Nodes Of Tree Research Articles

A branch-and-bound algorithm for parametric mixed-binary nonlinear programs

AbstractAs rapid response to changes becomes more imperative, optimization under uncertainty has continued to grow in both the continuous and mixed-integer fields. We design a branch-and-bound (BB) algorithm for mixed-binary nonlinear optimization problems with parameters in general locations. At every node of the BB tree we apply a state-of-the-art algorithm we have recently developed to approximately optimize parametric programs containing objectives and constraints biconvex in the variables and parameters. Numerical results are included.

Adaptive fuzzy neighborhood decision tree

Decision tree algorithms have gained widespread acceptance in machine learning, with the central challenge lying in devising an optimal splitting strategy for node sample subspaces. In the context of continuous data, conventional approaches typically involve fuzzifying data or adopting a dichotomous scheme akin to the CART tree. Nevertheless, fuzzifying continuous features often entails information loss, whereas the dichotomous approach can generate an excessive number of classification rules, potentially leading to overfitting. To address these limitations, this study introduces an adaptive growth decision tree framework, termed the fuzzy neighborhood decision tree (FNDT). Initially, we establish a fuzzy neighborhood decision model by leveraging the concept of fuzzy inclusion degree. Furthermore, we delve into the topological structure of misclassified samples under the proposed decision model, providing a theoretical foundation for the construction of FNDT. Subsequently, we utilize conditional information entropy to sift through original features, prioritizing those that offer the maximum information gain for decision tree nodes. By leveraging the conditional decision partitions derived from the fuzzy neighborhood decision model, we achieve an adaptive splitting method for optimal features, culminating in an adaptive growth decision tree algorithm that relies solely on the inherent structure of real-valued data. Experimental evaluations reveal that, compared with advanced decision tree algorithms, FNDT exhibits a simple tree structure, stronger generalization capabilities, and superior performance in classifying continuous data.

Pruned tree-structured temporal convolutional networks for quality variable prediction of industrial process

In real industrial processes, the rapid and accurate acquisition of quality variables is essential. Therefore, this paper proposes a pruned tree-structured temporal convolutional network (PT-TCN) for efficient and accurate variables prediction. First, a novel tree network is developed, utilizing dilated causal convolution blocks as nodes to avoid the loss of local information. Each node extracts distinct local information, and by concatenating all tree nodes, the network can capture a comprehensive range of temporal scales. Then, to avoid the increased complexity caused by the tree structure, we design an online two-stage pruning strategy to compress the tree network without introducing additional computations. During the training process, blocks are initially pruned based on the correlation assessment between quality variables and tree nodes. Subsequently, weight normalization layers are employed to evaluate the importance of output channels in blocks, thereby enabling intra-block channel pruning. The effectiveness of PT-TCN is verified on Tennessee Eastman benchmark process. In addition, experiments on the real zinc flotation process demonstrate that the proposed PT-TCN improves in R2 and MAE by 1.32% and 1.26% respectively in predicting quality variables, and it can reduce 91.8% parameters of the initial tree-structured TCN without sacrificing accuracy.

Kinematic Constrained RRT Algorithm with Post Waypoint Shift for the Shortest Path Planning of Wheeled Mobile Robots

This paper presents a rapidly exploring random tree (RRT) algorithm with an effective post waypoint shift, which is suitable for the path planning of a wheeled mobile robot under kinematic constraints. In the growth of the exploring tree, the nearest node that satisfies the kinematic constraints is selected as the parent node. Once the distance between the new node and the target is within a certain threshold, the tree growth stops and a target connection based on minimum turning radius arc is proposed to generate an initial complete random path. The most significant difference from traditional RRT-based methods is that the proposed method optimizes the path based on Dubins curves through a post waypoint shift after a random path is generated, rather than through parent node selection and rewiring during the exploring tree growth. Then, it is proved that the method can obtain an optimal path in terms of the shortest length. The optimized path has good convergence and almost does not depend on the state of the initial random path. The comparative test results show that the proposed method has significant advantages over traditional RRT-based methods in terms of the sampling point number, the tree node number, and the path node number. Subsequently, an efficient method is further proposed to avoid unknown obstacles, which utilizes the original path information and thus effectively improves the new path planning efficiency. Simulations and real-world tests are carried out to demonstrate the effectiveness of this method.

Facilitating subgroup identification: the use of decision trees in breast cancer screening uptake

Abstract Introduction Organized breast cancer screening (BCS) programs are effective prevention measures for women aged 50-69 to prevent the sixth cause of death in Germany. It is unclear which sociodemographic factors and potential interactions are associated with never-attendance. Explorative approaches such as decision trees offer an inductive approach to intersectional subgroup identification based on different computational decisions. This study discusses two approaches for estimating the likelihood of not attending BCS in Germany. Methods Women aged 50-69 (N = 3,644) were selected from the German 2020 European Health Interview Survey. We estimate the risk of not attending BCS first by employing cross-classification regression analysis utilising known social dimensions and second by leveraging the nodes of the best-performing decision tree as exposure variables. Results The first approach, adjusting for age, found that women born in Germany had 1.97 higher odds (p = 0.015) of never attending BCS than high-income women not born in Germany. Conditional Inference Tree (mincriterion= 0.6040046, maxdepth=3) adjusted to optimise sensitivity and the Area Under the Curve (71.43% sensitivity, 63.21% AUC), identified 8 relevant intersectional groups characterised by unique combinations of family status, perceived social support, working situation, experienced physical limitation, and region, with the highest odds of 4.85 (p < 0.001) of not attending BCS for women living with their couple and children or non-conventional household constellations who perceived little, uncertain or a lot of social support. Conclusions Using explorative decision trees for subgroup identification, the study provides more detailed insights into women at higher risk of not attending BCS in Germany, aiding, on the one hand, more precise health reporting data and, on the other hand, enhanced preventive public health interventions. Key messages • Explorative decision trees for subgroup identification allow for more detailed insights into women at higher risk of not attending BCS in Germany for enhanced preventive public health interventions. • Women living with their couple and children or non-conventional constellations who perceived little, uncertain or a lot of social support are at the highest odds of never attending BCS in Germany.

Tree sequences as a general-purpose tool for population genetic inference.

As population genetics data increases in size new methods have been developed to store genetic information in efficient ways, such as tree sequences. These data structures are computationally and storage efficient, but are not interchangeable with existing data structures used for many population genetic inference methodologies such as the use of convolutional neural networks (CNNs) applied to population genetic alignments. To better utilize these new data structures we propose and implement a graph convolutional network (GCN) to directly learn from tree sequence topology and node data, allowing for the use of neural network applications without an intermediate step of converting tree sequences to population genetic alignment format. We then compare our approach to standard CNN approaches on a set of previously defined benchmarking tasks including recombination rate estimation, positive selection detection, introgression detection, and demographic model parameter inference. We show that tree sequences can be directly learned from using a GCN approach and can be used to perform well on these common population genetics inference tasks with accuracies roughly matching or even exceeding that of a CNN-based method. As tree sequences become more widely used in population genetics research we foresee developments and optimizations of this work to provide a foundation for population genetics inference moving forward.

Metapopulation model of phage therapy of an acute Pseudomonas aeruginosa lung infection.

Phage therapy is increasingly employed as a compassionate treatment for severe infections caused by multidrug-resistant (MDR) bacteria. However, the mixed outcomes observed in larger clinical studies highlight a gap in understanding when phage therapy succeeds or fails. Previous research from our team, using in vivo experiments and single-compartment mathematical models, demonstrated the synergistic clearance of acute P. aeruginosa pneumonia by phage and neutrophils despite the emergence of phage-resistant bacteria. In fact, the lung environment is highly structured, prompting the question of whether immunophage synergy explains the curative treatment of P. aeruginosa when incorporating realistic physical connectivity. To address this, we developed a metapopulation network model mimicking the lung branching structure to assess phage therapy efficacy for MDR P. aeruginosa pneumonia. The model predicts the synergistic elimination of P. aeruginosa by phage and neutrophils but emphasizes potential challenges in spatially structured environments, suggesting that higher innate immune levels may be required for successful bacterial clearance. Model simulations reveal a spatial pattern in pathogen clearance where P. aeruginosa are cleared faster at distal nodes of the bronchial tree than in primary nodes. Interestingly, image analysis of infected mice reveals a concordant and statistically significant pattern: infection intensity clears in the bottom before the top of the lungs. The combined use of modeling and image analysis supports the application of phage therapy for acute P. aeruginosa pneumonia while emphasizing potential challenges to curative success in spatially structured in vivo environments, including impaired innate immune responses and reduced phage efficacy.

Classes and phyla of the kingdom Fungi

AbstractFungi are one of the most diverse groups of organisms with an estimated number of species in the range of 2–3 million. The higher-level ranking of fungi has been discussed in the framework of molecular phylogenetics since Hibbett et al., and the definition and the higher ranks (e.g., phyla) of the ‘true fungi’ have been revised in several subsequent publications. Rapid accumulation of novel genomic data and the advancements in phylogenetics now facilitate a robust and precise foundation for the higher-level classification within the kingdom. This study provides an updated classification of the kingdom Fungi, drawing upon a comprehensive phylogenomic analysis of Holomycota, with which we outline well-supported nodes of the fungal tree and explore more contentious groupings. We accept 19 phyla of Fungi, viz. Aphelidiomycota, Ascomycota, Basidiobolomycota, Basidiomycota, Blastocladiomycota, Calcarisporiellomycota, Chytridiomycota, Entomophthoromycota, Entorrhizomycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota, Sanchytriomycota, and Zoopagomycota. In the phylogenies, Caulochytriomycota resides in Chytridiomycota; thus, the former is regarded as a synonym of the latter, while Caulochytriomycetes is viewed as a class in Chytridiomycota. We provide a description of each phylum followed by its classes. A new subphylum, Sanchytriomycotina Karpov is introduced as the only subphylum in Sanchytriomycota. The subclass Pneumocystomycetidae Kirk et al. in Pneumocystomycetes, Ascomycota is invalid and thus validated. Placements of fossil fungi in phyla and classes are also discussed, providing examples.

Tree sequences as a general-purpose tool for population genetic inference.

As population genetics data increases in size new methods have been developed to store genetic information in efficient ways, such as tree sequences. These data structures are computationally and storage efficient, but are not interchangeable with existing data structures used for many population genetic inference methodologies such as the use of convolutional neural networks (CNNs) applied to population genetic alignments. To better utilize these new data structures we propose and implement a graph convolutional network (GCN) to directly learn from tree sequence topology and node data, allowing for the use of neural network applications without an intermediate step of converting tree sequences to population genetic alignment format. We then compare our approach to standard CNN approaches on a set of previously defined benchmarking tasks including recombination rate estimation, positive selection detection, introgression detection, and demographic model parameter inference. We show that tree sequences can be directly learned from using a GCN approach and can be used to perform well on these common population genetics inference tasks with accuracies roughly matching or even exceeding that of a CNN-based method. As tree sequences become more widely used in population genetics research we foresee developments and optimizations of this work to provide a foundation for population genetics inference moving forward.

IDSV-GCN: Integrating Dual Syntactic Views Graph Convolutional Network for aspect-based sentiment analysis

Aspect-based sentiment analysis (ABSA) aims to predict the sentiment polarity towards given aspects in a sentence. Recent research has highlighted that graph neural networks based on syntactic dependency trees effectively convey rich syntactic information and are suitable for ABSA tasks. Most existing work typically adopt either dependency type or minimum distance between nodes in the original syntactic tree to construct different views. However, existing work overlooks the high-dimensional local feature information in dependency relations, resulting in inadequate exploration of this view. Meanwhile, most work ignores that the minimum distance view and the dependency view can be complementary and integrated in syntactic analysis. Unfortunately, directly adding the two views introduces noise issues, leading to unsatisfactory results after their integration. To address these issues, this paper introduces an integrating dual syntactic views graph convolutional network (IDSV-GCN) model that seamlessly integrates dependency type view and minimum distance view, enabling comprehensive utilization of syntactic structure and information. To better address the computation of weights in the dependency type view, we innovatively propose a fusion attention mechanism. This approach effectively captures both global and local feature information. To more effectively integrate the two views and reduce the impact of noise, we employ a syntactic mask layer to filter out noise in the dependency type view and highlighting important dependency feature information. Then, we construct a minimum distance weight matrix based on the matrix obtained from the dependency type view. Finally, we merge the two matrices and feed them into the GCN to facilitate the model’s learning of syntactic information. Experimental results on three widely-used benchmark datasets demonstrate that our proposed IDSV-GCN model outperforms state-of-the-art methods.

Optimizing hierarchical classifiers with parameter tuning and confidence scoring

Hierarchical classifiers play a crucial role in addressing complex classification tasks by breaking them down into smaller, more manageable sub-tasks. This paper continues a series of works, focused on the technical Ukrainian texts hierarchical classification, specifically the classification of repair works and spare parts used in automobile maintenance and servicing. We tackle the challenges posed by multilingual data inputs – specifically Ukrainian, Russian, and their hybrid – and the lack of standard data cleaning models for the Ukrainian language. We developed a novel classification algorithm, which employs TF-IDF victimization with unigrams and bigrams, keyword selection, and cosine similarity for classification. This paper describes a method for training and evaluating a hierarchical classification model using parameter tuning for each node in a tree structure. The training process involves initializing weights for tokens in the class tree nodes and input strings, followed by iterative parameter tuning to optimize classification accuracy. Initial weights are assigned based on predefined rules, and the iterative process adjusts these weights to achieve optimal performance. The paper also addresses the challenge of interpreting multiple confidence scores from the classification process, proposing a machine learning approach using Scikit-learn's GradientBoostingClassifier to calculate a unified confidence score. This score helps assess the classification reliability, particularly for unlabeled data, by transforming input values, generating polynomial parameters, and using logarithmic transformations and scaling. The classifier is fine-tuned using hyper parameter optimization techniques, and the final model provides a robust confidence score for classification tasks, enabling the verification and classification results optimization across large datasets. Our experimental results demonstrate significant improvements in classification performance. Overall classification accuracy nearly doubled after training, reaching 92.38 %. This research not only advances the theoretical framework of hierarchical classifiers but also provides practical solutions for processing large-scale, unlabeled datasets in the automotive industry. The developed methodology can enhance various applications, including automated customer support systems, predictive maintenance, and decision-making processes for stakeholders like insurance companies and service centers. Future work will extend this approach to more complex tasks, such as extracting and classifying information from extensive text sources like telephone call transcriptions.

The expression dependence graph

The system dependence graph (SDG) is a widely used program representation for the static analysis of programs. In particular, it is the standard way to represent control and flow dependences between the statements of a program. It is at the core of program slicing, a technique that extracts the part of a program that can influence a given program point (the so-called slicing criterion). In this paper, we identify several program slicing situations (e.g., list comprehensions, try-catch and for) where the representation provided by the SDG is imprecise, and we present an alternative program representation, which is indeed an extension of the SDG, that solves these situations. We call this extension the expression dependence graph (EDG). The EDG redefines the SDG by increasing the granularity of its nodes to abstract syntax tree (AST) nodes. The implications of this change include an improvement in precision, the appearance of new kinds of dependences (besides control and flow dependences), and the possibility of selecting any (sub)expression as the slicing criterion.

Impact of seismotectonic source zoning and seismic parameter: Sensitivity study on probabilistic seismic hazard assessment

The demarcation of seismic area source zones plays a pivotal role in probabilistic seismic hazard assessment (PSHA). In this study, we developed five distinct seismotectonic area source models, integrating large and small areas based on geological, tectonic, and seismological data. Logic tree methodology is utilized in FRISK88M for PSHA. Analysis revealed higher hazards in models with larger area sources compared to those with smaller ones. Hazard deaggregation of seismotectonic model-5 (SM5) is examined and sensitivity analysis of various logic tree nodes is investigated in terms of percent deviation w.r.t mean hazard at various spectral and return periods. The findings underscore that recurrence methods fall into "insensitive level" (≤5%), source mechanism and a-value distribution belong to "low sensitive level" (>5–15%), magnitude distribution lies in "medium sensitive level" (>15–25%), b-value distribution belongs to "high sensitive level" (>25–35%), and ground motion prediction equations (GMPEs) and depth distribution falls into "very high sensitive level" (>35%) in relation to seismic hazard.

Coordinated measurement of marine economy: High-quality and low-carbon development in China

The marine economy needs high-quality development, as severe greenhouse effect has become a global concern and carbon emission reduction has been an essential target of marine economy growth. However, a lack of synergistic research in the field of marine economy development and carbon emissions has hindered progress. This study explores the critical interactive relationship between the high-quality and low-carbon development in China's marine economy, aiming to foster green development in coastal urban agglomerations and enhance ecological security alongside economic growth. Despite the importance, comprehensive analysis across multiple dimensions of high-quality and low-carbon development of marine economy remains scarce. This paper establishes a systematic and scientific evaluation index system, utilizing text analysis technology and the Panel Vector Autoregression Model (PVAR) to quantitatively assess the complex system relationship between these dimensions. The results including: (1) The development of a 23 nodes tree structure through a bottom-up, multi-level coding method, effectively addressing the complexity of the current evaluation system for high-quality development of the marine economy. (2) Moran's I of subsystems are all negative, presenting an obvious high-low agglomeration characteristics. The discovery that intra-group differences exceed inter-group ones in marine economic development, indicates that the need for synergistic development among the provinces within marine economic circles. (3) The identification of significant bidirectional interactions between open and shared high-quality development and low-carbon development, with a notable lag effect in responses. The predominant role of innovation in all subsystems underscores the centrality of the marine innovation environment and factors as key drivers in the synergy of high-quality and low-carbon development in the marine economy.

Electromigration Analysis for Interconnects Using Improved Graph Convolutional Network with Edge Feature Aggregation.

Electromigration (EM) is a critical reliability issue in integrated circuits and is becoming increasingly significant as fabrication technology nodes continue to advance. The analysis of the hydrostatic stress, which is paramount in electromigration studies, typically involves solving complex physical equations (partial differential equations, or PDEs in this case), which is time consuming, inefficient and not practical for full-chip EM analysis. In this paper, a novel approach is proposed, conceptualizing circuit interconnect trees as a graph within a graph neural network framework. Using finite element solution software, ground truth hydrostatic stress values were obtained to construct a dataset of interconnected trees with hydrostatic stress values for each node. An improved Graph Convolutional Network (GCN) augmented with edge feature aggregation and attention mechanism was then trained employing the dataset, yielding a model capable of predicting hydrostatic stress values for nodes in an interconnect tree. The results show that our model demonstrated a 15% improvement in the Root Mean Square Error (RMSE) compared to the original GCN model and improved the solution speed greatly compared to traditional finite element software.

A machine learning approach to rank pricing problems in branch-and-price

This paper presents a novel approach exploiting machine learning to enhance the efficiency of the branch-and-price algorithm. The focus is, specifically, on problems characterized by multiple pricing problems. Pricing problems often constitute a substantial portion of CPU time due to their repetitive nature. The primary contribution of this work includes the introduction of a machine learning-based ranker that strategically guides the search for new columns in the column generation process. The master problem solution is analyzed by the ranker, which then suggests an order for solving the pricing problems to prioritize those with the potential to improve the master problem the most. This prioritization mechanism is essential in speeding up the column generation since, by identifying new columns early in the process, we can terminate the search procedure sooner. Furthermore, our technique exhibits applicability across all nodes of the branching tree, making it a valuable tool for solving a wide range of optimization problems. We demonstrate the usefulness of this approach in the challenging domain of operating room scheduling, an area that has seen limited exploration in the context of machine learning. Extensive experimental evaluations underline the effectiveness of the developed algorithm, consistently outperforming traditional search strategies in terms of time, number of solved pricing problems, searched nodes in the branching tree, and performed column generation iterations.

F1ALA: ultrafast and memory-efficient ancestral lineage annotation applied to the huge SARS-CoV-2 phylogeny.

The unprecedentedly large size of the global SARS-CoV-2 phylogeny makes any computation on the tree difficult. Lineage identification (e.g. the PANGO nomenclature for SARS-CoV-2) and assignment are key to track the virus evolution. It requires annotating clade roots of lineages to unlabeled ancestral nodes in a phylogenetic tree. Then the lineage labels of descendant samples under these clade roots can be inferred to be the corresponding lineages. This is the ancestral lineage annotation problem, and matUtils (a package in pUShER) and PastML are commonly used methods. However, their computational tractability is a challenge and their accuracy needs further exploration in huge SARS-CoV-2 phylogenies. We have developed an efficient and accurate method, called "F1ALA", that utilizes the F1-score to evaluate the confidence with which a specific ancestral node can be annotated as the clade root of a lineage, given the lineage labels of a set of taxa in a rooted tree. Compared to these methods, F1ALA achieved roughly an order of magnitude faster yet with ∼12% of their memory usage when annotating 2277 PANGO lineages in a phylogeny of 5.26 million taxa. F1ALA allows real-time lineage tracking to be performed on a laptop computer. F1ALA outperformed matUtils (pUShER) with statistical significance, and had comparable accuracy to PastML in tests on empirical and simulated data. F1ALA enables a tree refinement by pruning taxa with inconsistent labels to their closest annotation nodes and re-inserting them back to the pruned tree to improve a SARS-CoV-2 phylogeny with both higher log-likelihood and lower parsimony score. Given the ultrafast speed and high accuracy, we anticipated that F1ALA will also be useful for large phylogenies of other viruses. Codes and benchmark datasets are publicly available at https://github.com/id-bioinfo/F1ALA.

Research on sales strategies for target customers of electric vehicles based on gradient boosting ensemble trees

This paper focuses on the automotive industry, especially the new energy vehicle sector, which is vital for the economy and needs careful market sales decisions. It analyzes data from 1,964 potential customers, including their satisfaction and personal information. The study uses machine learning to create a math model and give sales advice. The data is first cleaned without changing its original structure, and then normalized using the Z-Score method. For any outlier values in the data, the mean of similar items is used to fill in gaps. Specifically, for 500 missing entries about the number of children (B7), the paper groups customers by age, calculates the frequency of children in each group, and uses these frequencies to fill in missing values.Using the cleaned data, the XGBoost algorithm ranks the factors influencing customer decisions. For Brand 1, the top factors are economy (a3), work experience (B10), and safety performance (a4). For Brand 2, comfort (a2), disposable income (B15), and mortgage expenses (B16) are key. For Brand 3, car loan expenses (B17), battery technology (a1), and again mortgage expenses (B16) are most important.The paper also addresses imbalanced data by using an XGBoost binary classification model. This model predicts the likelihood of buying an electric vehicle using the Sigmoid function on tree node weights. It evaluates the model using Precision, Recall, and Area Under the Receiver Operating Characteristic Curve (AUC), which works well even with imbalanced data. The Precision and Recall rates for all three brands are above 90%, with AUC over 85% for Brands 1 and 2, and over 75% for Brand 3. This shows that the model is effective and can be used in real-world situations.

Feature-Enhanced Multi-Task Learning for Speech Emotion Recognition Using Decision Trees and LSTM

Speech emotion recognition (SER) plays an important role in human-computer interaction (HCI) technology and has a wide range of application scenarios in medical medicine, psychotherapy, and other applications. In recent years, with the development of deep learning, many researchers have combined feature extraction technology with deep learning technology to extract more discriminative emotional information. However, a single speech emotion classification task makes it difficult to effectively utilize feature information, resulting in feature redundancy. Therefore, this paper uses speech feature enhancement (SFE) as an auxiliary task to provide additional information for the SER task. This paper combines Long Short-Term Memory Networks (LSTM) with soft decision trees and proposes a multi-task learning framework based on a decision tree structure. Specifically, it trains the LSTM network by computing the distances of features at different leaf nodes in the soft decision tree, thereby achieving enhanced speech feature representation. The results show that the algorithm achieves 85.6% accuracy on the EMO-DB dataset and 81.3% accuracy on the CASIA dataset. This represents an improvement of 11.8% over the baseline on the EMO-DB dataset and 14.9% on the CASIA dataset, proving the effectiveness of the method. Additionally, we conducted cross-database experiments, real-time performance analysis, and noise environment analysis to validate the robustness and practicality of our method. The additional analyses further demonstrate that our approach performs reliably across different databases, maintains real-time processing capabilities, and is robust to noisy environments.

Recursive two-stage evaluation model for dynamic decision making under ambiguity

In this paper, the two-stage-evaluation (TSE) model for decision making under ambiguity (He 2021) is extended to intertemporal setting in an axiomatic approach. The first set of axioms employed are commonly adopted for dynamic non-expected utility models in the literature. Besides these regular axioms, I also assume dynamic consistency and conditions which deliver a static TSE for consumption plans only pay non-zero consequences for one period. It is shown that these axioms hold if and only if these exists a recursively defined evaluation utility model representing decision maker (DM)’s preferences over consumption plans conditional on arriving at any node in an event tree. Such a recursive form implies that one can apply dynamic programming technique (rolling back the decision tree) to solve a dynamic decision making problem under TSE model. It can be shown that the solution for the recursively defined dynamic TSE model exists uniquely. Due to the “small domain” setup, the agent is short-sighted in the sense that they only process subjective probabilities over events defined on one period uncertainty over next period states, which differs from “far-sighted” assumption in most extant models that assume subjective probabilities exist over events defined on multiple periods. It is shown that under some extra conditions, our DM applies Bayes’ rule “updating’ her subjective beliefs.