Time Complexity Research Articles

Autoregressive modeling of self-threshold with practical application

Although linear time series models have wide applications for economic phenomena in general, they are not able to capture the behavior of many economic phenomena and applications, especially financial ones. As this type of series is characterized by modeling the kinetic state of the phenomena of asymmetry, structural changes, threshold, and others. Therefore, this shortcoming in linear modeling led to the emergence of non-linear models, which are models of various formats and not a model in one general format, as is the case in linear modeling. In order to overcome this shortcoming, most recent studies have adopted non-linear modeling, and (Tong, 1978) was one of the first who made a qualitative leap in the application of this type of models that depend on the analysis of the dynamics of financial and monetary time series and others, including autoregressive models of the self-threshold. (SETAR). This research aims to apply the (SETAR) model to a sample that represents the series of the percentage change in the shares of the Iraq Stock Exchange for the index (ISX60) for a group of companies, and then make an applied comparison of the methods of the mentioned model. Through the results of the applied side, it was found that the appropriate model for the research sample is the model SETAR (2;2,0) with the threshold (\gamma = 0.25). The model has outperformed SETAR (2;2,0) for having the lowest values ​​of the criteria (AIC, BIC, pooled-AIC, MAPE), and this model also outperformed the linear model AR (1).Research extracted from a master's thesis

Primal Logic of Information

Primal logic arose in access control; it has a remarkably efficient (linear time) decision procedure for its entailment problem. But primal logic is a general logic of information. In the realm of arbitrary items of information (infons), conjunction, disjunction, and implication may seem to correspond (set-theoretically) to union, intersection, and relative complementation. But, while infons are closed under union, they are not closed under intersection or relative complementation. It turns out that there is a systematic transformation of propositional intuitionistic calculi to the original (propositional) primal calculi; we call it Flatting. We extend Flatting to quantifier rules, obtaining arguably the right quantified primal logic, QPL. The QPL entailment problem is exponential-time complete, but it is polynomial-time complete in the case, of importance to applications (at least to access control), where the number of quantifiers is bounded.

Aircraft System Identification Using Multi-Stage PRBS Optimal Inputs and Maximum Likelihood Estimator

A new method to discover open-loop, unstable, longitudinal aerodynamic parameters, using a ‘two-stage optimization approach’ for designing optimal inputs, and with an application on the fighter aircraft platform, has been presented. System identification of supersonic aircraft requires formulating optimal inputs due to the extremely limited maneuver time, high angles of attack, restricted flight conditions, and the demand for an enhanced computational effect. A pre-requisite of the parametric model identification is to have a priori aerodynamic parameter estimates, which were acquired using linear regression and Least Squares (LS) estimation, based upon simulated time histories of outputs from heuristic inputs, using an F-16 Flight Dynamic Model (FDM). In the ‘first stage’, discrete-time pseudo-random binary signal (PRBS) inputs were optimized using a minimization algorithm, in accordance with aircraft spectral features and aerodynamic constraints. In the ‘second stage’, an innovative concept of integrating the Fisher Informative Matrix with cost function based upon D-optimality criteria and Crest Factor has been utilized to further optimize the PRBS parameters, such as its frequency, amplitude, order, and periodicity. This unique optimum design also solves the problem of non-convexity, model over-parameterization, and misspecification; these are usually caused by the use of traditional heuristic (doublets and multistep) optimal inputs. After completing the optimal input framework, parameter estimation was performed using Maximum Likelihood Estimation. A performance comparison of four different PRBS inputs was made as part of our investigations. The model performance was validated by using statistical metrics, namely the following: residual analysis, standard errors, t statistics, fit error, and coefficient of determination (R2). Results have shown promising model predictions, with an accuracy of more than 95%, by using a Single Sequence Band-limited PRBS optimum input. This research concludes that, for the identification of the decoupled longitudinal Linear Time Invariant (LTI) aerodynamic model of supersonic aircraft, optimum PRBS shows better results than the traditional frequency sweeps, such as multi-sine, doublets, square waves, and impulse inputs. This work also provides the ability to corroborate control and stability derivatives obtained from Computational Fluid Dynamics (CFD) and wind tunnel testing. This further refines control law design, dynamic analysis, flying qualities assessments, accident investigations, and the subsequent design of an effective ground-based training simulator.

Some efficient schemes of variational iteration method for handling Schrödinger equations in quantum mechanics

At the atomic level, one of the fundamental differential equations that describe the universe and everyday life is the Schrödinger equation in quantum mechanics. Solutions of Schrödinger equations have attracted the attention of researchers. In this study, the variational iteration method is used to handle three dimensional linear and nonlinear time dependent Schrödinger equations. Different iteration formulas have been constructed with the Lagrange multipliers. The accuracy of the approximate solutions obtained by using different iteration formulas of the variational iteration method is given with numerical examples. Comparisons of approximate solutions and exact solutions are shown with graphs. In addition, absolute error tables are included for these comparison results. As a result, it is seen that the variational iteration method gives approximations that converge to the exact solution more rapidly thanks to different iteration formulas.

Visual impairment prevention by early detection of diabetic retinopathy based on stacked auto-encoder

Diabetic retinopathy (DR) presents a significant concern among diabetic patients, often leading to vision impairment or blindness if left untreated. Traditional diagnosis methods are prone to human error, necessitating accurate alternatives. While various computer-aided systems have been developed to assist in DR detection, there remains a need for accurate and efficient methods to classify its stages. In this study, we propose a novel approach utilizing enhanced stacked auto-encoders for the detection and classification of DR stages. The classification is performed across one healthy (normal) stage and four DR stages: mild, moderate, severe, and proliferative. Unlike traditional CNN approaches, our method offers improved reliability by reducing time complexity, minimizing errors, and enhancing noise reduction. Leveraging a comprehensive dataset from KAGGLE containing 35,126 retinal fundus images representing one healthy (normal) stage and four DR stages, our proposed model demonstrates superior accuracy compared to existing deep learning algorithms. Data augmentation techniques address class imbalance, while SAEs facilitate accurate classification through layer-wise unsupervised pre-training and supervised fine-tuning. We evaluate our model’s performance using rigorous quantitative measures, including accuracy, recall, precision, and F1-score, highlighting its effectiveness in early disease diagnosis and prevention of blindness. Experimental results across different training/testing ratios (50:50, 60:40, 70:30, and 75:25) showcase the model’s robustness. The highest accuracy achieved during training was 93%, while testing accuracy reached 88% on a training/testing ratio of 75:25. Comparative analysis underscores the model’s superiority over existing methods, positioning it as a promising tool for early-stage DR detection and blindness prevention.

Between Inevitability and Hindsight: End-Times and the Loss of Agency in the Anthropocene

Judeo-Christian eschatological time has re-emerged in scholarly and popular discussions of climate apocalypse in the last decades, also in attempts to mobilise action against climate change. I argue that speaking about climate change as the eschatological endpoint in linear time undermines the call for action, understood as the contingent capacity for new beginnings. When the severity of climate change is made sense of by introducing an end to linear Chronos time, the result is a confusion in the direction and contingency of temporal politics, which effectively undermines action through speech. Eschatological, linear time frames the time for action as too narrow: first, by casting the end of time as inevitable, and second, by upsetting the chronology and direction of time as a prerequisite for politics. The conclusion is that climate eschatology is disempowering in Chronos time and that another temporal frame is needed to address climate change politically.

Efficient IP address retrieval using a novel octet based encoding technique for high speed lookup to improve network performance

As the Internet becomes increasingly popular, the number of users connected to it grows significantly. Consequently, the packet processing speed of network systems, such as routers, must be enhanced. IP lookup is a critical task used to find the next hop address by searching for the longest prefix match in the forwarding information base (FIB). The binary trie is one of the most popular software-based approaches for IP lookup. Prefix compression techniques can improve both the time and space complexity of IP lookups, thereby enhancing overall system performance. This paper proposes an efficient deterministic approach to encoding IP prefixes that reduces storage complexity. The proposed technique generates a unique index for each prefix using an encoder, enabling searches to be performed in constant time. Experimental results show that the proposed method improves lookup time by 73%, 65%, and 66% compared to the existing binary trie, path-compressed trie, and multibit trie, respectively. Additionally, it achieves approximately 63% memory savings over these existing techniques.

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.

Ridge Regressive Quadratic Multivalued Feature Matching Pursuit for Skill-based Employability Identification in Higher Education

Skill-based employability identification involves evaluating students' skills and determining their suitability for a specific job or industry. Data mining techniques have been developed for predicting student employability based on certain skills. Skills identification is a crucial step for students in understanding employability. However, accurate and time-efficient prediction of student employability has become a pivotal focus for educational institutions. This paper introduces a novel approach using data mining techniques called Ridge Regressive Quadratic Multivalued Projection Matching Pursuit (RRQMPMP) to identify skill-based employability for students in higher education with better accuracy and minimum time consumption. The proposed RRQMPMP technique includes two major processes namely preprocessing and feature selection. First, the number of features and student data are collected from the dataset. Then the preprocessing steps are executed, including three processes namely missing data handling, duplicate data removal, and normalization to clean the input dataset. The Ridge regressive imputation method is employed to handle missing data in the dataset. Subsequently, duplicate and non-duplicate data points are distinguished from the dataset using a simple matching distance measure. Finally, quadratic mean feature scaling is developed for the normalization process. With the preprocessed dataset, the feature selection step is performed by applying a Russell-Rao index multivalued projection matching pursuit. Based on the Russell-Rao similarity index value, pertinent and impertinent features are identified. Finally, pertinent features are selected for skill-based student employability prediction to achieve higher accuracy and minimize time consumption as well as space complexity. An experimental evaluation is carried out with respect to accuracy, error rate, time complexity, and space complexity for different numbers of student data. The quantitatively analyzed results indicate that the performance of the proposed RRQMPMP technique increases the accuracy of skill-based student employability prediction with minimum time and space complexity compared to conventional methods.

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

Models of Anomalous Diffusion and its analysis

The anomalous diffusion is characterized by deviation from Gaussian statistics and the absence of a linear time dependency in the mean square displacement. This study investigates anomalous diffusion processes that exhibit a power-law growth in mean square displacement as time progresses. The first stage is to create the model using random methods, that is, by using random walks. The following statement describes a continuous-time random walk model represented by a series of convolution-type integral equations depicting probability density functions. Fractional differential equations for time and space are derived from the master equations by choosing probability density functions with infinite first and/or second moments. The obtained model equations are analyzed with respect to elementary boundary value problems in constrained fields. The main focus is on studying elementary boundary value problems related to the generalized fractional time diffusion equation, especially using the fractional Caputo derivative. This equation applies a well-established maximum principle to stochastic partial differential equations of the elliptic and parabolic type (SPDEs). This concept is used to make preliminary estimates of the answer before using it to prove the uniqueness of the solution. To prove the existence of a solution, a clearly defined generalized solution is first generated using the spectroscopic method. Under certain additional circumstances, a comprehensive solution may be considered a solution in the traditional sense.

Fast simulation of identity-by-descent segments.

The worst-case runtime complexity to simulate haplotype segments identical by descent (IBD) is quadratic in sample size. We propose two main techniques to reduce the compute time, both of which are motivated by coalescent and recombination processes. We provide mathematical results that explain why our algorithm should outperform a naive implementation with high probability. In our experiments, we observe average compute times to simulate detectable IBD segments around a locus that scale approximately linearly in sample size and take a couple of seconds for sample sizes that are less than ten thousand diploid individuals. In contrast, we find that existing methods to simulate IBD segments take minutes to hours for sample sizes exceeding a few thousand diploid individuals. When using IBD segments to study recent positive selection around a locus, our efficient simulation algorithm makes feasible statistical inferences, e.g., parametric bootstrapping in analyses of large biobanks, that would be otherwise intractable.

Comparison of Some Optimizers in Long Short-Term Memory Networks with an Application to Tigris River Water Imports

The Long Short-Term Memory (LSTM) RNN architecture was developed to overcome the limitations of traditional RNNs in recognizing long-term dependencies in sequential input. LSTM networks and other neural network topologies rely heavily on optimizers for training. Every iteration of a gradient-based algorithm attempts to approach the minimizer/maximizer cost function by using the gradient's objective function information. Moreover, a comparative analysis of a number of optimizers is presented in this work, including FTRL, Nadam, Adagrad, Adadelta, SGD, RMSprop, and Adagrad. By directly affecting the objective function's convergence, the study emphasizes the crucial role optimizers play in improving gradient descent efficiency. This work fills a gap in the literature on choosing the best optimizers for time-series data by concentrating on water import statistics for the Tigris River. The results offer insightful information about how to choose optimizers wisely to reduce time complexity and increase accuracy. The results of the study show that these optimizers' performance is generally comparable when compared using the root mean square error (RMSE) criterion based on water data. However, Nadam produces RMSE values at 500 epochs that are lower than those of the other methods.

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.