus qubits) complexity of the simulation, it reduces the amount of space that must be stored in qubits. We prove asymptotically tight trade-offs for the spooky pebble game on a line with any pebble bound. This in turn gives a tight time-qubit tradeoff for simulating arbitrary classical sequential computation when using the spooky pebble game. For example, for all ϵ∈(0,1], any classical computation requiring time T and space S can be implemented on a quantum computer using only O(T/ϵ) gates and O(TϵS1−ϵ) qubits. This improves on the best known bound for the reversible pebble game with that number of qubits, which uses O(21/ϵT) gates. For smaller space bounds, we show that the spooky pebble game can simulate arbitrary computation with O(T1+ϵS−ϵ/ϵ) gates and O(S/ϵ) qubits whereas any simulation via the reversible pebble game requires Ω(S⋅(1+log⁡(T/S))) qubits.We also consider the spooky pebble game on more general directed acyclic graphs (DAGs), capturing fine-grained data dependency in computation. We show that for an arbitrary DAG even approximating the number of required pebbles in the spooky pebble game is PSPACE-hard. Despite this, we are able to construct a time-efficient strategy for pebbling binary trees that uses the minimum number of pebbles.

Binary Voronoi linear trees for the approximate solution of functional optimization problems

The need to find solutions in function form that optimize a given nonlinear cost functional arises routinely in many important areas of operations research and applied mathematics. In most practical cases, problems of this kind require a numerical solution based on some suitable class of approximating architectures. This paper introduces the use of binary Voronoi linear trees (BVLTs) for the approximate solution of a general class of functional optimization problems. The main features of the considered trees are (i) a splitting scheme based on a Voronoi bisection criterion and (ii) linear outputs in the leaves, which make the resulting models more flexible compared to classic trees with cuts parallel to the axes and constant outputs. At the same time, due to the binary recursive structure, BVLTs retain the well-known efficiency of decision tree architectures. Consistently with the typical tree construction framework, we provide a greedy algorithm for the approximate solution of the addressed functional optimization problem. Universal approximation capabilities of the proposed class of models are derived in the theoretical analysis, and the consistency of the solution is discussed as well. In order to improve accuracy and robustness, we also consider the use of BVLTs in ensemble fashion, through an aggregation scheme well suited to optimization purposes. Simulation tests involving various optimization problems are presented, showing how the proposed algorithm can cope well in complex multivariate contexts, especially in ensemble form.

An Efficient Traceable and Revocable Access Control Scheme for Smart Grids

In smart grids, power monitoring equipment produces large volumes of data that are exchanged between microgrids and the main grid. This data exchange can potentially expose users’ private information, including their living habits and economic status. Therefore, implementing secure and effective data access control mechanisms is crucial. Ciphertext-Policy Attribute-Based Encryption (CP-ABE) is a widely used encryption scheme in distributed systems, offering fine-grained access control. However, in CP-ABE systems, malicious users might leak decryption keys to third parties, creating a significant security threat. Thus, there is an urgent need for tracing mechanisms to identify and track these malicious users. Moreover, tracing and user revocation are complementary processes. Although using a binary tree for user revocation is efficient, it limits the number of users. This paper suggests an access control scheme that combines CP-ABE with blockchain to overcome these limitations, leveraging blockchain’s tamper-resistant features. This scheme enables user revocation, tracing, partial policy hiding, and ciphertext searchability, and it has been proven secure. Simulation results show that our approach reduces time overhead by 24% to 68%, compared to other solutions. While some solutions are similar in efficiency to ours, our approach offers more comprehensive functionality and better meets the security requirements of smart grids.

Shape parameters of evolutionary trees in theoretical computer science.

Shape parameters, e.g. balance indices, of evolutionary trees have been extensively studied under the Yule model in phylogenetics. Independently, many of the same parameters have also been studied for random binary search trees in computer science, where they measure the running time of algorithms. In fact, under the Yule and binary search tree models, these parameters have the same distribution, resulting in many identical discoveries. In this survey, we explain these connections and introduce some of the tools that have been used in computer science to derive stochastic results for shape parameters.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.

Use of Saliva Analytes as a Predictive Model to Detect Diseases in the Pig: A Pilot Study.

Saliva is gaining importance as a diagnostic sample in pigs. The aim of this research was to evaluate a panel of salivary analytes in three porcine diseases and establish predictive models to detect them. Saliva samples were obtained from healthy pigs (n = 97) and pigs affected by meningitis due to Streptococcus suis (n = 118), diarrhea due to enterotoxigenic Escherichia coli (ETEC, n = 77), and porcine reproductive and respiratory syndrome (PRRS, n = 52). The following biomarkers were analyzed: adenosine deaminase (ADA), haptoglobin (Hp), calprotectin (Calp), aldolase, alpha-amylase (sAA), lactate dehydrogenase (LDH), total protein (TP), and advanced oxidation protein products (AOPPs). Predictive models based on binary logistic regression and decision trees combining those analytes for detecting specific diseases were constructed. The results showed a different biomarker profile between the groups. S. suis and ETEC pigs showed higher values of ADA, Hp, Calp, aldolase, sAA, LDH, and TP than healthy pigs. Pigs with PRRS showed higher values of Hp, Calp, sAA, and LDH than healthy animals. The constructed predictive models showed overall accuracies of over 78% and 87% for differentiating ETEC and PRRS, respectively, whereas the models did not accurately predict S. suis infection. Salivary analytes show different changes in pigs depending on the disease, and the combination of these analytes can contribute to the prediction of different diseases. Further studies should be conducted in larger populations to confirm these findings and evaluate their possible practical applications.

Propensity Score Analysis of the Utility of Supervised Perioperative Abdominal Wall Exercises for the Prevention of Parastomal Hernia.

Retrospective studies have suggested that performing perioperative abdominal wall exercises may decrease the incidence of parastomal hernias. Objectives: This study seeks to assess the usefulness of supervised preoperative and postoperative abdominal wall exercises in the prevention of parastomal hernia. Methods: An observational study of patients who underwent a stoma, temporary or permanent, between January 2019 and December 2020, was performed. Minimum follow-up was 12 months. During the first 12 months of recruitment, patients were enrolled on a consecutive basis and assigned to the control group, and the remaining patients were assigned to the intervention group. A propensity score matching was performed to obtain totally comparable groups. A set of exercises was designed by the Rehabilitation Department, and their performance was supervised by physiotherapists and stoma therapists. The diagnosis of parastomal hernia was made by physical examination and computed axial tomography. Descriptive statistics of the study group were performed. Subsequently, prediction models for the occurrence of parastomal hernia were created based on binary logistic regression and classification trees. Results: After propensity matching and inclusion criteria, 64 patients were included (colostomy: n = 39, ileostomy: n = 25). Independent prognostic variables for parastomal hernias in colostomy were age (p = 0.044) and perioperative exercises (p = 0.003). The binary logistic regression model based on these variables gave an AUC of 97.6. The classification tree model included only perioperative exercises with an AUC of 92.5%. In the case of ileostomy, perioperative exercises were the only independent prognostic variable identified. The classification-tree-based model reported an AUC of 84%. Conclusions: The performance of supervised abdominal wall training and strengthening exercises may be useful in the prevention of parastomal hernias.

Detecting deviations from Kingman coalescence using two-site frequency spectra.

Demographic inference methods in population genetics typically assume that the ancestry of a sample can be modeled by the Kingman coalescent. A defining feature of this stochastic process is that it generates genealogies that are binary trees: no more than two ancestral lineages may coalesce at the same time. However, this assumption breaks down under several scenarios. For example, pervasive natural selection and extreme variation in offspring number can both generate genealogies with "multiple-merger" events in which more than two lineages coalesce instantaneously. Therefore, detecting violations of the Kingman assumptions (e.g. due to multiple mergers) is important both for understanding which forces have shaped the diversity of a population and for avoiding fitting misspecified models to data. Current methods to detect deviations from Kingman coalescence in genomic data rely primarily on the site frequency spectrum (SFS). However, the signatures of some non-Kingman processes (e.g. multiple mergers) in the SFS are also consistent with a Kingman coalescent with a time-varying population size. Here, we present a new statistical test for determining whether the Kingman coalescent with any population size history is consistent with population data. Our approach is based on information contained in the two-site joint frequency spectrum (2-SFS) for pairs of linked sites, which has a different dependence on the topologies of genealogies than the SFS. Our statistical test is global in the sense that it can detect when the genome-wide genetic diversity is inconsistent with the Kingman model, rather than detecting outlier regions, as in selection scan methods. We validate this test using simulations, and then apply it to demonstrate that genomic diversity data from Drosophila melanogaster is inconsistent with the Kingman coalescent.

DeepTree-AAPred: Binary tree-based deep learning model for anti-angiogenic peptides prediction.

DeepTree-AAPred: Binary tree-based deep learning model for anti-angiogenic peptides prediction.

Exploring the Structure of the Network Marketing Industry through Graph Parameters

Network Marketing is a business tool that builds a network of business partners or distributors by directly selling products and services through a word-of-mouth marketing strategy. NM graph is a graphical representation of the network marketing industry. Just like a graph consists of vertices and edges, network marketing consists of distributors/ business partners which represent the vertices of the NM graph, and edges determine the genealogy of the network. In this paper, we explore the structure of an NM graph by graph parameters and see how the graph reflects various properties of a network of people. It is seen that an NM graph is a rooted binary tree. The measure of the influence of a network and the measure of profitability of a network is determined. It is seen that the objective to maximize profit by allocating different stakes to different persons is a typical case of an assignment problem. The genealogy of a network can be determined by studying the adjacency matrix of the NM digraph. Graph parameter like eccentricity represents the strongest person in the network earning maximum profitability. The domination number acts as a measure of the stability of an NM graph.

A Simplex Model of Long Pathways in the Brain Related to the Minimalist Program in Linguistics

Marcolli, Chomsky, and Berwick described the minimalist program, proposed by Chomsky in generative linguistics, as an algebra of binary trees in an analogy of quantum physics on Feynman diagrams. In this paper, we proposed another model of the minimalist program based on simplicial Hodge theory by taking the relevant brain neural network into account. We focused on a long directed pathway connecting distant areas in the brain, and took the (abstract) simplex spanning the locations on the terminal area, which the signals going through the pathway can reach. The identity of each signal is represented by the symmetry of the corresponding face, consisting of locations receiving the signal simultaneously. Then, we showed that this model fits the minimalist program. Further, we calculated the spectrum and eigenspaces of the Hodge Laplacian in important cases and found their surprising rationality. According to this rationality, we could draw pictures of syntactic relations based only on the calculation without using linguistic knowledge. In addition, though word order depends on what language is used, and thus has nothing to do with the minimalist program, planar word arrangements are still possible and within the scope of our model.

Matrix-analytic Methods for the Evolution of Species Trees, Gene Trees, and Their Reconciliation

We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree. In this paper we present a method, where for a given choice of parameters, we are able to compute the likelihood for alternative reconciliations. We describe a Markovian binary tree (MBT) model for the evolution of species trees, a quasi-birth-and-death (QBD) model for the evolution of gene trees, and provide a recursive algorithm to compute the likelihood of a given reconciliation between a species tree and a gene tree. We derive our results using the theory of matrix-analytic methods, prove them using rigorous mathematics together with decomposition of sample path arguments, and describe algorithms for the computation of a range of useful metrics. We illustrate the theory with examples and provide the physical interpretations of the discussed quantities, with a focus on the practical applications of the theory to incomplete data.

Topological Analysis of Fractal Binary and Ternary Trees

Fractals are complex geometric objects that seem the same at different scales and have self-similarity. Because of this special characteristic, fractals can be used to simulate intricate biological processes. Fractal binary and ternary trees are novel data types that combine the productiveness of tree architectures with the ideas of fractal geometry. In addition to self-similarity and scalability, these trees have potential across a range of computer science and medical applications. The main goal of the study is to identify and analyze topological indices and graph entropy for fractal binary and fractal ternary trees. By examining indices such as the Randić index, Zagreb indices, and entropy measurements, the study aims to obtain a comprehensive knowledge of the structural complexity and information-theoretic properties of these fractal graphs. The study starts with the vertex and edge partitioning of fractal binary and ternary trees in order to distinguish different structural classes. Using these partitions, we obtained topological indices and graph entropy values for the fractal trees. Also, this study compares the topological indices for each fractal tree with the number of copies in the fractal dimension for a succession of graphs.

Research on Challenges and Solutions for Optimizing Read Rate in RFID Systems

Radio Frequency Identification (RFID) uses electromagnetic fields for the automatic identification and tracking of object tags, which is widely used in supply chain management, transport and retail. And key issues in its application encompass reliability, security, and privacy. In contrast to mainstream research that primarily focuses on solutions for security and privacy, the paper concentrates on boosting the overall reliability of RFID systems, particularly in fault detection of read rates. Through the review and analysis of the relevant literature, this paper highlights the key challenges and issues in the RFID field, particularly focusing on read rate. Various methods proposed to improve RFID read rates are reviewed, including hardware optimization, tag design, software algorithm improvement, and environmental adjustments. In addition, it outlines the effectiveness of different strategies, addresses the challenges faced in real-world applications, notes the limitations of the research, and proposes potential directions for future studies. The results demonstrate that anti-collision algorithms such as DFSA and improved binary tree search can effectively reduce signal conflicts in multi-tag environments

Random subsets of Cantor sets generated by trees of coin flips

We introduce a natural way to construct a random subset of a homogeneous Cantor set C in [0,1] via random labelings of an infinite M -ary tree, where M\geq 2 . The Cantor set C is the attractor of an equicontractive iterated function system \{f_{1},\dots,f_{N}\} that satisfies the open set condition with (0,1) as the open set. For a fixed probability vector (p_{1},\dots,p_{N}) , each edge in the infinite M -ary tree is independently labeled i with probability p_{i} , for all i=1,2,\dots,N . Thus, each infinite path in the tree receives a random label sequence of numbers from \{1,2,\dots,N\} . We define F to be the (random) set of those points x\in C which have a coding that is equal to the label sequence of some infinite path starting at the root of the tree. The set F may be viewed as a statistically self-similar set with extreme overlaps, and as such, its Hausdorff and box-counting dimensions coincide. We prove non-trivial upper and lower bounds for this dimension, and obtain the exact dimension in a few special cases. For instance, when M=N and p_{i}=1/N for each i , we show that F is almost surely of full Hausdorff dimension in C but of zero Hausdorff measure in its dimension. For the case of two maps and a binary tree, we also consider deterministic labelings of the tree where, for a fixed integer m\geq 2 , every m th edge is labeled 1 , and compute the exact Hausdorff dimension of the resulting subset of C .

Optimal Task Allocation and Sequencing for Flight Test Based on a Memetic Algorithm With Lexicographic Optimisation

ABSTRACTThe flight test plays an important role in the development of an aircraft. Currently, with the increasing complexity and higher validation requirements for aircraft, there is a crucial need to generate high‐quality flight test task schedules in an efficient way. This paper proposes a flight test task scheduling problem (FTTSP), which involves assigning suitable aircraft and executing the flight test tasks in a given order. Generally, the flight test duration (FTD) is the primary optimisation objective for the flight test task schedule, as it has a direct impact on aircraft development costs and the time to enter the market. In this study, the FTTSP not only considers FTD but also takes into account task transfer consumption (TTC). A mixed‐integer linear programming mathematical model is first formulated to describe the FTTSP characteristics with the optimisation of the FTD and the TTC in a sequential manner. Then, a memetic algorithm with lexicographic optimisation (MALO) is proposed, which can efficiently obtain a high‐quality solution and ensure that the most critical metric can be fully optimised. In MALO, a two‐vector encoding and a task logic relationship repair mechanism based on the binary tree are established. An idle time insertion decoding method is designed to improve the aircraft utilisation rate. In addition to the selection, crossover and mutation operators, a local search operator is designed to enhance the solution quality. Finally, the full‐scale test instances are generated for the FTTSP to evaluate the algorithm's performance. The numerical results demonstrate the effectiveness and competitiveness of the MALO in generating a high‐quality schedule for flight test tasks.

Structural Equation Modelling of Retinopathy of Prematurity Treatment Integrating Both Physical and Clinical Effects.

Background: We sought to develop a structural equation model (SEM) identifying physical and clinical risk factors associated with treatment for retinopathy of prematurity (ROP). Methods: This retrospective, observational, case-control study included 314 infants screened for ROP between April 2004 and July 2024. A bivariate binary logistic regression model, decision tree, and structural equation model (SEM) were employed to develop a more general model for ROP requiring treatment. Results: In the SEM, the factors significantly associated with ROP treatment included the retinal avascular area according to disk diameter (DD) (p < 0.001), weekly vascularisation rate (DD/w) (p < 0.001), and duration of intubation (days) (p < 0.001). In addition, the following significant associations were identified in both the bivariate analysis and the SEM: lower gestational age (p < 0.001) and birth weight (p <0.001) were associated with greater retinal avascular area; low postnatal weight gain (p < 0.027) was associated with a slow rate of retinal vascularisation; sepsis (p < 0.001), ductus arteriosus (p < 0.001), and the need for transfusion (p < 0.001) were associated with longer intubation mechanical ventilation (IMV). Conclusions: Lower gestational age, lower birth weight, sepsis, ductus arteriosus, transfusion, and lower weight gain increase the risk of requiring ROP treatment. In the SEM, this association is represented through three intermediate physical endogenous variables, namely, the greater temporal avascular area of the retina, the lower postnatal vascularisation rate, and the greater duration of IMV.

HA-SCINet based Carbon Emission Prediction of the Typical Park

Background: With the rapid economic growth and the accelerated process of industrialization, the production activities of enterprises within parks have significantly increased, leading to a continuous rise in carbon emissions. Under the context of the "dual carbon" goals, studying the prediction of carbon emissions in typical parks holds significant practical importance. It is not only a key measure to address climate change but also an important pathway to achieve sustainable development. Objective: In order to predict the carbon emissions of the typical park more accurately, we propose a carbon emissions prediction model HA-SCINet. Methods: The model uses a recursive downsampling-convolution-interaction architecture. In each layer, the long-term dependence in time series data is extracted by HyperAttention. Then through the L-layer SCI-Block of the binary tree structure, the down-sampling interactive learning extracts both short-term and long-term dependencies. These extracted features are merged and reorganized, and added to the original time series to generate a new sequence with enhanced predictability. Finally, employ a fully connected network for forecasting the enhanced sequence. The carbon emission data of the typical park serve as input, leading to higher accuracy prediction results through the Stacked K-layer stacked HA-SCINet. Results: The mean square error (MSE) and mean absolute error (MAE) of HA-SCINet prediction model are 0.0819 and 0.204 respectively, outperforming the mainstream Dlinear and Nlinear models Conclusion: The experimental results show that the devised model outperforms in predicting carbon emissions, and is better suited for forecasting carbon emissions within the context of the typical park.

Financial assets selection under the Factor Investing scheme with the support of a Machine Learning algorithm

In this article, the author examines one of the most viable Machine Learning methods for its expeditious implementation in the financial industry, which does not require high computing capacity as required by the most sophisticated Artificial Intelligence techniques that have emerged today. This is the binary tree classification method, which is a supervised learning algorithm, part of the arsenal of Machine Learning algorithms. This algorithm can be applied efficiently with a medium computing capacity and adequate knowledge of Machine Learning techniques. An appropriate understanding of the behavior of financial markets is essential for its good implementation, particularly of the reports issued by publicly traded companies. The case study of this algorithm in the financial industry is in a modern asset allocation scheme known as Factor Investing. The implementation of Binary Trees for this task is suitable, as it is an asset classification task. This study shows that through machine learning, specifically binary trees, investors and portfolio managers can identify factors that support their investment strategies.