Index Tree Research Articles

Two-Matchings with Respect to the General Sum-Connectivity Index of Trees

A vertex-degree-based topological index φ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by mG,k. Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index φ. This number was denoted by mkG,φ and called the k-matchings of G with respect to the topological index φ. It turns out that m1G,φ=φG, and so for k≥2, the k-matching numbers mkG,φ can be viewed as kth order topological indices which involve both the topological index φ and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices SCα, over the set Tn of trees with n vertices, when α is a real number in the interval −1,0.

Temporal variation in the oral microbiome and the prediction of early childhood caries in different ethnicities.

Globally, early childhood caries (ECC) is a significant public health concern, necessitating effective prediction and prevention strategies. This study aimed to explore variations in the oral microbiome of saliva from pre-school Han and Uyghur children during ECC development and establish a predictive model based on temporal oral microbiome changes. Saliva samples were collected from a single kindergarten every three months over six months. Forty-four pre-school children provided 132 samples, categorized into six groups: (1) HEF (healthy pre-school Han children), (2) HEO (Han children with caries), (3) HEP (Han children with progressive caries), (4) WEF (healthy pre-school Uyghur children), (5) WEO (Uyghur children with caries), and (6) WEP (Uyghur children with progressive caries). Illumina Miseq sequencing identified oral microbiome differences between groups and time points. The Random Forest (RF) algorithm established ECC prediction models. The T1HEO group exhibited significantly higher Chaol index, observed species index, PD whole tree index, and Shannon index than the T2HEO group (p < 0.01). Similarly, the T1WEO group had significantly higher Chaol index, observed species index, and PD whole tree index than the T2WEO group (p < 0.05). The AUROC value for the ECC prediction model based on temporal oral flora changes was 0.517 (95% CI: 0.275-0.759) for pre-school Han children and 0.896 (95% CI: 0.78-1.00) for pre-school Uyghur children. In the onset of caries in pre-school Han children, bacterial species richness and community diversity in saliva declined, paralleled by a decrease in bacterial species richness in pre-school Uyghur children's oral saliva. The ECC prediction model grounded on temporal oral microflora changes exhibited robust predictive power, particularly for pre-school Uyghur children, potentially leading to more effective ECC prevention measures.

Phyto-sociological changes in the Goima Forest, Gujarat due to human disturbances and their implications for conservation

Aim: The study aimed to understand the phytosociological changes by the impact of forest fringe human disturbance on the Goima forest of Valsad district in Gujarat. Methodology: The study area was classified into different tree canopy density and disturbance classes, and ecological indices were calculated for each class following the quadrate survey method. Results: A total of 772 individual plants of 141 species from 53 families were recorded during quadrate sampling, with variations in aspects being especially important predictors of biotic diversity. The study found that the maximum taxa of trees (30), herbs (24), and grasses (7) were reported in the high-disturbance class, while for shrubs (16) and climbers (10), it was in the middle-disturbance class. Dominance (D)was higher in the moderately dense forest as well as in the moderate disturbance class for trees (0.11, 0.13), shrubs (0.24, 0.21), herbs (0.13, 0.12), but for climbers, D was higher in dense forest (0.40) and in moderate disturbance class (0.22), and for grasses, it was higher in the moderately dense forest (0.69) and less disturbed class (0.58). Shannon's index (H) for trees (2.93), herbs (2.85), and grasses (1.68) was maximum in the higher disturbance class, while for shrubs (2.23) and climbers (2.10), it was highest in the low disturbance class. Interpretation: The study highlights that the phytosociology of the Goima forest changes due to human disturbances. The importance of understanding and conserving biodiversity in the Goima forest, especially given its unique flora and its critical role in supporting local communities. The research provides valuable scientific information that can aid in the better management and protection of the forest area. Key words: Canopy class, Goima forest, Human disturbance, Phytodiversity, Species distribution

Searching rooms with top-k passenger flows using indoor trajectories

In a wide variety of applications, such as indoor position selection for advertising and setting rents of different shops in a shopping mall, it is better to get the passenger flow of each room. In the indoor space, the positions of users are commonly captured by the indoor positioning system consisting of static positioning devices. And the sequence of all tracking events with the same user ordered by the corresponding time is the indoor trajectory of this user. Thus, in this paper, we define and study two essential queries named Rooms with top-k passenger flows at a Timestamp query (RkT for short) and Rooms with top-k passenger flows within a time Interval query (RkI for short), i.e., how to search rooms with top-k passenger flows at a timestamp and within a time interval in the past using indoor trajectories, respectively. For the indoor positioning system, there are only limited static positioning devices deployed in the indoor space on account of the cost. And the detection ranges of these static positioning devices only cover a small part of the indoor space. When a user is in the undetected state, there is uncertainty in its position combined with the quite complex indoor topology. Such uncertainty brings great challenges to determining the passenger flow in each room. Considering the distribution of static positioning devices, we propose a new method about how to reasonably infer where a user is in the undetected state and the corresponding probability based on its indoor trajectory and the complex indoor topology. In order to quickly retrieve the set of indoor trajectories, we propose a full Binary tree indexing indoor trajectories divided by Time intervals (BiT for short), which is built on the given set of indoor trajectories. Based on the index BiT, we propose PAT Algorithm and PAI Algorithm to efficiently process RkT and RkI queries, respectively. Extensive experiment results demonstrate superior performance of PAT Algorithm and PAI Algorithm.

Mathematical models for traffic-source PM2.5 dispersion in an urban street canyon considering the capture capability of roadside trees

Rapid urbanization increases the densely built-up blocks, the population and vehicles. Large amounts of particulate matter (PM), especially PM2.5 (PM with an aerodynamic diameter of 2.5μm or less), from vehicle exhaust are critical to human health. In typical street canyons in hot and humid regions, traffic-source PM usually diffuses to the densely built-up blocks through roadside trees. Roadside trees are a double-edged sword, serving as “guards” to absorb PM2.5 while may lead to PM2.5 gathering in street levels, thereby influencing the PM2.5 dispersion in the densely built-up blocks. To quantify the dispersion process, this study proposed traffic-source PM2.5 dynamic dispersion models considering the capture capability of roadside trees and built-up blocks based on the OSPM model. Due to the difficulty in obtaining the adsorption and deposition rate of the proposed models, the numerical simulations by ENVI-met software were used to solve and obtain the relationship between capture capability and characteristic index of roadside trees. Subsequently, The accuracy and effectiveness of the proposed traffic-source PM2.5 dynamic dispersion models were verified through field experimental data. Results show that the calculated PM2.5 concentration significantly linearly increased with the measured values with the determined coefficient (R2) of 0.98, and the first-order coefficient close to 1. It indicates that the proposed traffic-source PM2.5 dispersion model accurately quantified the impact of roadside trees on PM2.5 and its concentration dispersion process to the built-up blocks. This study provides suggestions for designing characteristic indexes of roadside trees and built-up blocks to improve the air quality of urban street canyons.

Spatial Pattern of Host Tree Size, Rather than of Host Tree Itself, Affects the Infection Likelihood of a Fungal Stem Disease.

The spatial pattern of diseased forest trees is a product of the spatial pattern of host trees and the disease itself. Previous studies have focused on describing the spatial pattern of diseased host trees, and it remains largely unknown whether an antecedent spatial pattern of host/nonhost trees affects the infection pattern of a disease and how large the effect sizes of the spatial pattern of host/nonhost trees and host size are. The results from trivariate random labeling showed that the antecedent pattern of the host ash tree, Fraxinus mandshurica, but not of nonhost tree species, impacted the infection pattern of a stem fungal disease caused by Inonotus hispidus. To investigate the effect size of the spatial pattern of ash trees, we employed the SADIE (Spatial Analysis by Distance IndicEs) aggregation index and clustering index as predictors in the GLMs. Globally, the spatial pattern (vi index) of ash trees did not affect the infection likelihood of the focal tree; however, the spatial pattern of DBH (diameter at breast height) of ash trees significantly affected the infection likelihood of the focal tree. We sampled a series of circular plots with different radii to investigate the spatial pattern effect of host size on the infection likelihood of the focal tree locally. The results showed that the location (patch/gap) of the DBH of the focal tree, rather than that of the focal tree itself, significantly affected its infection likelihood in most plots of the investigated sizes. A meta-analysis was employed to settle the discrepancy between plots of different sizes, which led to results consistent with those of global studies. The results from meta-regression showed that plot size had no significant effects.

Temporal subgraph matching method for multi-connected temporal graph

Temporal graph matching is used to find a matching subgraph set that satisfies temporal and topological information on the temporal graph. It is widely used in real scenarios and provides important support for big data mining and analysis. Most existing matching methods take the single-connected graph as the matching graph, which has a high computational cost. Simultaneously, the construction and matching complexity of its index on multi-connected temporal subgraph matching is high. To solve the above problems, we propose a new temporal subgraph matching problem for multi-connected temporal graphs and proposes the corresponding efficient filtering-selecting-matching three-stage multi-connected temporal subgraph matching method. In the filtering stage, a vertex-based filter is proposed to generate a candidate temporal subgraph set. In the select phase, a set of temporal subgraphs satisfying the vertex mapping is found. In the matching stage, the single-filter temporal subgraph matching method and temporal subgraph matching based on the temporal information tree index method are proposed to solve the problems that the edges of multi-connected temporal subgraphs cannot be mapped and the single graph matching efficiency is low, respectively. The experimental results show that the proposed method improves the matching accuracy, and the corresponding index size is reduced.

Complete solution to open problems on exponential augmented Zagreb index of chemical trees

One of the crucial problems in combinatorics and graph theory is characterizing extremal structures with respect to graph invariants from the family of chemical trees. Cruz et al. (2020) [7] presented a unified approach to identify extremal chemical trees for degree-based graph invariants in terms of graph order. The exponential augmented Zagreb index (EAZ) is a well-established graph invariant formulated for a graph G asEAZ(G)=∑vivj∈E(G)e(didjdi+dj−2)3, where di signifies the degree of vertex vi, and E(G) is the edge set. Due to some special counting features of EAZ, it was not covered by the aforementioned unified approach. As a result, the exploration of extremal chemical trees for this invariant was posed as an open problem in the same article. The present work focuses on generating a complete solution to this problem. Our findings offer maximal and minimal chemical trees of EAZ in terms of the graph order n.

Privacy-preserving top-[formula omitted] spatio-temporal keyword preference query

With the rapid advancement of location-based services and mobile devices, spatial keyword query attracts increasing attention. In this paper, we focus on a new query type known as top-k spatio-temporal keyword preference query. This kind of query considers both the spatial object itself and other spatial objects in the neighborhood to return k spatial objects with the highest score. These k spatial objects satisfy spatial and temporal constraints, while their scores are determined by the keyword similarity of the neighboring spatial objects. We propose a scheme to enable privacy-preserving top-k spatio-temporal keyword preference queries. To effectively represent temporal information, we employ time vectors to denote time periods, allowing us to assess whether the data satisfies temporal constraints based on the inner product of time vectors. Furthermore, we adopt a two-step strategy to execute the query. The first step is to find all Points of Interest (POIs) that meet the spatial and temporal constraints. The second step is to calculate the score of each POI and return the top-k POIs with the highest score. To enhance query efficiency, we build a tree index structure that can achieve sub-linear query complexity. Additionally, we utilize EASPE algorithm to encrypt both the index and the query, ensuring privacy-preserving capabilities. Security analysis proves that our scheme satisfies CQA2-security. At the same time, experimental evaluation validates the query performance of our scheme.

APB-tree: An Adaptive Pre-built Tree Indexing Scheme for NVM-based IoT Systems

APB-tree: An Adaptive Pre-built Tree Indexing Scheme for NVM-based IoT Systems

On ABS Estrada index of trees

On ABS Estrada index of trees

Urban Biodiversity Index for Trees: A Climate Adaptation Measure for Cities Based on Tree Inventories

A historically large percentage of the world’s population has moved to urban areas in the past few decades, causing various negative effects for the environment, such as air, noise, water, and light pollution; land degradation; and biodiversity loss. Under the current climate crisis, cities are anticipated to play an essential part in adaptation strategies to extreme atmospheric events. This study aims at developing indicators at an urban scale that can highlight adaptation progress by investigating relevant data (especially in situ) and statistics at a pan-European level in support of the EU’s strategy for adapting to the impacts of climate change. The proposed indicator, Urban Biodiversity Indicator for Trees (UBI4T), which can be derived from city tree inventories, assesses one essential component of urban biodiversity by computing the proportion of native, alien, invasive, and toxic tree species spatially across a city. According to our findings (applying the UBI4T for Amsterdam and exploring its policy potential for Barcelona), the UBI4T can offer crucial information for decision and policy makers, as well as stakeholders of a city, with the aim of conducting dedicated and effective strategic initiatives to restore, improve, and protect nature in the urban environment, thus contributing to adaptation and resilience to extreme atmospheric events in cities.

P-276 Endometrial microbiome diversity and the local macrophages populations during the mid-secretory phase

Abstract Study question Are there any quantitative associations between endometrial macrophages populations and microorganisms’ diversity? Summary answer The quantities and spatial distribution of endometrial macrophages populations correlated significantly with several microbiome diversity indices. What is known already Numerous studies have linked the relative abundance of Lactobacilli with a receptive endometrium, while the presence of multiple other bacterial species has been implicated in implantation failure. Another determinant of endometrial receptivity is the local immune cell composition and its inflammatory status. Knowing that the microbiome affects the immune system, it is worth studying the potential interplay between bacterial composition and immune cell populations in the endometrium during its receptive state. The present study aimed to investigate associations between the quantity and distribution of endometrial macrophages populations and the local microbiome diversity during the mid-secretory phase of the menstrual cycle. Study design, size, duration This prospective observational study was conducted between April 2021 and January 2023. Endometrial biopsies were collected from 25 female patients of reproductive age on day 7 after luteinising hormone surge. Eligibility criteria included no endometrial pathologies, no history of recent or chronic inflammatory or infectious disease, no recent antibiotic treatment, and no endocrinological, autoimmune or oncological conditions. Participants/materials, setting, methods Half of each biopsy was used for immunohistochemistry with CD11c + (Proteintech) and CD163 + (Quartett) to reveal pro- and anti- inflammatory macrophages, respectively. Their quantities and spatial distribution were analysed by HALO® image analysis software. The remaining endometrial tissue underwent DNA isolation and subsequent 16S rRNA (v4-v5 region) gene sequencing to determine endometrial microbiota composition. Alpha diversity indices - Good’s coverage, Shannon and phylogenic diversity - were evaluated and tested for correlation with the macrophages metrics. Main results and the role of chance The observed median percentage and range of the studied macrophages populations in the endometrial stroma were: 1.16% (2.98) CD11c+ macrophages and 1.96% (4.48) CD163+ macrophages. The evaluated alpha diversity indices were: 0.99±0.01 Good’s coverage, 2.53±1.20 Shannon and 38.56±15.43 phylogenic diversity.The CD11c+ macrophages percentage was not related to the microbial diversity of the studied samples. The percentage of the CD163+ macrophages, however, showed significant correlation with the Good’s coverage alpha diversity index (R = 0.397, p = 0.04). The median distance between CD11c+ and CD163+ cells in the endometrial stroma was 63.7µm (108.36) and it was significantly related to the Shannon alpha diversity index (R=-0.347, p = 0.05) and phylogenic diversity whole tree index (R=-0.367, p = 0.05).In summary, the anti-inflammatory macrophages percentage in the mid-secretory endometrial stroma is positively related to the local microbial diversity. Moreover, the distances between the pro- and anti-inflammatory macrophages populations in the endometrium are negatively associated to Shannon and PD whole tree alpha diversity indices. Limitations, reasons for caution The results of this study should be confirmed in a larger study population. Wider implications of the findings This study’s findings indicate that there is a correlation of the endometrial macrophages quantity and stromal distribution with the endometrial microbiome diversity. The association between these determinants of endometrial receptivity could help in understanding the fine tuning of the endometrium for accepting the embryo. Trial registration number The current research was funded by the National Science Fund, Ministry of Education, Bulgaria, Contract № KP-06-N53/14/16.11.2021.

A privacy-preserving image retrieval scheme with access control based on searchable encryption in media cloud

With the popularity of the media cloud computing industry, individuals and organizations outsource image computation and storage to the media cloud server to reduce the storage burden. Media images usually contain a large amount of private information. To prevent disclosure of privacy of the image owners, media images are encrypted before uploading to the server. However, this operation will greatly limit the utilization of the image for the user, such as content-based image retrieval. We propose an efficient similarity query algorithm with access control based on Bkd-tree in this paper, in which a searchable encryption scheme is designed for similarity image retrieval, and the encrypted image is used to extract image features by a pre-trained CNN model. The Bkd-tree is utilized to generate an index tree for the image features to speed up retrieval and make it faster than linear indexing. Finally, the security performances of the proposed scheme is analyzed and the performance of this scheme is evaluated by experiments. The results show that the security of the image content and image features can be ensured, and it has a shorter retrieval time and higher retrieval efficiency.

Multiplicative Sombor index of trees

Multiplicative Sombor index of trees

Sharp Upper Bound for Harmonic Index of Trees with Given Total Domination Number

Let \( G=(V,E) \) be a simple connected graph with vertex set \( G \) and edge set \( E \). The harmonic index of graph \( G \) is the value \( H(G)=\sum_{uv\in E(G)} \frac{2}{d_u+d_v} \), where \( d_x \) refers to the degree of \( x \). We obtain an upper bound for the harmonic index of trees in terms of order and the total domination number, and we characterize the extremal trees for this bound.

On the maximum atom-bond sum-connectivity index of molecular trees

Let G be a graph with V(G) and E(G), as vertex set and edge set, respectively. The atom-bond sum-connectivity (ABS) index is a vertex-based topological index which is defined as ABS ( G ) = ∑ ab ∈ E ( G ) ϱ a + ϱ b − 2 ϱ a + ϱ b , where ϱ a is the degree of the vertex a. In this paper, we obtain sharp upper bounds for the ABS index of molecular trees in terms of order and number of branching vertices and vertices of degree two.

Limit Law for Zagreb and Wiener Indices of Random Exponential Recursive Trees

The Wiener index is the sum of distances of all pairs of nodes in a graph; and the Zagreb index is defined as the sum of squares of the degrees of nodes in a rooted tree. In this note, we calculate the first two moments of the Wiener and Zagreb indices of random exponential recursive trees (random ERTs) from two systems of recurrence relations. Then, by an application of the contraction method, we characterize the limit law for a scaled Zagreb index of ERTs. Via the martingale convergence theorem, we also show the almost sure convergence and quadratic mean convergence of an appropriately scaled Wiener index that is indicative of the distance of two randomly chosen nodes.

Impact of a water restriction on the summer climatic benefits of trees inside an outdoor street canyon scale model

Trees may help reduce the increasing human thermal stress in cities caused by the Urban Heat Island phenomenon and the multiplication and intensification of heatwaves through the climatic benefits they provide: cast shadows and transpiration. However, the multiplication of droughts may lower the water supply of street trees and impact their development and climatic benefits. The transpiration and radiation interception of two alignments of potted ornamental apple trees (Malus Coccinella® ‘Courtarou’) planted in a 1/5 scale street canyon experiencing contrasted water supplies were monitored during an 8-week period of summer 2022. Compared to well-watered trees, the transpiration of water-restricted trees was reduced quickly and strongly by 81 % on average. A noticeable reduction of the leaf area index of the water-restricted trees led to a decrease of their radiation interception which however remained higher than 69 % of the incident radiation measured without trees. No noticeable air temperature difference was measured under the tree crowns of both alignments of trees but the Universal Thermal Climate Index calculated under the water-restricted trees increased by on average 1 °C. Radiation interception appeared to be responsible for the major part of the daily total amount of energy dissipated. A noticeable reduction of the daily total amount of energy dissipated by the WR trees was mostly attributed to the reduction of their transpiration which may explain why both alignments of trees kept providing noticeable climatic benefits.

GTS: GPU-based Tree Index for Fast Similarity Search

Similarity search, the task of identifying objects most similar to a given query object under a specific metric, has gathered significant attention due to its practical applications. However, the absence of coordinate information to accelerate similarity search and the high computational cost of measuring object similarity hinder the efficiency of existing CPU-based methods. Additionally, these methods struggle to meet the demand for high throughput data management. To address these challenges, we propose GTS, a GPU-based tree index designed for the parallel processing of similarity search in general metric spaces, where only the distance metric for measuring object similarity is known. The GTS index utilizes a pivot-based tree structure to efficiently prune objects and employs list tables to facilitate GPU computing. To efficiently manage concurrent similarity queries with limited GPU memory, we have developed a two-stage search method that combines batch processing and sequential strategies to optimize memory usage. The paper also introduces an effective update strategy for the proposed GPU-based index, encompassing streaming data updates and batch data updates. Additionally, we present a cost model to evaluate search performance. Extensive experiments on five real-life datasets demonstrate that GTS achieves efficiency gains of up to two orders of magnitude over existing CPU baselines and up to 20x efficiency improvements compared to state-of-the-art GPU-based methods.