Rebalance Research Articles

Optimal Algorithms for Sorting Permutations with Brooms

Sorting permutations with various operations has applications in genetics and computer interconnection networks where an operation is specified by its generator set. A transposition tree T=(V,E) is a spanning tree over n vertices v1,v2,…vn. T denotes an operation in which each edge is a generator. A value assigned to a vertex is called a token or a marker. The markers on vertices u and v can be swapped only if the pair (u,v)∈E. The initial configuration consists of a bijection from the set of vertices v1,v2,…,vn to the set of markers (1,2,⋯,n−1,n). The goal is to sort the initial configuration of T, i.e., an input permutation, by applying the minimum number of swaps or moves in T. Computationally tractable optimal algorithms to sort permutations are known only for a few classes of transposition trees. We study a class of transposition trees called a broom and its variation a double broom. A single broom is a tree obtained by joining the centre vertex of a star with one of the two leaf vertices of a path graph. A double broom is an extension of a single broom where the centre vertex of a second star is connected to the terminal vertex of the path in a single broom. We propose a simple and efficient algorithm to obtain an optimal swap sequence to sort permutations with the transposition tree broom and a novel optimal algorithm to sort permutations with a double broom. We also introduce a new class of trees named millipede tree and prove that D* yields a tighter upper bound for sorting permutations with a balanced millipede tree compared to D′. Algorithms D* and D′ are designed previously.

Root grafts matter for inter-tree water exchange - a quantification of water translocation between root grafted mangrove trees using field data and model based indication.

Trees interconnected through functional root grafts can exchange resources, but the effect of exchange on trees remains under debate. A mechanistic understanding of resources exchange via functional root grafts will help understand their ecological implications for tree water exchange for individual trees, groups of trees, and forest stands. To identify the main patterns qualitatively describing the movement of sap between grafted trees, we reviewed available literature on root grafting in woody plants that focus on tree allometry and resource translocation via root grafts. We then extended the BETTINA model, which simulates mangrove (Avicennia germinans) tree growth on the individual tree scale, in order to synthesize the available empirical information. Using allometric data from a field study in mangrove stands, we simulated potential water exchange and analyzed movement patterns between grafted trees. In the simulations, relative water exchange ranged between -9.17 and 20.3 %, and was driven by gradients of water potential, i.e. differences in tree size and water availability. Moreover, the exchange of water through root grafts alters the water balance of trees and their feedback with the soil: grafted trees that receive water from their neighbors reduce their water uptake. Our individual-tree modelling study is a first theoretical attempt to quantify root graft-mediated water exchange between trees. Our findings indicate that functional root grafts represent a vector of hydraulic redistribution, helping to maintain the water balance of grafted trees. This non-invasive approach can serve as a fundament for designing empirical studies to better understand the role of grafted root interaction networks on a broader scale.

Leveraging Write Heterogeneity of Phase Change Memory on Supporting Self-Balancing Binary Tree

With the increasing demand of massive/big data applications, non-volatile memory (NVM), such as phase change memory (PCM), has become a promising candidate to replace DRAM because of its low leakage power, non-volatility, and high density. However, most of the existing memory read/write intensive algorithms and data structures are not aware of the PCM write heterogeneity in terms of both energy consumption and latency. In particular, self-balancing binary search trees, which are widely used to manage massive data in the big-data era, were designed without the consideration of PCM characteristics. Thus, the multiple rotations of the tree balancing process would degrade the memory performance. This work explores the relations among nodes and analyzes tree operations, and the node indexing and address mapping are redesigned to reduce the tree management overhead on single-level cell (SLC) PCM by decreasing the number of bit flips of tree rotations. When multi-level cell (MLC) PCM is included, our address mapping algorithm is developed to reduce the total energy consumption and latency with considerations of the heterogeneous write operations of different cell states. Experimental results show that our solution significantly outperforms the original implementation of a self-balancing binary search tree when the amount of data is large.

HSCR: Hierarchical structured cluster routing protocol for load balanced wireless sensor networks

AbstractThe robustness of wireless sensor networks (WSNs) has made it a preferred choice for many applications. WSNs should perform the intended sensing task with a limited amount of energy. Clustering methodology is used to reduce sensor nodes' energy consumption and increase the network lifetime by organizing nodes into independent groups. In this article, a hierarchical structured cluster routing (HSCR) protocol based on the principle of an m‐way balanced tree has been proposed for multi‐hop intra‐cluster communication and offload the cluster head. It enhances the network performance by providing an underlying architecture that reduces the intra‐cluster communication distance and the amount of data sent to the cluster head. In the proposed HSCR protocol, an m‐way tree‐based hierarchical structure has been proposed in which balanced structure is formed within each cluster so that data aggregation is performed at each intermediate parent node. The proposed approach can be implemented over any communication protocol used in WSNs. Simulation results prove that the proposed algorithms outperform traditional clustering algorithms, LEACH and CT‐RPL, in terms of network stability, energy consumption, and network lifetime. Simulation results affirm that the proposed algorithms outperform traditional clustering algorithms, LEACH and CT‐RPL, in terms of network stability, energy consumption, average intra‐cluster communication distance and network lifetime by 105.32%, 49.23%, 14.98%, 109.31%, and 35.75%, 15.32%, 17%, 24.31%, respectively.

Mathematics of coalescent gene trees

Using the coalescent process continuously until all the lineages have become one, we get different possible gene trees. In this paper I had computed the probabilities of such different gene trees that occur depending on the way lineages can form. In particular I had shown the probability of any 3 sample gene tree is 1/3 and for four samples resembling caterpillar gene trees the probability is 1/18 and probability for any balanced gene tree with 4 samples is 1/9. I have also proved a theorem providing the number of ranked gene trees. This estimate will help us to determine the probability of any gene tree.

Responses of tree growth and biomass production to nutrient addition in a semi-deciduous tropical forest in Africa.

Experimental evidence of nutrient limitations on primary productivity in Afrotropical forests is rare and globally underrepresented yet are crucial for understanding constraints to terrestrial carbon uptake. In an ecosystem-scale nutrient manipulation experiment, we assessed the early responses of tree growth rates among different tree sizes, taxonomic species, and at a community level in a humid tropical forest in Uganda. Following a full factorial design, we established 32 (eight treatments × four replicates) experimental plots of 40 × 40 m each. We added nitrogen (N), phosphorus (P), potassium (K), their combinations (NP, NK, PK, and NPK), and control at the rates of 125 kg N ha-1 year-1 , 50 kg P ha-1 year-1 and 50 kgK ha-1 year-1 , split into four equal applications, and measured stem growth of more than 15,000 trees with diameter at breast height (dbh) ≥1cm. After 2 years, the response of tree stem growth to nutrient additions was dependent on tree sizes, species and leaf habit but not community wide. First, tree stem growth increased under N additions, primarily among medium-sized trees (10-30 cm dbh), and in trees of Lasiodiscus mildbraedii in the second year of the experiment. Second, K limitation was evident in semi-deciduous trees, which increased stem growth by 46% in +K than -K treatments, following a strong, prolonged dry season during the first year of the experiment. This highlights the key role of K in stomatal regulation and maintenance of water balance in trees, particularly under water-stressed conditions. Third, the role of P in promoting tree growth and carbon accumulation rates in this forest on highly weathered soils was rather not pronounced; nonetheless, mortality among saplings (1-5cm dbh) was reduced by 30% in +P than in -P treatments. Although stem growth responses to nutrient interaction effects were positive or negative (likely depending on nutrient combinations and climate variability), our results underscore the fact that, in a highly diverse forest ecosystem, multiple nutrients and not one single nutrient regulate tree growth and aboveground carbon uptake due to varying nutrient requirements and acquisition strategies of different tree sizes, species, and leaf habits.

Balanced Multi-Channel Data Collection in Wireless Sensor Networks

Data collection is an essential task in Wireless Sensor Networks (WSNs). In data collection process, the sensor nodes transmit their readings to a common base station called Sink. To avoid a collision, it is necessary to use the appropriate scheduling algorithms for data transmission. On the other hand, multi-channel design is considered as a promising technique to reduce network interference and latency of data collection. This technique allows parallel transmissions on different frequency channels, thus time latency will be reduced. In this paper, we present a new scheduling method for multi-channel WSNs called Balanced Multi Channel Data Collection (Balanced MC-DC) Algorithm. The proposed protocol is based on using both Non-Overlapping Channels (NOC) and Partially Overlapping Channels (POC). It uses a new approach that optimizes the processes of tree construction, channel allocation, transmission scheduling and balancing simultaneously. Extensive simulations confirm the superiority of the proposed algorithm over the existing algorithms in wireless sensor networks.

Robust, Universal Tree Balance Indices.

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet, existing indices are not defined for all rooted trees, are unreliable for comparing trees with different numbers of leaves, and are sensitive to the presence or absence of rare types. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless' index but can account for population sizes, are defined for trees with any degree distribution, and enable meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalized reciprocal of Sackin's index. Hence, we both unify and generalize the two most popular existing tree balance indices. Our indices are intrinsically normalized and can be computed in linear time. We conclude that these more widely applicable indices have the potential to supersede those in current use. [Cancer; clone tree; Colless index; Sackin index; species tree; tree balance.].

Joinable Parallel Balanced Binary Trees

In this article, we show how a single function, join , can be used to implement parallel balanced binary search trees ( BSTs ) simply and efficiently. Based on join , our approach applies to multiple balanced tree data structures, and a variety of functions for ordered sets and maps. We describe our technique as an algorithmic framework called join-based algorithms . We show that the join function fully captures what is needed for rebalancing trees for a variety of tree algorithms, as long as the balancing scheme satisfies certain properties, which we refer to as joinable trees. We discuss four balancing schemes that are joinable: AVL trees, red-black trees, weight-balanced trees, and treaps. We present a variety of tree algorithms that apply to joinable trees, including insert , delete , union , intersection , difference , split , range , filter , and so on, most of them also parallel. These algorithms are generic across balancing schemes. Many algorithms are optimal in the comparison model, and we provide a general proof to show the efficiency in work for joinable trees. The algorithms are highly parallel, all with polylogarithmic span (parallel dependence). Specifically, the set-set operations union , intersection , and difference have work \( O(m\log (\frac{n}{m}+1)) \) and polylogarithmic span for input set sizes \( n \) and \( m\le n \) . We implemented and tested our algorithms on the four balancing schemes. In general, all four schemes have quite similar performance, but the weight-balanced tree slightly outperforms the others. They have the same speedup characteristics, getting around 73 \( \times \) speedup on 72 cores (144 hyperthreads). Experimental results also show that our implementation outperforms existing parallel implementations, and our sequential version achieves close or much better performance than the sequential merging algorithm in C++ Standard Template Library (STL) on various input sizes.

Effects of Girdling Intensity, Pruning Season and Thinning on Tree Growth, Crown Vigor and Wound Recovery in Japanese Larch

To ensure sustainable forestry, it is important to establish efficient management procedures for seed orchards. We evaluated the effects of thinning, pruning season and girdling intensity on tree growth and vigor in an old Larix kaempferi seed orchard. Even after four years, tree size (crown width and tree height) increased, resulting in light intensity of an un-thinned class decreasing. Thinning counteracted the decrease in light intensity associated with tree growth, but it had no effect on promoting tree growth. Tree crown status was scored based on vigor and health. No significant difference in crown vigor was observed between unpruned and winter-pruned trees, but the summer-pruning class showed significantly lower vigor. Five years after girdling, trees with low and moderate girdling levels maintained high crown vigor, similar to intact trees, while the crown vigor of trees subjected to severe girdling was significantly lower. This is the first study to quantitatively model trends in remaining girdling depth over time, and to show that the half decay period was ca. 2–3 years. Our findings suggested that management procedures that combine moderate-level girdling, winter pruning and thinning to maintain rPPFD at 50% are well-suited to balancing tree vigor and reproduction in seed orchards.

Lowering the T-depth of Quantum Circuits via Logic Network Optimization

The multiplicative depth of a logic network over the gate basis {∧ , ⊕ , ¬} is the largest number of ∧ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based logic synthesis algorithm to reduce the multiplicative depth of logic networks. It makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations. Our algorithm has applications to cryptography and quantum computing, as a reduction in the multiplicative depth directly translates to a lower T -depth of the corresponding quantum circuit. Our experimental results show improvements in T -depth over state-of-the-art methods and over several hand-optimized quantum circuits, for instance, of AES, SHA, and floating-point arithmetic.

Effects of Pulsed-Wave Chromotherapy and Guided Relaxation on the Theta-Alpha Oscillation During Arrest Reaction.

The search for the best wellness practice has promoted the development of devices integrating different technologies and guided meditation. However, the final effects on the electrical activity of the brain remain relatively sparse. Here, we have analyzed of the alpha and theta electroencephalographic oscillations during the realization of the arrest reaction (AR; eyes close/eyes open transition) when a chromotherapy session performed in a dedicated room [Rebalance (RB) device], with an ergonomic bed integrating pulsed-wave light (PWL) stimulation, guided breathing, and body scan exercises. We demonstrated that the PWL induced an evoked-related potential characterized by the N2-P3 components maximally recorded on the fronto-central areas and accompanied by an event-related synchronization (ERS) of the delta–theta–alpha oscillations. The power of the alpha and theta oscillations was analyzed during repeated ARs testing realized along with the whole RB session. We showed that the power of the alpha and theta oscillations was significantly increased during the session in comparison to their values recorded before. Of the 14 participants, 11 and 6 showed a significant power increase of the alpha and theta oscillations, respectively. These increased powers were not observed in two different control groups (n = 28) who stayed passively outside or inside the RB room but without any type of stimulation. These preliminary results suggest that PWL chromotherapy and guided relaxation induce measurable electrical brain changes that could be beneficial under neuropsychiatric perspectives.

Optimized 2D ball trees for shape layout applications

The interactive creation of 2D layouts involving irregular shapes such as text or images is typically carried out using a pointing device to select elements and drag them to new positions on a page. We propose augmenting layout interaction with two operations: overlap avoidance and grouping by distance. Since these are computationally expensive and may hinder the fluidity of the interaction, we examine several techniques that aim at implementing these features in an efficient manner. These techniques involve the approximation of 2D shapes by collections of balls (circles) which are then organized in ball trees, a bounding volume hierarchy. In particular, we discuss a new algorithm for approximating shapes with a reduced set of balls, as well as enhanced ball tree construction algorithms. These are used to implement algorithms to group shapes hierarchically by distance and to allow dragging with collision avoidance, in the context of a proof-of-concept web application for laying out shapes extracted from segmented images.

The performance of outgroup-free rooting under evolutionary radiations

Tree rooting implies a temporal dimension to phylogenies. Only after defining the position of the root node is that the ancestral-descendant relationship between branches can be fully deduced. Rooting has been usually carried out by employing evolutionarily close outgroup lineages, which is a drawback when these lineages are unavailable or unknown. Alternatively, outgroup-free rooting methods were proposed, which rely on the constancy of evolutionary rates to varying degrees. In this work we analyzed the performance of two of these methods, the midpoint rooting (MPR) and the minimal ancestor deviation (MAD), in rooting topologies evolved under challenging scenarios of fast evolutionary radiations derived from empirical data, characterized by short internal branches near the crown node. Considering all branch length combinations investigated, both methods exhibited average success rates below 50%, although MAD slightly outperformed MPR. Moreover, tree balance significantly impacted the relative performance of the methods. We found that, in four-taxa unrooted trees, the outcome of whether both methodologies will correctly root the tree can be roughly predicted by two simple dimensionless metrics: the coefficient of variation of the external branch lengths, and the ratio between the internal branch length to the total sum of branch lengths, which were employed to devise a general linear model that allowed calculating the probability of correct placing the root node for any four-taxa tree. We predicted that the performance of both outgroup-free rooting methods on loci representing the placental mammal radiation ranged between 50% and 75%.

On the Maximum Agreement Subtree Conjecture for Balanced Trees

We give a counterexample to the conjecture of Martin and Thatte that two balanced rooted binary leaf-labelled trees on $n$ leaves have a maximum agreement subtree (MAST) of size at least $n^{\frac{1}{2}}$. In particular, we show that for any $c>0$, there exist two balanced rooted binary leaf-labelled trees on $n$ leaves such that any MAST for these two trees has size less than $c n^{\frac{1}{2}}$. We also improve the lower bound of the size of such a MAST to $n^{\frac{1}{6}}$.

Quantifying the importance of deep root water uptake for apple trees’ hydrological and physiological performance in drylands

In drylands, planted trees generally develop roots through mechanisms that enhance their capacity to forage for resources, particularly water, in deep soils and thus survive droughts. However, it remains unclear how and to what extent, lack of access to deep root water uptake will affect the water balance, growth and production of trees in water-limited ecosystems. To address this gap, we designed a novel experiment to partition soils and roots below 200 cm depth from higher layers in a dryland orchard on China’s Loess Plateau to evaluate the response of apple (Malus pumila Mill.) trees to the lack of deep roots and access to deep soil resource in 2019 and 2020 (when a natural extreme drought occurred). We found that without partitioning apple trees clearly used deep soil water, thereby causing more soil desiccation than partitioned trees, especially during the drought. The unavailability of deep soil water resulted in much greater water stress, which cause a decrease of 36 % in transpiration, 20 % in photosynthesis rate and 32 % in mid-day leaf water potential relative to unpartitioned trees. Consequently, the yield and quality of apple trees also clearly decreased 11 % and 15 %. These findings suggest that the absence of uptake of deep soil water by roots reduced trees’ drought resistance. However, the partitioned trees had clearly higher water use efficiency (WUE) than the unpartitioned trees, although in both cases WUE was strongly reduced by the extreme drought. Our results demonstrate that deep soil resources and roots play key roles in trees’ responses to drought, and are likely to play crucial roles in future ecosystem dynamics.

Evolution of distributed detection performance over balanced binary relay tree networks with bit errors

Target detection based on wireless sensor networks can be considered as a distributed binary hypothesis testing problem. In this paper, the evolution of detection error probability with the increase in the network scale is studied for the balanced binary relay tree network with channel noise. Firstly, the iterative expressions of false-alarm probability and missed-detection probability depending on the number of tree network layers are given. Then, the iterative process of two types of error probabilities in the network space is described as a discrete nonlinear switched dynamic system, and the dynamic properties of two types of error probabilities are analyzed in a plane rectangular coordinate system. A globally attractive invariant set of the state of the dynamic system, which is not related to the channel noise, is derived. The switching mode of the system and the total error probability in the invariant set are further analyzed, and a necessary and sufficient convergence condition of the total error probability is provided. Based on this condition, the following detection properties of the network are revealed: (1) as long as the channel bit error probability is not zero, the total error probability does not tend to zero as the network size grows to infinity; (2) when the channel bit error probability is greater than \(\frac{2-\sqrt{3}}{2}\), the total error probability will continue to increase with the increase in the network size.

Multi-criteria text mining model for COVID-19 testing reasons and symptoms and temporal predictive model for COVID-19 test results in rural communities.

This study is conducted to build a multi-criteria text mining model for COVID-19 testing reasons and symptoms. The model is integrated with a temporal predictive classification model for COVID-19 test results in rural underserved areas. A dataset of 6895 testing appointments and 14 features is used in this study. The text mining model classifies the notes related to the testing reasons and reported symptoms into one or more categories using look-up wordlists and a multi-criteria mapping process. The model converts an unstructured feature to a categorical feature that is used in building the temporal predictive classification model for COVID-19 test results and conducting some population analytics. The classification model is a temporal model (ordered and indexed by testing date) that uses machine learning classifiers to predict test results that are either positive or negative. Two types of classifiers and performance measures that include balanced and regular methods are used: (1) balanced random forest and (2) balanced bagged decision tree. The balanced or weighted methods are used to address and account for the biased and imbalanced dataset and to ensure correct detection of patients with COVID-19 (minority class). The model is tested in two stages using validation and testing sets to ensure robustness and reliability. The balanced classifiers outperformed regular classifiers using the balanced performance measures (balanced accuracy and G-score), which means the balanced classifiers are better at detecting patients with positive COVID-19 results. The balanced random forest achieved the best average balanced accuracy (86.1%) and G-score (86.1%) using the validation set. The balanced bagged decision tree achieved the best average balanced accuracy (83.0%) and G-score (82.8%) using the testing set. Also, it was found that the patient history, age, testing reasons, and time are the key features to classify the testing results.

Ranked Keyword Search over Encrypted Cloud Data Through Machine Learning Method

Ranked keyword search over encrypted data has been extensively studied in cloud computing as it enables data users to find the most relevant results quickly. However, existing ranked multi-keyword search solutions cannot achieve efficient ciphertext search and dynamic updates with forward security simultaneously. To solve the above problems, we first present a basic Machine Learning-based Ranked Keyword Search (ML-RKS) scheme in the static setting by using the k-means clustering algorithm and a balanced binary tree. ML-RKS reduces the search complexity without sacrificing the search accuracy, but is still vulnerable to forward security threats when applied in the dynamic setting. Then, we propose an Enhanced ML-RKS (called ML-RKS <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$^{+}$</tex></formula> ) scheme by introducing a permutation matrix. ML-RKS <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$^{+}$</tex></formula> prevents cloud servers from making search queries over newly added files via previous tokens, thereby achieving forward security. The security analysis proves that our schemes protect the privacy of indexes, query tokens and keywords. Empirical experiments using the real-world dataset demonstrate that our schemes are efficient and feasible in practical applications.

Mirror symmetry for the Tate curve via tropical and log corals

We introduce tropical corals, balanced trees in a half-space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve. This implies that the homogeneous coordinate ring of the mirror to the Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming a prediction of homological mirror symmetry.