Time Complexity Research Articles

A finite difference method on uniform meshes for solving the time-space fractional advection-diffusion equation

In order to investigate linear time and spatial fractional advection equations, we present a finite difference scheme (FDS) in this paper. The fractional Taylor series method for u at tj+1 and xi+1 is used to approximate the fractional derivatives. First, we construct our numerical scheme (NS) for the mathematical model. In the second part, we study the stability and convergence of our numerical scheme. Finally, the numerical simulations of the fractional advection equation, using the FDM, is plotted for several values of fractional parameters α and ν. It will be shown that the convergence is achieved properly which confirms the effectiveness of the proposed algorithm.

A multi-threshold image segmentation method based on arithmetic optimization algorithm: A real case with skin cancer dermoscopic images

Abstract Multi-threshold image segmentation (MTIS) is a crucial technology in image processing, characterized by simplicity and efficiency, and the key lies in the selection of thresholds. However, the method's time complexity will grow exponentially with the number of thresholds. To solve this problem, an improved arithmetic optimization algorithm (ETAOA) is proposed in this paper, an optimizer for optimizing the process of merging appropriate thresholds. Specifically, two optimization strategies are introduced to optimize the optimal threshold process: elite evolutionary strategy (EES) and elite tracking strategy (ETS). First, to verify the optimization performance of ETAOA, mechanism comparison experiments, scalability tests, and comparison experiments with nine state-of-the-art peers are executed based on the benchmark functions of CEC2014 and CEC2022. After that, to demonstrate the feasibility of ETAOA in the segmentation domain, comparison experiments were performed using ten advanced segmentation methods based on skin cancer dermatoscopy image datasets under low and high thresholds, respectively. The above experimental results show that the proposed ETAOA performs outstanding optimization compared with benchmark functions. Moreover, the experimental results in the segmentation domain show that ETAOA has superior segmentation performance under low and high threshold conditions.

Consequence of War on Diabetic Mellitus patients in Tigray region, Ethiopia: a longitudinal study

BackgroundStudies of the world health organization indicated that Diabetes is on the rise. The occurrence of diabetes is steadily increasing everywhere, most markedly in the world’s middle and low-income countries. The aim of this study is to explore the consequence of war on the sugar level of diabetic mellitus patients.MethodsA retrospective longitudinal study with a sample of 67 diabetic mellitus patients was used. As a result, longitudinal different models, which are generalized linear mixed effects and nonlinear mixed effect models were fitted on the continuous response variable, the Sugar Level of the diabetic patients.ResultsThe results depicted that Blood Sugar Level of the patients increases over time. Moreover, as age, weight, medication, total cholesterol, high density lipoprotein (HDL), creatinine and linear time effect increase, Blood Sugar Level increases significantly, whereas triglyceride and low density lipoprotein increase, Blood Sugar Level of the adult Diabetes mellitus patients decreases.ConclusionThe war has significant effect on the poor control of blood glucose level of the adult diabetic patients in Tigray region, Ethiopia. Due to the war, siege or blockages, in return there were rare of medicine, the patients were not taking their medicines on time, and they did not get enough insulin as well.

Forecasting Potato Prices in Agra: Comparison of Linear Time Series Statistical vs. Neural Network Models

Forecasting Potato Prices in Agra: Comparison of Linear Time Series Statistical vs. Neural Network Models

A Polynomial-Time Algorithm for Detection of Uncovered Transitions in a Petri Net-Based Concurrent System

This paper introduces a novel algorithm for the efficient verification of a Petri net-based concurrent control system. The proposed method is based on the computation of transition invariant coverage to detect possible errors in the modelled system. Transition invariants play a crucial role in ensuring the correctness and reliability of such systems; however, existing methods often struggle with high computational demand, especially in the case of large and complex systems. The proposed approach addresses this challenge by performing a fast polynomial-time analysis to identify uncovered transitions, thereby streamlining the verification process. The effectiveness and efficiency of the proposed technique is verified experimentally with a set of 386 test modules (benchmarks) and compared against two well-known established methods: the classical method proposed by Martínez–Silva (as a reference algorithm) and PIPE (Platform Independent Petri Net Editor) tool. The results of the experiments confirm high performance of the presented algorithm, which was able to compute results for all the tested cases. In contrast, both the reference algorithm as well as the PIPE tool failed to deliver results for all examined models within one hour. The proposed algorithm is especially useful in early design stages, offering system designers timely insights into potential issues.

Evidence of quadratic time dependence of the kinetics in a continuous order-disorder transition

Evidence of quadratic time dependence of the kinetics in a continuous order-disorder transition

An Innovative Linear Wireless Sensor Network Reliability Evaluation Algorithm

In recent years, wireless sensor networks (WSNs) have become a crucial technology for infrastructure monitoring. To ensure the reliability of monitoring services, evaluating the network’s reliability is particularly important. Sensor nodes are distributed linearly when monitoring linear structures, such as railway bridges, forming what is known as a Linear Wireless Sensor Network (LWSN). Although existing evaluation methods, such as enumeration and Binary Decision Diagram (BDD)-based methods, can be used to assess the reliability of various types of networks, their efficiency is relatively low. Therefore, we classified network states based on the number of failed nodes located at the network’s ends and analyzed the arrangement characteristics of nodes under different network states. This paper proposed a new reliability assessment method for LWSNs. This method is based on the combinatorial patterns of nodes and uses the concept of integer partitions to calculate the total number of states at different performance levels, applying probability formulas to assess network reliability. Compared to Multi-Valued Decision Diagram (MDD)-based evaluation algorithms, this method is suitable for large-scale LWSNs and offers lower time complexity.

Fast Comparative Analysis of Merge Trees Using Locality Sensitive Hashing.

Scalar field comparison is a fundamental task in scientific visualization. In topological data analysis, we compare topological descriptors of scalar fields-such as persistence diagrams and merge trees-because they provide succinct and robust abstract representations. Several similarity measures for topological descriptors seem to be both asymptotically and practically efficient with polynomial time algorithms, but they do not scale well when handling large-scale, time-varying scientific data and ensembles. In this paper, we propose a new framework to facilitate the comparative analysis of merge trees, inspired by tools from locality sensitive hashing (LSH). LSH hashes similar objects into the same hash buckets with high probability. We propose two new similarity measures for merge trees that can be computed via LSH, using new extensions to Recursive MinHash and subpath signature, respectively. Our similarity measures are extremely efficient to compute and closely resemble the results of existing measures such as merge tree edit distance or geometric interleaving distance. Our experiments demonstrate the utility of our LSH framework in applications such as shape matching, clustering, key event detection, and ensemble summarization.

Complexity of Maker–Breaker games on edge sets of graphs

We study the algorithmic complexity of Maker–Breaker games played on the edge sets of general graphs. We mainly consider the perfect matching game and the H-game. Maker wins if she claims the edges of a perfect matching in the first, and a copy of a fixed graph H in the second. We prove that deciding who wins the perfect matching game and the H-game is PSPACE-complete, even for the latter in small-diameter graphs if H is a tree. Toward finding the smallest graph H for which the H-game is PSPACE-complete, we also prove that such an H of order 51 and size 57 exists.We then give several positive results for the H-game. As the H-game is already PSPACE-complete when H is a tree, we mainly consider the case where H belongs to a subclass of trees. In particular, we design two linear-time algorithms, both based on structural characterizations, to decide the winners of the P4-game in general graphs and the K1,ℓ-game in trees. Then, we prove that the K1,ℓ-game in any graph, and the H-game in trees are both FPT parameterized by the length of the game, notably adding to the short list of games with this property, which is of independent interest.Another natural direction to take is to consider the H-game when H is a cycle. While we were unable to resolve this case, we prove that the related arboricity-k game is polynomial-time solvable. In particular, when k=2, Maker wins this game if she claims the edges of any cycle.

Structural analysis of physical gel networks using graph neural networks

We employ graph neural networks (GNN) to analyse and classify physical gel networks obtained from Brownian dynamics simulations of particles with competing attractive and repulsive interactions. Conventionally such gels are characterized by their position in a state diagram spanned by the packing fraction and the strength of the attraction. Gel networks at different regions of such a state diagram are qualitatively different although structural differences are subtile while dynamical properties are more pronounced. However, using graph classification the GNN is capable of positioning complete or partial snapshots of such gel networks at the correct position in the state diagram based on purely structural input. Furthermore, we demonstrate that not only supervised learning but also unsupervised learning can be used successfully. Therefore, the small structural differences are sufficient to classify the gel networks. Even the trend of data from experiments with different salt concentrations is classified correctly if the GNN was only trained with simulation data. Finally, GNNs are used to compute backbones of gel networks. As the node features used in the GNN are computed in linear time O(N), the use of GNN significantly accelerates the computation of reduced networks on a particle level.Graphic abstract

Reliability of running gait variability measures calculated from inertial measurement units.

Changes to the variability within biomechanical signals may reflect a change in the health of the human system. However, for running gait variability measures calculated from wearable device data, it is unknown whether a between-day difference reflects a shift in system dynamics reflective of a change in human health or is a result of poor between-day reliability of the measurement device or the biomechanical signal. This study investigated the reliability of stride time and sacral acceleration variability measures calculated from inertial measurement units (IMUs). Nineteen runners completed six treadmill running trials on two occasions seven days apart. Stride time and sacral acceleration signals were obtained using IMUs. Stride time variability and complexity were calculated using the coefficient of variation (CV) and detrended fluctuation analysis (DFA), respectively. Sacral acceleration regularity was quantified using sample entropy with a range of input parameters m (vector length) and r (similarity threshold). Between-day reliability was assessed using the intraclass correlation coefficient (ICC), standard error of measurement (SEM) and minimum detectable change. Stride time CV displayed moderate relative reliability (ICC = 0.672), but with a large absolute minimum detectable change=0.525%, whilst stride time DFA-α displayed poor relative reliability (ICC = 0.457) and yielded large minimum detectable changes (≥ 0.208). Sample entropy displayed good relative reliability in mediolateral and resultant sacral acceleration signals for certain combinations of the parameters m and r, although again with large minimum detectable changes. Researchers should be cognisant of these reliability metrics when interpreting changes in running gait variability measures in clinical contexts.

Localized Evaluation for Constructing Discrete Vector Fields.

Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. We couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.

A LLM-driven and motif-informed linearizing graph transformer for Web API recommendation

The rapid growth in the number of Web APIs makes it difficult for developers to find the appropriate ones. To tackle this issue, researchers have created various powerful automatic approaches for recommendations. Recently, a range of graph neural networks, drawing inspiration from Transformers, have incorporated global attention to enhance recommendations. However, these approaches still have limitations in terms of processing information between nodes and utilizing other valid information, which reduces their effectiveness in large-scale Web API recommendations. To tackle these problems, this paper introduces a novel positional and semantic encoding method and motif-based linearizing graph Transformer for automatic Web API recommendation. We integrate the semantic information of the nodes into the positional information by using a fine-tuned large language model and graph attention mechanism. Furthermore, we leverage motif information to alter the computational sequence of the Vanilla Transformer, achieving linear time complexity. Experimental results on the two real-world datasets demonstrate the suitability of our model for Web API recommendation, surpassing existing state-of-the-art methods. In summary, our proposed technique exhibits promising results for Web API recommendation and underscores the potential of global attention in this field.

An efficient method for privacy protection in big data analytics using oppositional fruit fly algorithm

This work employs anonymization techniques to safeguard privacy. Data plays a vital role in corporate decision-making in the current information-centric landscape. Various sectors, like banking and healthcare, gather confidential information on a daily basis. This information is disseminated by multiple sources through numerous methods. Securing sensitive data is of paramount importance for any data mining application. This study safeguarded confidential information using an anonymization technique. Several machine learning methodologies have a deficiency in accuracy. The study seeks to generate superior and more precise results compared to alternative methodologies. For large datasets, numerous solutions exhibit increased time complexity and memory use. For huge datasets, numerous solutions require more time and memory. The enhanced fuzzy C-means (FCM) algorithm surpasses existing approaches in terms of both accuracy and information preservation. This study provides a comprehensive analysis of data anonymization utilizing the oppositional fruit fly approach, a technique that enhances privacy. The clustering method being presented utilizes an enhanced version of the FCM algorithm. The secrecy of the recommended oppositional fruit fly algorithm is effective. The comparison demonstrated that the proposed research enhanced both accuracy and privacy in comparison to two existing methods. The existing strategy outperforms data anonymization-based privacy preservation by 82.17%, while the suggested method surpasses it by 94.17%.

Detection and segmentation of meningioma tumors using improved cloud empowered visual geometry group (cloud-ivgg) deep learning structure

Detection and segmentation of meningioma brain tumor is a complex process due to its similar textural pattern with other tumors. In this paper Meningioma Tumor Detection System (MTDS) approach is proposed to detect and classify the meningioma brain images from the healthy brain images. The training work flow of the proposed MTDS approach consists of Spatial Gabor Transform (SGT), feature computations and deep learning structure. The features are computed from the meningioma brain image dataset images and the normal brain image dataset images and these features are fed into the classification architecture. In this paper, the proposed CLOUD-IVGG architecture is derived from the existing Cloud empowered Visual Geometry Group (VGG) architecture to improve the detection rate of the proposed system and to decrease the computational time complexity. The testing work flow of the proposed system is also consist of SGT, feature computation and the CLOUD-IVGG architecture to produce the classification result of the source brain images into either normal or meningioma. Further, the tumor regions in this meningioma image have been located using the Morphological segmentation algorithm. In this research work, two independent resource brain imaging datasets has been involved to estimate and validate the performance efficiency of the proposed MTDS. The datasets are Kaggle Brain Imaging (KBI) and BRATS Imaging 2020 (BI20). The performance efficiency has been analyzed with respect to detection rate, precision, recall and Jaccard index

Comparing Statistical and Machine Learning Methods for Time Series Forecasting in Data-Driven Logistics—A Simulation Study

Many planning and decision activities in logistics and supply chain management are based on forecasts of multiple time dependent factors. Therefore, the quality of planning depends on the quality of the forecasts. We compare different state-of-the-art forecasting methods in terms of forecasting performance. Differently from most existing research in logistics, we do not perform this in a case-dependent way but consider a broad set of simulated time series to give more general recommendations. We therefore simulate various linear and nonlinear time series that reflect different situations. Our simulation results showed that the machine learning methods, especially Random Forests, performed particularly well in complex scenarios, with the differentiated time series training significantly improving the robustness of the model. In addition, the time series approaches proved to be competitive in low noise scenarios.

Analysis of Facility Quality at “Kemit Forest Education” Tourism on Visitor Satisfaction

“Kemit Forest Education” Tourism Object in Cilacap Regency is famous for its selfie locations and recreational rides in the highlands, and has an educational element. In 2019, this destination entered the top 10 in Cilacap. However, many visitors complain about the facilities provided. This study aims to measure visitor satisfaction with existing facilities and provide suggestions for improvement. By using 7 Sapta Pesona and 4A variables, and using 100 respondents based on the calculation of the Sample Linear Time Function. This study uses the Customer Satisfaction Index (CSI) and Importance Performance Analysis (IPA) methods whose results are processed using IBM SPSS Statistic 22 software, the results show a satisfaction level (CSI) of 68% (satisfied category). The results of the IPA method show that the Cartesian quadrant analysis identifies 5 attributes in quadrant I (top priority) and 4 attributes in quadrant III (low priority) that need to be improved and maintained. This can be interpreted that visitors to “Kemit Forest Education” tours are satisfied with the facilities that have been provided but have not maximized the performance provided by “Kemit Forest Education” tours.

Toward a Generalizable Machine-Learned Potential for Metal-Organic Frameworks.

Machine-learned potentials (MLPs) have transformed the field of molecular simulations by scaling "quantum-accurate" potentials to linear time complexity. While they provide more accurate reproduction of physical properties as compared to empirical force fields, it is still computationally costly to generate their training data sets from ab initio calculations. Despite the emergence of foundational or general MLPs for organic molecules and dense materials, it is unexplored if one general MLP can be effectively developed for a wide variety of nanoporous metal-organic frameworks (MOFs) with different chemical moieties and geometric properties. Herein, by leveraging upon data-efficient equivariant MLPs, we demonstrate the possibility of developing a general MLP for nearly 3000 Zn-based MOFs. After curating a training data set comprising augmented MOF structures generated from density functional theory optimization, we validate the reliability of the general MLP in predicting accurate forces and energies when evaluated on a test set with chemically distinct MOF structures. Despite incurring slightly higher errors on structures containing rare chemical moieties, the general MLP can reliably reproduce physical (e.g., vibrational, thermodynamic, and mechanical) properties for a large sample of Zn-based MOFs. Crucially, by developing one MLP for many MOFs, the computational cost of high-throughput screening is potentially reduced by a few orders of magnitude. This enables us to predict quantum-accurate properties for notable Zn-MOFs that were previously uninvestigated via expensive theoretical calculations. To facilitate computational discovery among other families of complex chemical structures, we provide our data set and codes in the public Zenodo repository.

Advances in Cryptographic Algorithms: The Mathematics behind Secure Communication

This research discusses the mathematical aspects and evolution of cryptographic algorithms and underlines the importance of these principles for current digital communication protection. Cryptography uses algorithms from mathematical areas like modular arithmetic, finite field and elliptic curve to ensure that data being transferred is coded and decoded. Consequently, the contexts of symmetric algorithms such as AES or asymptotic systems like RSA and ECC are analyzed with reference to their mathematical components and usage. It also assesses the time complexity, security in general, and weak points of these algorithms using the backdrop of current and future risks such as those posed by quantum computing. Quantum technologies produce great difficulties for original cryptographic systems, which leads to the need to create quantum-secure ones. The project discusses selected post-quantum cryptographic techniques like lattice based, code based, and hash based cryptographic technique and evaluates if these can provide security in post-quantum world. Furthermore, the importance of cryptographic algorithm used in various sectors like business finance, healthcare units, blockchain technology, and other security-based sectors are discussed including how it has revolutionized the field of secured communication systems. Consequently, the results highlighted the role of mathematical creativity in enhancing cryptographic defense, repairing the flaws, and preparing for the subsequent technology change. In this light, this project enriches the comprehension of the dynamics of utilizing cryptography in securing digital systems from theoretical research to implementation.

Accelerating ETCD Insertion Operations through Advanced Complexity Reduction

Complexity is a critical aspect of distributed systems, and etcd is no exception. As a distributed key-value store, etcd's complexity arises from its need to balance consistency, availability, and partition tolerance. Etcd's architecture is designed to minimize complexity, with a simple and intuitive API. However, beneath the surface, etcd's implementation is complex, involving sophisticated algorithms and data structures. Etcd's use of a distributed consensus protocol, such as Raft, adds complexity to its design. Additionally, etcd's support for transactions, watches, and compaction introduces additional complexity. Despite this complexity, etcd's design is carefully optimized to ensure high performance and reliability. Etcd's complexity is also mitigated by its modular design, which allows developers to easily understand and modify individual components. Overall, etcd's complexity is a necessary consequence of its ambitious goals and requirements. By carefully managing complexity, etcd is able to provide a reliable and efficient distributed key-value store. Etcd's complexity is also influenced by its use of distributed locking and leader election protocols. Furthermore, etcd's support for multiple storage backends and network protocols adds additional complexity. The insertion operation in etcd using a T-tree involves finding the correct location for the new key-value pair and inserting it into the tree. The time complexity of this operation is O(log n), where n is the number of keys in the tree, because the T-tree is self-balancing and the height of the tree remains relatively constant. The deletion operation in etcd using a T-tree involves finding the key-value pair to be deleted and removing it from the tree. The time complexity of this operation is O(log n), where n is the number of keys in the tree, because the T-tree is self-balancing and the height of the tree remains relatively constant. We will work on to improve the performance of the operations by reducing the complexity with the usage of relevant data structure in T-Tree operations