Time Complexity Research Articles

A REFINED CLASSIFICATION OF THE SUBSET SUM PROBLEM IN POLYNOMIAL TIME COMPLEXITY

The problem considered is the selection of at least one subset from a set (array) of distinct positive integers, such that the sum of the subset's elements exactly matches a given target sum (target certificate). According to R. M. Karp, this problem belongs to the class of NP-complete problems. Diophantine equations and an auxiliary problem, which facilitates the solution of the original problem and has independent scientific interest, have been introduced. A novel method has been developed, which includes proven lemmas and theorems. These results enable the development of efficient and straightforward algorithms for solving the subset sum problem. The time and space complexity for selecting the required subsets do not exceed the square of the length of the original set. An analytical framework has been proposed for managing indices within the original set. These algorithms are applicable to solving problems related to the independent set of cardinality k and the k-vertex cover problem. Additionally, we present examples to confirm claimed results. It should be noted that the time complexity of sorting an array of integers is proportional to the square of the array's size, and this problem belongs to class P. Therefore, based on the newly developed method, it can be inferred that the subset sum problem, originally classified as NP-complete within the NP class, also belongs to P.

Using Variable Data-Independent Acquisition for Capillary Electrophoresis-Based Untargeted Metabolomics.

Capillary electrophoresis coupled with tandem mass spectrometry (CE-MS/MS) offers advantages in peak capacity and sensitivity for metabolic profiling owing to the electroosmotic flow-based separation. However, the utilization of data-independent MS/MS acquisition (DIA) is restricted due to the absence of an optimal procedure for analytical chemistry and its related informatics framework. We assessed the mass spectral quality using two DIA techniques, namely, all-ion fragmentation (AIF) and variable DIA (vDIA), to isolate 60-800 Da precursor ions with respect to annotation rates. Our findings indicate that vDIA, coupled with the updated MS-DIAL chromatogram deconvolution algorithm, yields higher spectral matching scores and annotation rates compared to AIF. Additionally, we evaluated a linear migration time (MT) correction method using internal standards to accurately align chromatographic peaks in a data set. Postcorrection, the data set exhibited less than 0.1 min MT drifts, a difference mostly equivalent to that of conventional reverse-phase liquid chromatography techniques. Moreover, we conducted MT prediction for metabolites recorded in mass spectral libraries and metabolite structure databases containing a total of 469,870 compounds, achieving an accuracy of less than 1.5 min root mean squares. Our platform provides a peak annotation platform utilizing MT information, accurate precursor m/z, and the MS/MS spectrum recommended by the metabolomics standards initiative. Applying this procedure, we investigated metabolic alterations in lipopolysaccharide (LPS)-induced macrophages, characterizing 170 metabolites. Furthermore, we assigned metabolite information to unannotated peaks using an in silico structure elucidation tool, MS-FINDER. The results were integrated into the nodes in the molecular spectrum network based on the MS/MS similarity score. Consequently, we identified significantly altered metabolites in the LPS-administration group, where glycinamide ribonucleotide, not present in any spectral libraries, was newly characterized. Additionally, we retrieved metabolites of false-negative hits during the initial spectral annotation procedure. Overall, our study underscores the potential of CE-MS/MS with DIA and computational mass spectrometry techniques for metabolic profiling.

Enhancing robustness and time efficiency of random vector functional link with optimized affine parameters in activation functions and orthogonalization

Random Vector Functional Link (RVFL) is a widely used learning technique due to its less computational complexity, fast learning speed, and ease of implementation. However, generalization ability of RVFL is not good because its randomly generated parameters in the hidden layer makes input data distribution vulnerable to saturated regime of an activation function. For making data distribution evenly distributed within the hidden layer, this paper proposes a robust and efficient affine-transformation-based RVFL approach, termed as RT-ATRVFL, with optimized parameters. The proposed RT-ATRVFL, introduces sparse and shallow network in RVFL, that uses a subset of hidden layer structure, and obtains optimized and robust affine parameters for an activation function. This way it not only avoids saturated regime, but also learns the non-linearity more effectively and efficiently. This paper also investigates the different variants of the proposed approaches viz., RT-ATRVFL-ORTHO, RT-ATRVFL-CLOG, and RT-ATRVFL-CLOG-ORTHO using orthogonalization and cloglogm activation functions. For a thorough investigation of the proposed approaches, we conduct extensive experiments considering 28 benchmark classification datasets for a set of [60,2000] Monte Carlo runs. We show that our proposed approaches are more generalized and reliable, and outperform the affine-transformation-based extreme learning machine (ATELM) and its variants in terms of accuracy and computational time. Also, analysis of the results through well-accepted metrics such as Levene’s test, inter quartile range, mean absolute deviation and standard deviation confirms that proposed RT-ATRVFL and its other introduced variants are more robust than their respective counterparts. Results of two well-known statistical significance tests: Wilcoxon test and Friedman ranking, and the time complexity analysis also establishes the superiority of the proposed RT-ATRVFL approach and its other variants over their respective counterparts.

Sink location problems in dynamic flow grid networks

A dynamic flow network consists of a directed graph, where nodes called sources represent locations of evacuees, and nodes called sinks represent locations of evacuation facilities. Each source and each sink are given supply representing the number of evacuees and demand representing the maximum number of acceptable evacuees, respectively. Each edge is given capacity and transit time. Here, the capacity of an edge bounds the rate at which evacuees can enter the edge per unit time, and the transit time represents the time which evacuees take to travel across the edge. The evacuation completion time is the minimum time at which each evacuee can arrive at one of the evacuation facilities. Given a dynamic flow network without sinks, once sinks are located on some nodes or edges, the evacuation completion time for this sink location is determined. We then consider the problem of locating sinks to minimize the evacuation completion time, called the sink location problem. The problems have been given polynomial-time algorithms only for limited networks such as paths [1–3], cycles [1], and trees [4–6], but no polynomial-time algorithms are known for more complex network classes. In this paper, we prove that the 1-sink location problem can be solved in polynomial-time when an input network is a grid with uniform edge capacity and transit time.

Linear Time Train Contraction Minor Labeling for Railway Line Capacity Analysis

AbstractWhen no more than one train is feasibly contained in the separation headway times of two other trains, a triangular gap problem-based method is used to compute the consumed capacity in linear time. This is a strong condition limiting its applicability, while real-world operations often feature mixed traffic of various speeds, creating more complex structures beyond the characterization of a triangular gap. In this paper, we attempt to investigate the multi-train gap scenario and provide a general solution to the railway timetable structure and capacity analysis problem. Given a timetable, we use an incidence graph, the so-called train contraction minor, for representing the consecutive train operations and show that a longest path for spanning the compressed timetable is any path in a graph induced by some topological subsequence of trains that connects the predefined vertices in the train contraction minor. By vector-valued vertex labeling of this minor, we acquire an efficient algorithm that computes the consumed capacity of the timetable. Our algorithm runs in O(mn) time, where m and n are the number of trains and stations, respectively, and is free from the limitation and outperforms the near-linear time policy iteration implementation in the max-plus system of train operations. A toy example and a real-world case study demonstrate the effectiveness and computational performance of the proposed method. The proposed method based on train contraction minor contributes to the railway operations community by promoting the efficient computation of railway line capacity into linear time.

Series form solutions of time–space fractional Black–Scholes model via extended He-Aboodh algorithm

The objective of the current study is analyze linear and nonlinear time–space fractional Black–Scholes models via modified homotopy perturbation method (m-HPM). In current investigation, memory effects in financial markets are explored through fractional derivative in Caputo sense. The effectiveness of proposed methodology is checked numerically by finding residual errors and presented in tables. These tables also provide a benchmark for the comparison with already existing results in literature. Furthermore, solutions are graphically analyzed via 3D and contour plots across a range of parameters under varying market conditions. Analysis confirms the efficiency of m-HPM for predicting solutions of time–space fractional Black–Scholes models. The current study can contribute in understanding the applications of fractional calculus in finance, and can be a valuable computational tool for pricing financial derivatives in fractional environments.

Revolutionizing Public Health Surveillance: Computational Solution for Dengue Prediction

Dengue fever is a rapidly growing vector-borne viral illness that is posing a threat to an increasing number of areas worldwide. Numerous scientists have focused on various strategies to stop and limit the spread of illness. Additionally, the development of a variety of methods for ascertaining and predictive modeling through quantifiable, numerical analysis of machine learning (ML) is investigated. This research introduces a novel cubic-kernelized support vector machine with a bee optimizer (CSVM-BO) approach for dengue identification. The climate data is initially collected and preprocessed utilizing the decimal scale normalization method. In addition, we provide a feature extraction approach for linear discriminant analysis (LDA), which attempts to extract essential information for early identification and risk assessment. The findings demonstrate that the framework suggested in this research has considerable benefits in public health for dengue prediction and that our proposed CSVM-BO technique performs optimally in terms of latency (5 s), time complexity (0.62 s), and accuracy (98.57%). The problems identified by this thorough study offer a helpful foundation for epidemiology and public health research.

A Novel Method of Secured Data Distribution Using Sharding Zkp and Zero Trust Architecture in Blockchain Multi Cloud Environment

In the era of cloud computing, guaranteeing the safety and effectiveness of data management is of utmost importance. This investigation presents a novel approach that amalgamates the sharding concept, encryption, zero-knowledge proofs (zkp), and blockchain technology for secure data retrieval and data access control to improve data security, efficiency in cloud storage and migration. Further, we utilize user-specific digital wallets for secure encryption keys in order to encrypt the file before storing into the cloud. As Large files (greater than 50 MB) or Big data files (greater than 1 TB) require greater computational complexity, we leverage the sharding concept to enhance both space and time complexity in cloud storage. Hence, the large files are divided into shards and stored in different database servers. We also employ a blockchain smart contract to enhance secure retrieval of the file and also a secure access method, which ensures the privacy of the user. The zk-snark protocol is utilized to ensure the safe transfer of data between different cloud services. By utilizing this approach, data privacy is preserved, as only the proof of the data’s authenticity is shared with the verifier at the destination cloud, rather than the actual data themselves. The suggested method tackles important concerns related to data protection, privacy, and efficient resource utilization in cloud computing settings by ensuring it meets all the cloud policies required to store data. Since the environment maintains the privacy of the user data and the raw data of the user is not stored anywhere, the entire environment is set up as a Zero trust model.

On the Discovery/Creation of Transitional Time: Discussion of Steinbock

ABSTRACT Certain aspects of the temporal dimension in analysis are taken up in light of Steinbock’s illuminating exploration of a Winnicott case report. Following Steinbock’s portrayal of the interrelation of linear and non-linear time dimensions, some consideration is given to the many different kinds of time encountered in analysis, and to the function of the frame in creating a specifically analytic experience of time duration. The concept of Transitional time is proposed to describe this peculiarly analytic state of consciousness in which heterodox qualities of psychical experience can be woven together, and the multi-dimensionality of time itself is integrated into the experience of going-on-being.

A Unified Hardware Design for Multiplication, Division, and Square Roots Using Binary Logarithms

Multiplication, division, and square root operations introduce significant challenges in digital signal processing (DSP) systems, traditionally requiring multiple operations that increase execution time and hardware complexity. This study presents a novel approach that leverages binary logarithms to perform these operations using only addition, subtraction, and shifts, enabling a unified hardware implementation—a marked departure from conventional methods that handle these operations separately. The proposed design, involving logarithm and antilogarithm calculations, exhibits an algebraically symmetrical pattern that further optimizes the processing flow. Additionally, this study introduces innovative log-domain correction terms specifically designed to minimize computation errors—a critical improvement over existing methods that often struggle with precision. Compared to standard hardware implementations, the proposed design significantly reduces hardware resource utilization and power consumption while maintaining high operational frequency.

Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability

We show that feasibility of the $t^\text{th}$ level of the Lasserre semidefinite programming hierarchy for graph isomorphism can be expressed as a homomorphism indistinguishability relation. In other words, we define a class $\mathcal{L}_t$ of graphs such that graphs $G$ and $H$ are not distinguished by the $t^\text{th}$ level of the Lasserre hierarchy if and only if they admit the same number of homomorphisms from any graph in $\mathcal{L}_t$. By analysing the treewidth of graphs in $\mathcal{L}_t$, we prove that the $3t^\text{th}$ level of Sherali--Adams linear programming hierarchy is as strong as the $t^\text{th}$ level of Lasserre. Moreover, we show that this is best possible in the sense that $3t$ cannot be lowered to $3t-1$ for any $t$. The same result holds for the Lasserre hierarchy with non-negativity constraints, which we similarly characterise in terms of homomorphism indistinguishability over a family $\mathcal{L}_t^+$ of graphs. Additionally, we give characterisations of level-$t$ Lasserre with non-negativity constraints in terms of logical equivalence and via a graph colouring algorithm akin to the Weisfeiler--Leman algorithm. This provides a polynomial time algorithm for determining if two given graphs are distinguished by the $t^\text{th}$ level of the Lasserre hierarchy with non-negativity constraints.

High-order approximation of Caputo–Prabhakar derivative with applications to linear and nonlinear fractional diffusion models

Abstract In this study, we devise a high-order numerical scheme to approximate the Caputo–Prabhakar derivative of order α ∈ (0, 1), using an rth-order time stepping Lagrange interpolation polynomial, where 3 ≤ r ∈ N $3\le r\in \mathbb{N}$ . The devised scheme is a generalization of the existing schemes developed earlier. Further, we adopt the discussed scheme for solving a linear time fractional advection–diffusion equation and a nonlinear time fractional reaction–diffusion equation with Dirichlet type boundary conditions. We show that the discussed method is unconditionally stable, uniquely solvable and convergent with convergence order O(τ r+1−α , h 2), where τ and h are the temporal and spatial step sizes, respectively. Without loss of generality, applicability of the discussed method is established by illustrative examples for r = 4, 5.

Phonocardiogram Signal Analysis Based Premature Cardiac Influence Detection using Resnet50 CNN for Public Health Protection

Phonocardiogram (PCG) signal analysis plays a crucial role in the early detection of cardiac abnormalities, which is essential for public health protection. The premature disease prediction is tedious because the feature analysis takes place dimensionality problems which leads poor accuracy. The prevailing ensemble learning models’ methods doesn’t concentrate disease margin facts and properties during classification produce higher false rate because for adjusting feature margins gets lower accuracy. To resolve this problem, we propose a efficient Fuzzy c-means feature modality based Resnet50-RNN to detect premature cardiac influence detection for improving public health. The research proposes a method for premature cardiac influence detection using a ResNet50 Convolutional Neural Network (CNN) model for early prediction of heart disease. To address the issue of imbalanced data, Synthetic Minority Oversampling Technique (SMOTE) is employed for preprocessing. The Cardiac Disease Influence Rate (CDIR) is then used to identify the maximum deficiency-affected feature margins. Fuzzy c-means is utilized to select the mutual features associated with the heart disease influence rate. The ResNet50 CNN model is employed for classification, enabling the prediction of disease margins by risk category. The proposed system effectively identifies the disease based on the disease-affected scaling margin, leading to early disease impact prediction with higher accuracy, specificity, F1-measure, and lower false rates compared to other existing systems. The implementation also demonstrates reduced time complexity.

Efficient Intrusion Detection in Patient Health Records Based on LSTM-Based RNN

Advancements in Information and Communication Technology applications play an important role in the field of healthcare and bio-medical engineering. The process of image processing and analysis starts from receiving visual information to giving out the description of the scene for improving the visual appearance of the human viewer and extract the features of the data. Moreover, IDS can be deployed along with other security mechanisms as a line of defence to ensure security of system and network resources. There have been various efforts in designing IDS using Machine Learning (ML) techniques. Additionally, by developing a hybrid strategy for intrusion detection and classification and using feature engineering approaches to extract significant features for learning, among other things, efforts have been made to improve the classification performance of ML-based IDS. However, as networking technology have advanced, attack types have evolved as well. For this reason, an efficient and successful intrusion detection and classification system must be created. To address the issue and achieve good generalization ability for intrusion detection and classification, the paper presents empirical analysis of LSTM based RNN classifiers. The suggested methods' effectiveness is assessed using a range of performance metrics, such as recall, f-score, accuracy, precision, and False Positive Rate (FPR). The LSTM based RNN method recognize attacks with 99.2% accuracy with minimum time complexity (5 s).

Health Care Surveillance Using Machine Learning and Data Analytics

Any country's healthy population are a true asset. Both developed and developing nations are spending enormous sums of money to strengthen their "healthcare systems" and the required "health infrastructure." Globally, only few countries have a proactive approach to healthcare. The pandemic that has been going on recently has taught countries hard lessons about how important it is to have strong healthcare systems. The formulation of effective health policies and initiatives depends heavily on studies on Public Health Surveillance (PHS) and the conclusions that follow. This task has become clearer with the introduction of modern computing techniques and technology. Humanity has always been saved by technology when it is applied correctly. In this context, the most promising machine learning techniques are applied in this work. An empirical investigation of RBFN classifiers is presented in this paper. A variety of performance criteria, including recall, f-score, accuracy, precision, and False Positive Rate (FPR), are used to evaluate the efficacy of the recommended procedures. The RBFN approach has the highest accuracy and the least amount of time complexity in identifying health diseases.

Design of two-loop FOPID-FOPI controller for inverted cart-pendulum system

The inverted cart-pendulum system (ICPS) consists in having a pendulum mounted on a sliding cart, with the pivot point fixed. This real time experiment indeed looks like a rocket and its functionality is akin to a rocket. These are the launchers and the missile guidance and control as well as construction anti-seismic measures also. The control aim in these systems is to maintain the inverted pendulum vertically stable. The system is causal but unstable and, therefore, has no minimum phase. Therefore, the right half plane pole and zero are close to each other. Therefore, the stability of the system can be considered as problematic at some points. Unfortunately, linear time- invariant (LTI) classical controllers are incapable of offering suffient loop robustness for such systems. This paper aims to project a two-loop fractional order controller (2-LFOC) design to stabilize a higher-order nonlinear inverted cart-pendulum system (ICPS). The modeling, linearization, and control of ICPS are demonstrated in this work. The control target is adjusted so that the inverted pendulum stabilizes in its upright state when the cart reaches the required point. To fulfill the control objective, two-loop FOPID-FOPI controllers are proposed, and the Levenberg Marquardt algorithm (LMA) is utilized to tune the controllers. A novel nonlinear integral of time-associated absolute-error (ITAE) based fitness formula considering the settling time and rise time is used to fit the controller parameters for 2-LFOC. A performance comparison with the PID controller in terms of different time domain parameters such as rise_time (T R ), peak_time (T P ), settling_time (T S ), maximum overshoot (OS M ), maximum undershoot (US M ) and steady-state error (E SS ) are investigated. Stability analysis using Riemann surface observation of the system compensated with the proposed controller is presented in this work. The robust behavior of the two-loop FOPID-FOPI controller is verified by the application of disturbances in the system and the Reimann surface observation.

Effective Value Analysis of Fuzzy Similarity Relation in HQSS for Efficient Granulation.

Hierarchical quotient space structure (HQSS), as a typical description of granular computing (GrC), focuses on hierarchically granulating fuzzy data and mining hidden knowledge. The key step of constructing HQSS is to transform the fuzzy similarity relation into fuzzy equivalence relation. However, on one hand, the transformation process has high time complexity. On the other hand, it is difficult to mine knowledge directly from fuzzy similarity relation due to its information redundancy, i.e., sparsity of effective information. Therefore, this article mainly focuses on proposing an efficient granulation approach for constructing HQSS by quickly extracting the effective value of fuzzy similarity relation. First, the effective value and effective position of fuzzy similarity relation are defined according to whether they could be retained in fuzzy equivalence relation. Second, the number and composition of effective values are presented to confirm that which elements are effective values. Based on these above theories, redundant information and sparse effective information in fuzzy similarity relation could be completely distinguished. Next, both isomorphism and similarity between two fuzzy similarity relations are researched based on the effective value. The isomorphism between two fuzzy equivalence relations is discussed based on the effective value. Then, the algorithm with low time complexity for extracting effective values of fuzzy similarity relation is introduced. On the basis, the algorithm for constructing HQSS is presented to realize efficient granulation of fuzzy data. The proposed algorithms could accurately extract effective information from the fuzzy similarity relation and construct the same HQSS with the fuzzy equivalence relation while greatly reducing the time complexity. Finally, relevant experiments on 15 UCI datasets, 3 UKB datasets, and 5 image datasets are shown and analyzed to verify the effectiveness and efficiency of the proposed algorithm.

Low‐complexity algorithms for generating frequency hopping sequences with good aperiodic hamming correlation property

AbstractIn this letter, novel methods for quickly generating frequency hopping (FH) sequences with good out‐of‐phase peak aperiodic Hamming auto‐correlation (PAHAC) property are proposed. Compared with brute‐force search algorithm, the proposed algorithms have an obvious advantage on their time complexity. Results show that the algorithms can generate FH sequences with optimal/quasi‐optimal PAHAC performance in all tested cases.

FROM MONEY TRANSFERS TO MEAL TABLES: UNRAVELLING THE NEXUS OF REMITTANCES, FOOD SECURITY, AND ECONOMIC GROWTH IN TURKEY

The link between remittances, food security, and economic growth is a complex and important element of the economic development of the society. The study aims to explore the causality relationships between Remittances, Food Security and Economic Growth in the Turkish economy. The period of study from 1974 to 2018 and annual data of Remittances, Calories intake (as a proxy for the food security) and Economic Growth are used in the framework of time series. Techniques such as Zivot-Andrews (ZA) unit root, Toda-Yamamoto (TY), Breitung-Candelon (BCG), and Hatemi-J tests are used to detect the causality assessing the direction of it. The main findings consist of: (i) the presence of cointegration of rank two among series, the lack of linear TY time domain causality; (ii) the presence of BCG spectral causality from Calories intake to Growth only in medium period at 10% significance and, (iii) the presence of asymmetric causality from Remittances to Growth in positive changes, from Growth to Calories intake in negative changes and from Calories intake to Remittances in positive changes respectively at 1,5, and 1% significance. These results provide policymakers with valuable insights into the complexity nature of the relationship among remittances, food security, and economic growth, guiding them in designing effective strategies for poverty alleviation, sustainable development, and inclusive growth.

Efficiently bounding deadline miss probabilities of Markov chain real-time tasks

In real-time systems analysis, probabilistic models, particularly Markov chains, have proven effective for tasks with dependent executions. This paper improves upon an approach utilizing Gaussian emission distributions within a Markov task execution model that analyzes bounds on deadline miss probabilities for tasks in a reservation-based server. Our method distinctly addresses the issue of runtime complexity, prevalent in existing methods, by employing a state merging technique. This not only maintains computational efficiency but also retains the accuracy of the deadline-miss probability estimations to a significant degree. The efficacy of this approach is demonstrated through the timing behavior analysis of a Kalman filter controlling a Furuta pendulum, comparing the derived deadline miss probability bounds against various benchmarks, including real-time Linux server metrics. Our results confirm that the proposed method effectively upper-bounds the actual deadline miss probabilities, showcasing a significant improvement in computational efficiency without significantly sacrificing accuracy.