On the communication complexity of graph properties

The regularity lemma of Szemeredi turned out to be the most powerful tool for studying the testability of graph properties in the dense graph model. In fact, as we argue in this paper, this lemma can be used in order to prove (essentially) all the previous results in this area. More precisely, a barrier for obtaining an efficient testing algorithm for a graph property P was having an efficient regularity lemma for graphs satisfying P. The problem is that for many natural graph properties (e.g. triangle freeness) it is known that a graph can satisfy P and still only have regular partitions of tower-type size. This means that there was no viable path for obtaining reasonable bounds on the query complexity of testing such properties. In this paper we consider the property of being induced C_4-free, which also suffers from the fact that a graph might satisfy this property but still have only regular partitions of tower-type size. By developing a new approach for this problem we manage to overcome this barrier and thus obtain a merely exponential bound for testing this property. This is the first substantial progress on a problem raised by Alon in 2001, and more recently by Alon, Conlon and Fox. We thus obtain the first example of an efficient testing algorithm that cannot be derived from an efficient version of the regularity lemma.

We study two variants of the Balanced Tree Partition (BTP for short) problem, whose goal is to find the minimum number of edges such that a partition of vertices into sets of equal size can be obtained after deleting those edges. We consider the BTP problem over trees with virtual nodes, which is motivated by the real applications in storing tree structured data distributively. Different from the traditional BTP problem, after deleting an edge from the tree, two virtual nodes must be added to provide the ability to recover the edge when computing, which will increase the size of some set in the partition and the set may become too large and need further splitting. Depending on whether or not to consider the partition set number k to be a parameter, to investigate the balanced tree partition methods over trees with virtual nodes, we formally defined two specific problems, \(k\)-VBTP and VBTP. The computational complexity and inapproximability of \(k\)-VBTP are analyzed, for the VBTP problem, a polynomial time algorithm is designed to find the optimal solution based on dynamic programming. Finally, the connections between \(k\)-VBTP and VBTP are built, and based the algorithm for VBTP, we design a heuristic algorithm for \(k\)-VBTP with performance guarantee.

A multioperator genetic algorithm for the traveling salesman problem with job-times

Linear Decision Trees, Subspace Arrangements, and Mobius Functions

This dissertation is concerned with the application of notions and methods from the field of information theory to the field of communication complexity. It consists of two main parts. In the first part of the dissertation, we prove lower bounds on the randomized two-party communication complexity of functions that arise from read-once boolean formulae. A read-once boolean formula is a formula in propositional logic with the property that every variable appears exactly once. Such a formula can be represented by a tree, where the leaves correspond to variables, and the internal nodes are labeled by binary connectives. Under certain assumptions, this representation is unique. Thus, one can define the depth of a formula as the depth of the tree that represents it. The complexity of the evaluation of general read-once formulae has attracted interest mainly in the decision tree model. In the communication complexity model many interesting results deal with specific read-once formulae, such as disjointness and tribes. In this dissertation we use information theory methods to prove lower bounds that hold for any read-once formula. Our lower bounds are of the form n(f )/c^d(f ) , where n(f ) is the number of variables and d(f ) is the depth of the formula, and they are optimal up to the constant in the base of the denominator. In the second part of the dissertation, we explore the applicability of the information-theoretic method in the number-on-the-forehead model. The work of Bar-Yossef, Jayram, Kumar & Sivakumar [BYJKS04] revealed a beautiful connection between Hellinger distance and two-party randomized communication protocols. Inspired by their work and motivated by the open questions in the number-on-the-forehead model, we introduce the notion of Hellinger volume. We show that it lower bounds the information cost of multi-party protocols. We provide a small toolbox that allows one to manipulate several Hellinger volume terms and also to lower bound a Hellinger volume when the distributions involved satisfy certain conditions. In doing so, we prove a new upper bound on the difference between the arithmetic mean and the geometric mean in terms of relative entropy. Finally, we show how to apply the new tools to obtain a lower bound on the informational complexity of the ANDk function.

Regional landslide susceptibility prediction (LSP) research is of great significance to the prevention and control of landslides. This study focuses on the LSP modelling based on the decision tree model. Taking the northern part of An’yuan County of Jiangxi Province as an example, 14 environmental factors including elevation, gully density and lithology are obtained based on geographical information system (GIS) and remote sensing satellite. Frequency Ratio method and C5.0 decision tree (DT) model are coupled to build DT model for LSP modelling. Then the predicted results are graded into five attribute intervals. Finally, LSP performance of DT model is evaluated by comparing the area value under the receiver operating characteristic curve (ROC) and classification of landslide susceptibility. The results show that the AUC accuracy of the C5.0 DT model is 0.805, and the LSP results of the C5.0 DT model are consistent with the actual distribution pattern of landslides in this County.

Badminton is a demanding sport that requires effective workload management to enhance performance and prevent injuries. This study developed a machine learning-based Decision Tree (DT) model to create personalized workload management strategies for 73 young elite badminton players, averaging 6 years of experience. Players underwent anthropometric and fitness assessments, with external loads measured via triaxial accelerometers and internal loads through rate of perceived exertion (RPE) during training and competition. K-means clustering categorized players into high, moderate, and low external workload levels. High-load players were generally older, taller, heavier, and exhibited superior flexibility, grip strength, and countermovement jump performance. Moderate-load players excelled in balance and leg endurance, while low-load players showed greater upper body strength, quicker reaction times, and higher perceived exertion. A sensitivity analysis was conducted to evaluate the impact of tree depth on model performance, followed by a comparative assessment of the Decision Tree (DT) model and multinomial Logistic Regression (MLR). The results demonstrated that the DT model outperformed the MLR, achieving 92% accuracy in predicting external loads compared to the MLR's 57%. This highlights the DT model's superior capability to provide tailored workload recommendations, thereby enhancing athletic performance and reducing the risk of injury.

Teicoplanin 24-h loading dose regimen using a decision tree model to target serum trough concentration of 15–30 μg/mL: A retrospective study

To develop a logistic regression model, artificial neural network (ANN) model and decision tree (DT) model for the progression of mild cognitive impairment (MCI) to Alzheimer's disease (AD) to compare the performance of the three models. A total of 425 patients with MCI were screened from the original cohort. The actual follow up included 361 patients, with AD as the outcome variable. Three kinds of prediction models were developed: a logistic regression model, ANN model and DT model. The performance of all three models was measured with accuracy, sensitivity, positive predictive value and area under the receiver operating characteristic curve. A total of 121 patients with MCI developed AD, and the average conversion rate was 9.49% per year. The ANN model had higher accuracy (89.52 ± 0.36%), area under the receiver operating characteristic curve (92.08 ± 0.12), sensitivity (82.11 ± 0.42%) and positive predictive value (75.26 ± 0.86%) than the other two models. The first five important predictors of the ANN model were, in order, ADL score, age, urine AD-associated neuronal thread protein, alcohol consumption and smoking. For the DT model, they were age, activities of daily living score, family history of dementia, urine AD-associated neuronal thread protein and alcohol consumption. For the logistic regression model, they were age, sex, activities of daily living score, alcohol consumption and smoking. The logistic regression, ANN and DT models performed well at predicting the transition from MCI to AD with ideal stability. However, the ANN model had the best predictive value. Increased age, activities of daily living score, urine AD-associated neuronal thread protein, alcohol consumption, smoking and sex were important factors. Geriatr Gerontol Int 2021; 21: 43-47.

It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the quantum query complexity of f is linearly related to the degree of a non-deterministic polynomial for f. We also prove a quantum-classical gap of 1 vs. N for query complexity for a total f. In the case of quantum communication complexity there is a (partly undetermined) relation between the complexity of f and the logarithm of the rank of its communication matrix. We show that the quantum communication complexity of f is linearly related to the logarithm of the rank of a version of the communication matrix and that it can be exponentially smaller than its classical counterpart.

To develop and test decision tree (DT) models to classify physical activity (PA) intensity from accelerometer output and Gross Motor Function Classification System (GMFCS) classification level in ambulatory youth with cerebral palsy (CP) and compare the classification accuracy of the new DT models to that achieved by previously published cut points for youth with CP. Youth with CP (GMFCS levels I-III) (N = 51) completed seven activity trials with increasing PA intensity while wearing a portable metabolic system and ActiGraph GT3X accelerometers. DT models were used to identify vertical axis (VA) and vector magnitude (VM) count thresholds corresponding to sedentary (SED) (<1.5 METs), light-intensity PA (LPA) (≥1.5 and <3 METs) and moderate-to-vigorous PA (MVPA) (≥3 METs). Models were trained and cross-validated using the "rpart" and "caret" packages within R. For the VA (VA_DT) and VM DT (VM_DT), a single threshold differentiated LPA from SED, whereas the threshold for differentiating MVPA from LPA decreased as the level of impairment increased. The average cross-validation accuracies for the VC_DT were 81.1%, 76.7%, and 82.9% for GMFCS levels I, II, and III. The corresponding cross-validation accuracies for the VM_DT were 80.5%, 75.6%, and 84.2%. Within each GMFCS level, the DT models achieved better PA intensity recognition than previously published cut points. The accuracy differential was greatest among GMFCS level III participants, in whom the previously published cut points misclassified 40% of the MVPA activity trials. The GMFCS-specific cut points provide more accurate assessments of MVPA levels in youth with CP across the full spectrum of ambulatory ability.

In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function f on n=2k bits defined by a complete binary tree of NAND gates of depth k, which achieves R0(f) = O(D(f)0.7537…). We show this is false by giving an example of a total boolean function f on n bits whose deterministic query complexity is Ω(n/log(n)) while its zero-error randomized query complexity is O(√n). We further show that the quantum query complexity of the same function is O(n1/4), giving the first example of a total function with a super-quadratic gap between its quantum and deterministic query complexities. We also construct a total boolean function g on n variables that has zero-error randomized query complexity Ω(n/log(n)) and bounded-error randomized query complexity R(g) = O(√n). This is the first super-linear separation between these two complexity measures. The exact quantum query complexity of the same function is QE(g) = O(√n). These functions show that the relations D(f) = O(R1(f)2) and R0(f) = O(R(f)2) are optimal, up to poly-logarithmic factors. Further variations of these functions give additional separations between other query complexity measures: a cubic separation between Q and R0, a 3/2-power separation between QE and R, and a 4th power separation between approximate degree and bounded-error randomized query complexity. All of these examples are variants of a function recently introduced by Goos, Pitassi, and Watson which they used to separate the unambiguous 1-certificate complexity from deterministic query complexity and to resolve the famous Clique versus Independent Set problem in communication complexity.

Statistical models are essential to understand the occurrence and spread of microbes to support decision-making in microbiology and epidemiology. Antimicrobial resistance (AMR) is a multifaceted global problem and a significant threat to sustainable modern healthcare. This thesis aims to identify knowledge gaps in the AMR research field and explain the added value of using statistical models and novel spatiotemporal data to predict and identify risk factors for the occurrence and spread of AMR. Strategic action plans to tackle the increasing international threat of AMR are based upon research agendas that are informed using knowledge gaps in the AMR research field. Currently, these knowledge gaps are identified manually and are often subjective. Chapter 2 describes how bibliometric data-driven methodology can be used to identify knowledge gaps in AMR research. To this end, twenty years of AMR related articles were extracted using the PubMed search engine. With structural topic modelling I identified the topics comprising the AMR research field, while topic clusters were created using hierarchical clustering on the topic proportions. Potential AMR knowledge gaps were obtained using Spearman’s correlation between topic clusters and topics and between individual topics. A total of 88 topics and seven topic clusters were identified from 158 616 scientific AMR research articles. In total, 421 potential knowledge gaps were identified between the topic clusters and topics and 2 663 between individual topics. Key knowledge gaps between molecular and laboratory AMR research were highlighted. The knowledge gaps between AMR research regarding water and the environment and both institutional and international surveillance topics were highlighted at the topic level. These results provide an innovative, data-driven way to identify knowledge gaps in AMR research. Surgical site infections (SSI) make up 19.6% of healthcare-associated infections (HAIs) in Europe [98]. Risk factor identification studies for the occurrence of SSI do not usually specify how continuous variables cut-offs are determined. In most cases, they use standard medical cut-offs without considering the data being studied. Chapter 3 identifies the risk factors for the occurrence of SSI for digestive, thoracic and orthopaedic system surgeries using standard medical and data-driven cut-off values. Retrospective surgical procedure data, individual electronic health records, pharmaceutical data and laboratory data were used from the Erasmus MC University Medical Centre in The Netherlands. Risk factors for the occurrence of SSI were identified using a multivariate forward-step logistic regression model. Standard medical cut-off values were compared with cut-offs determined from the data. For digestive, orthopaedic and thoracic system surgical procedures, the risk factors identified for the occurrence of SSI were preoperative temperature of 38 oC and antibiotics used at the time of surgery. C-reactive protein (CRP) and the duration of the surgery were identified as risk factors for digestive surgical procedures. Being an adult (age ≥ 18) was identified as a protective effect for thoracic surgical procedures. Data-driven cut-off values identified for temperature, age, and CRP, explained the occurrence of SSI outcome up to 19.5% better than standard medical cut-off values. Future studies should investigate if data-driven cut-offs can add value to explain the clinical outcome being modelled and not solely rely on standard medical cut-off values for continuous variables to identify risk factors. Transmission of harmful microorganisms (HMO) poses a major threat to patients and healthcare workers in healthcare settings. The most effective countermeasure against these transmissions is the adherence to hand hygiene policies, but adherence rates are relatively low and vary over space and time. The spatiotemporal effects of varying levels hand hygiene compliance on the transmission and spread of hand-transmitted HMO in a closed healthcare setting must still be quantified. Chapter 4 describes how identifies healthcare worker occupation group of potential super-spreaders and the spatiotemporal effects on the hand transmission of HMO quantified for varying levels of hand hygiene compliance (HHC) caused by this group using their spatiotemporal movements. Spatiotemporal data were collected in the University Medical Center Groningen (UMCG) using radio frequency identification technology. The effects of five probability distributions of HHC and three harmful microorganism transmission rates were simulated using a dynamic agent-based simulation model. The effects of initial simulation assumptions on the simulation results were quantified using five risk outcomes. Nurses were identified as the potential super-spreader healthcare worker occupation group. During lack of HHC (5%) and high transmission rates (5% per contact moment), a colonised nurse can transfer microbes to three of the 17 healthcare worker or patients encountered during the 98.4 minutes of visiting 23 rooms while colonised. The HMO transmission potential for nurses is higher during weeknights (5 pm – 7 am) and weekends as compared to weekdays (7 am – 5 pm). Spatiotemporal behaviour and social mixing patterns of healthcare can change the expected number of hand transmissions and spread HMO by super-spreaders in a closed healthcare setting. These insights can be used to evaluate spatiotemporal safety behaviours and develop infection prevention and control strategies. Vancomycin-resistant enterococci (VRE) is can cause severe patient health and monetary burdens. The odds of a hospital patient acquiring VRE increases when using antibiotics and when prior room occupants had VRE, but the antibiotic use of prior room occupants are often neglected. Chapter 5 describes how the occurrence and spread of VRE can be explained using intrahospital patient movements (IPM) and their antibiotic use between hospital wards. Retrospective IPM, antibiotic use and PCR screening data were used from a hospital in the Netherlands. A dynamic directed spatiotemporal graph was developed, and together with the PageRank algorithm used to calculate two daily centrality measures to summarise the flow of patients and antibiotics at the ward level. With a decision tree and random forest model I predicted the daily occurrence of VRE for every ward and compared the models’ performance using a 30% test sample. The decision tree model produced a simple set of rules that can be used to determine the daily probability of VRE occurrence for each hospital ward. The decision tree model achieved an area under the curve of 0.685 and the random forest model 0.886 on the test set. These results confirm that the random forest model performs better than a single decision tree for all levels of model sensitivity and specificity at the cost of model simplicity. An early warning system for VRE can be developed and inform infection prevention plans and outbreak strategies further using these results. In summary, this thesis showed that data-driven statistical models can improve our understanding of antimicrobial resistance. It considers how different sources of spatiotemporal data may be used to predict its occurrence and spread of AMR in hospitals.

The classification model in machine learning has been employed to address different problems. Machine Learning classification is an effective method to realize customer churn prediction. This article provides a comparative study of machine learning from the perspective of predicting customer churn. Customer churn is one of the obstacles hindering the development of companies. Through classification approaches based on machine learning, customer churn can be predicted precisely, thus providing decision-making capabilities to these companies. Customer churn prediction is a typical classification problem and can be addressed by the use of a decision tree or random forest model. In this paper, decision tree and random forest models are employed to predict customer churn, using sales data provided by a chemical company from 2012 to 2020. We analyze the underlying risk of customer churn and the customer churn factors, including the low-priced count (LC), total amount of money (TM), and creation time (CT). The prediction results of the two models are evaluated by calculating various metrics. The experimental results indicate that the low-priced count (LC) is the most essential factor for customer churn. The results of the comparison, considering the training error and generalization error including: confusion matrix, ROC curve, AUC, precision, recall, and F1 score, reveal that the random forest model has better prediction accuracy than the decision tree model.

Landslide susceptibility zonation method based on C5.0 decision tree and K-means cluster algorithms to improve the efficiency of risk management