Time Complexity Research Articles

Robust Incremental Broad Learning System for Data Streams of Uncertain Scale.

Due to its marvelous performance and remarkable scalability, a broad learning system (BLS) has aroused a wide range of attention. However, its incremental learning suffers from low accuracy and long training time, especially when dealing with unstable data streams, making it difficult to apply in real-world scenarios. To overcome these issues and enrich its relevant research, a robust incremental BLS (RI-BLS) is proposed. In this method, the proposed weight update strategy introduces two memory matrices to store the learned information, thus the computational procedure of ridge regression is decomposed, resulting in precomputed ridge regression. During incremental learning, RI-BLS updates two memory matrices and renews weights via precomputed ridge regression efficiently. In addition, this update strategy is theoretically analyzed in error, time complexity, and space complexity compared with existing incremental BLSs. Different from Greville's method used in the original incremental BLS, its results are closer to the solution of one-shot calculation. Compared with the existing incremental BLSs, the proposed method exhibits more stable time complexity and superior space complexity. The experiments prove that RI-BLS outperforms other incremental BLSs when handling both stable and unstable data streams. Furthermore, experiments demonstrate that the proposed weight update strategy applies to other random neural networks as well.

Coordinate-Free and Low-Order Scaling Machine Learning Model for Atomic Partial Charge Prediction for Any Size of Molecules.

The atomic partial charge is of great importance in many fields, such as chemistry and drug-target recognition. However, conventional quantum-based computing of atomic charges is relatively slow, limiting further applications of atomic charge analysis. With the help of machine learning methods, various kinds of models appear to speed up atomic charge calculations. However, there are still some concerning problems. Some models based on geometric coordinates require high-accuracy geometry optimization as a preprocess, while other models have a limitation on the size of input molecules that narrow the applications of the model. Here, we propose a machine learning atomic charge model based on a message-passing featurizer. This preprocessing featurizer can quickly extract atomic environment information from a molecule according to the connectivity inside the molecule. The resulting descriptor can be used with a neural network to quickly predict the atomic partial charge. The model is able to automatically adapt to any size of molecule while remaining efficient and achieves a root-mean-square error in the Hirshfeld charge prediction of 0.018e, with an overall time complexity of O(n2). Thus, this model could enlarge the range of applications of atomic partial charge to more fields and cases.

Enforcing Temporal Consistency in Migration History Inference.

In addition to undergoing evolution, members of biological populations may also migrate between locations. Examples include the spread of tumor cells from the primary tumor to distant metastases or the spread of pathogens from one host to another. One may represent migration histories by assigning a location label to each vertex of a given phylogenetic tree such that an edge connecting vertices with distinct locations represents a migration. Some biological populations undergo comigration, a phenomenon where multiple taxa from distinct lineages simultaneously comigrate from one location to another. In this work, we show that a previous problem statement for inferring migration histories that are parsimonious in terms of migrations and comigrations may lead to temporally inconsistent solutions. To remedy this deficiency, we introduce precise definitions of temporal consistency of comigrations in a phylogenetic tree, leading to three successive problems. First, we formulate the temporally consistent comigration problem to check if a set of comigrations is temporally consistent and provide a linear time algorithm for solving this problem. Second, we formulate the parsimonious consistent comigrations (PCC) problem, which aims to find comigrations given a location labeling of a phylogenetic tree. We show that PCC is NP-hard. Third, we formulate the parsimonious consistent comigration history (PCCH) problem, which infers the migration history given a phylogenetic tree and locations of its extant vertices only. We show that PCCH is NP-hard as well. On the positive side, we propose integer linear programming models to solve the PCC and PCCH problems. We demonstrate our algorithms on simulated and real data.

Association of plasma biomarkers of Alzheimer's disease and related disorders with cognition and cognitive decline: The MYHAT population-based study.

Plasma biomarkers of Alzheimer's disease and related dementias predict global cognitive performance and decline over time; it remains unclear how they associate with changes in different dementia syndromes affecting distinct cognitive domains. In a prospective study with repeated assessments of a randomly selected population-based cohort (n=787, median age 73), we evaluated performance and decline in different cognitive domains over up to 8 years in relation to plasma concentrations of amyloid beta 42/40 (Aβ42/40) ratio, phosphorylated tau181 (p-tau181), neurofilament light chain (NfL), and glial fibrillary acidic protein (GFAP). Cross-sectionally, memory showed the strongest associations with p-tau181, and attention, executive, and visuospatial functions with NfL.Longitudinally, memory decline was distinguishable with all biomarker profiles dichotomized according to data-driven cutoffs, most efficiently with Aβ42/40. GFAP and Aβ42/40 were the best discriminators of decline patterns in language and visuospatial functions, respectively. These relatively non-invasive tests may be beneficial for clinical screening after replication in other populations and validation through neuroimaging or cerebrospinal fluid analysis. We performed a prospective study with up to 8 years of repeated domain-specific cognitive assessments and baseline plasma Alzheimer's disease and related dementias biomarker measurements in a randomly selected population-based cohort. We considered distinct growth curves of trajectories of different cognitive domains and survival bias induced by missing data by adding quadratic time and applying joint modeling technique. Cross-sectionally, memory showed the strongest associations with plasma phosphorylated tau181, while attention, executive, and visuospatial functions were most strongly associated with neurofilament light chain. Longitudinally, memory and visuospatial declines were most efficiently distinguished by dichotomized amyloid beta 42/40 profile among all plasma biomarkers, while language was by dichotomized glial fibrillary acidic protein. These relatively non-invasive tests may be beneficial for clinical screening; however, they will need replication in other populations and validation through neuroimaging and/or cerebrospinal fluid assessments.

Shaping the time to be a good teacher: a case study on teacher excellence and time ownership in a British transnational university

ABSTRACT This study is about a lecturer protecting herself and her teaching from the university’s increasing demands on her personal and timeless time. The British university is shaped by a fundamental arrhythmia: the co-existence of digital time, that academics are encouraged to embrace working from anywhere at any time; and analogical time, the linear time of classes, deadlines, and required administrative tasks. Pressured by these competing demands on their time and responsibilities, research and surveys show that academics feel alienated as university time arrhythmia ‘devours’ both their thinking and personal time and can compromise their wellbeing. This case study aims at uncovering the connection between the lecturer’s practices of teaching excellence, her administrative work and university time. Qualitative content analysis of semi-structured interviews illustrates how university time and teaching excellence are related, and university arrhythmia can actually be used to protect good teaching. This lecturer skilfully managed university time-devouring arrhythmia: when the university used an analogical logic of time, she used digital time, and vice versa. By doing this, she protected her personal and timeless time as well as her own teaching from mounting demands of teacher excellence, measured by the university’s simultaneous and conflicting digital and analogical logics of time.

Stability Analysis via Impedance Modelling of a Real-World Wind Generation System with AC Collector and LCC-Based HVDC Transmission Grid

This paper studies the stability of a real-world wind farm, Bison Wind Generation System (BWGS) in the state of North Dakota in the United States. BWGS uses an AC collector grid rated at 34.5 kV and a symmetrical bipolar high-voltage DC (HVDC) transmission grid rated at ±250 kV. The HVDC line transfers a total power of 0.5 GW, while both the HVDC rectifier and inverter substations use line-commuted converters (LCCs). The LCC-based rectifier adopts constant DC current control to regulate HVDC current, while the inverter operates in constant extinction angle control mode to maintain a fixed HVDC voltage. This paper proposes a frequency scan-based approach to obtain the d–q impedance model of (i) BWGS AC collector grids with Type 4 wind turbines that use permanent magnet synchronous generators (PMSGs) and two fully rated converters, and (ii) an LCC-HVDC system. The impedance frequency response of the BWGS is acquired by exciting the AC collector grid and LCC-HVDC with multi-sine voltage perturbations during its steady-state operation. The resulting voltage and current signals are subjected to a fast Fourier transform (FFT) to extract frequency components. By analyzing the impedance frequency response measurement of BWGS, a linear time–invariant (LTI) representation of its dynamics is obtained using the vector fitting (VF) technique. Finally, a Bode plot is applied, considering the impedance of the BWGS and grid to perform stability analyses. This study examines the influence of the short circuit ratio (SCR) of the grid and the phase lock loop (PLL) frequency bandwidth on the stability of the overall system. The findings provide valuable insights for the design and verification of an AC collector and LCC-based HVDC transmission systems. The findings suggest that the extraction of the impedance model of a real-world wind farm, achieved through frequency scanning and subsequent representation as an LTI system using VF, is regarded as a robust, suitable, and accurate methodology for investigating the dynamics, unstable operating conditions, and control interaction of the wind farm and LCC-HVDC system with the AC grid.

Unveiling the Neutral Difference and Its Automated Search

Given a differential characteristic and an existing plaintext pair that satisfies it (referred to as a right pair), generating additional right pairs at a reduced cost is an appealing prospect. The neutral bit technique, referred to as neutral differences throughout this paper, provides a solution to this challenge. Traditionally, the search for neutral differences has heavily depended on experimental testing, leading to limitations in the search range. In this work, we propose the neutral difference table and establish a link between boomerang cryptanalysis and neutral differences. Furthermore, we propose an automated search for neutral differences to address the problem of a limited search range of neutral differences, as previous approaches relied on experimental testing. This approach provides a basis for the subspace spanned by the neutral differences, and we apply this technique to both SPECK32 and LEA, where the predicted results closely match the experimental ones. Consequently, we present the improved differential-linear distinguishers for SPECK32 and LEA, along with the 18-round attacks on LEA192 and LEA256 with the lowest time complexity up to date.

Neighborhood based computational approaches for the prediction of lncRNA-disease associations

MotivationLong non-coding RNAs (lncRNAs) are a class of molecules involved in important biological processes. Extensive efforts have been provided to get deeper understanding of disease mechanisms at the lncRNA level, guiding towards the detection of biomarkers for disease diagnosis, treatment, prognosis and prevention. Unfortunately, due to costs and time complexity, the number of possible disease-related lncRNAs verified by traditional biological experiments is very limited. Computational approaches for the prediction of disease-lncRNA associations allow to identify the most promising candidates to be verified in laboratory, reducing costs and time consuming.ResultsWe propose novel approaches for the prediction of lncRNA-disease associations, all sharing the idea of exploring associations among lncRNAs, other intermediate molecules (e.g., miRNAs) and diseases, suitably represented by tripartite graphs. Indeed, while only a few lncRNA-disease associations are still known, plenty of interactions between lncRNAs and other molecules, as well as associations of the latters with diseases, are available. A first approach presented here, NGH, relies on neighborhood analysis performed on a tripartite graph, built upon lncRNAs, miRNAs and diseases. A second approach (CF) relies on collaborative filtering; a third approach (NGH-CF) is obtained boosting NGH by collaborative filtering. The proposed approaches have been validated on both synthetic and real data, and compared against other methods from the literature. It results that neighborhood analysis allows to outperform competitors, and when it is combined with collaborative filtering the prediction accuracy further improves, scoring a value of AUC equal to 0966.AvailabilitySource code and sample datasets are available at: https://github.com/marybonomo/LDAsPredictionApproaches.git

Do Implicit Learning Deficit and Dyslexia Go Together? An fMRI and Behavioral Study

AbstractWhat is the relationship between literacy skills and implicit learning? To address previous mixed findings, we compared school‐aged readers, typical (CON, n = 54) and with dyslexia (DYS, n = 53), in relation to their performance on a serial reaction time task. For the first time, we also included an isolated spelling deficit group (ISD, n = 30) to control for distinctive effects of reading and spelling deficits. A linear reaction times analysis did not reveal between‐group differences in implicit learning. However, further examination revealed that most CON (65%) and ISD (63%) were implicit learners, whereas most DYS were nonlearners (64%). Brain activity showed differences in early learning phases: CON learners and DYS nonlearners activated the left inferior frontal gyrus (IFG) and left insula more than other groups. Our findings imply that implicit learning is more frequently disrupted in children with dyslexia than in typical readers, and that activation of the left IFG and insula contributes to effective learning in the latter group but it does not in the former.

ОЦІНКА ОБЧИСЛЮВАЛЬНОЇ СКЛАДНОСТІ ГЕНЕТИЧНОГО АЛГОРИТМУ

The article is devoted to the estimation of computational complexity of a genetic algorithm as one of the key tools for solving optimisation problems. The theoretical aspects of computational complexity of algorithms and the interrelation of elements of a genetic algorithm are considered. The main types of computational complexity of algorithms are described: time, simple and asymptotic. Five basic rules for calculating the asymptotic complexity are given. A mathematical apparatus for estimating the asymptotic complexity of a genetic algorithm is presented, which takes into account the costs of forming the initial population and performing evolution. Evolution occurs through iterations, during which generations of individuals are subjected to certain operations in order to find an optimal solution (crossing, mutation, chromosome decoding, etc.). GA, as a global search algorithm, is considered to find the optimal path without getting stuck in local minima. To assess the computational complexity of GA, we consider solving the traveling salesman problem (TSP) for 28 cities of Ukraine using a modified TSPLIB library and the DEAP platform created in the Python programming language. A block diagram of the GA is presented, the main elements of which are the tournament selection operator, the ordered crossover operator, and the inversion mutation operator. The influence of the population size and the number of generations on the asymptotic complexity of the genetic algorithm in solving the TSP problem is studied. The study considered changing the size of the GA population from 50 to 500 with a step of 50, while for each such value four sets of the number of generations were modelled: from 50 to 200 with a step of 50. Based on the obtained results, we show a linear dependence of the GA execution time on the size of the considered input data. It is shown that the smallest time complexity of the presented GA for the given TSP problem is 0.33848 seconds with a population size of 50 and a similar number of generations, while the largest value is 3.752734 seconds with a population size of 500 and a number of generations of 200. The obtained results can be used to optimise the performance of a GA in the TSP problem.

H-mrk-means: Enhanced Heuristic mrk-means for Linear Time Clustering of Big Data Using Hybrid Meta-heuristic Algorithm

Big data is generally derived with a large volume and combined categories of attributes like categorical and numerical. Among them, [Formula: see text]-prototypes have been adopted into MapReduce structure, and thus, it provides a better solution for the huge range of data. However, [Formula: see text]-prototypes need to compute all distances among every data point and cluster centres. Moreover, the computations of distances are redundant as data points are often present in similar clusters after fewer iterations. Nowadays, to cluster huge-scale datasets, one of the efficient solutions is [Formula: see text]-means. However, [Formula: see text]-means is not intrinsically appropriate to execute in MapReduce due to the iterative nature of this technique. Moreover, for every iteration, [Formula: see text]-means should perform an independent MapReduce job but, it leads to higher Input/Output (I/O) overhead at every iteration. This research paper presents a novel enhanced linear time clustering for handling big data called Heuristic mrk-means (H-mrk-means) using optimized [Formula: see text]-means on the MapReduce model. In order to manage big data that is time series in nature, the sampling and MapReduce framework are adopted, which utilize different machines for processing data. Before initiating the main clustering process, a sampling process is adopted to get the noteworthy information. The two main phases of the developed method are the map phase (divide and conquer) and the reduce phase (final clustering). In the map phase, the data are divided into diverse chunks that should be stored in assigned machines. In the reduce phase, data clustering is performed. Here, the cluster centroid of data is tuned with the help of hybrid Tunicate-Deer Hunting Optimization (T-DHO) algorithm by attaining a newly derived objective function. This type of optimal tuning of solution enhances the efficiency of clustering when compared over normal iterative [Formula: see text]-means and mrk-means clustering. The experimental evaluation on varied counts of chunks using the proposed H-mrk-means has attained higher quality of clustering results and faster execution times evaluated with other clustering approaches.

Enhancing Field Multiplication in IoT Nodes with Limited Resources: A Low-Complexity Systolic Array Solution

Enhancing Field Multiplication in IoT Nodes with Limited Resources: A Low-Complexity Systolic Array Solution

Conjunctive Queries with Negation and Aggregation: A Linear Time Characterization

In this paper, we study the complexity of evaluating Conjunctive Queries with negation (\cqneg). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called free-connex signed-acyclic queries. We show that no other queries admit such an algorithm subject to lower-bound conjectures. Second, we extend our algorithm to Conjunctive Queries with negation and aggregation over a general semiring, which we call Functional Aggregate Queries with negation (\faqneg). Such an algorithm achieves constant delay enumeration for the same class of queries but with a slightly increased preprocessing time, which includes an inverse Ackermann function. We show that this surprising appearance of the Ackermmann function is probably unavoidable for general semirings but can be removed when the semiring has a specific structure. Finally, we show an application of our results to computing the difference of CQs.

Dynamic modes of Notch transcription hubs conferring memory and stochastic activation revealed by live imaging the co-activator Mastermind.

Developmental programming involves the accurate conversion of signalling levels and dynamics to transcriptional outputs. The transcriptional relay in the Notch pathway relies on nuclear complexes containing the co-activator Mastermind (Mam). By tracking these complexes in real time, we reveal that they promote the formation of a dynamic transcription hub in Notch ON nuclei which concentrates key factors including the Mediator CDK module. The composition of the hub is labile and persists after Notch withdrawal conferring a memory that enables rapid reformation. Surprisingly, only a third of Notch ON hubs progress to a state with nascent transcription, which correlates with polymerase II and core Mediator recruitment. This probability is increased by a second signal. The discovery that target-gene transcription is probabilistic has far-reaching implications because it implies that stochastic differences in Notch pathway output can arise downstream of receptor activation.

Dynamic modes of Notch transcription hubs conferring memory and stochastic activation revealed by live imaging the co-activator Mastermind

Developmental programming involves the accurate conversion of signalling levels and dynamics to transcriptional outputs. The transcriptional relay in the Notch pathway relies on nuclear complexes containing the co-activator Mastermind (Mam). By tracking these complexes in real time, we reveal that they promote the formation of a dynamic transcription hub in Notch ON nuclei which concentrates key factors including the Mediator CDK module. The composition of the hub is labile and persists after Notch withdrawal conferring a memory that enables rapid reformation. Surprisingly, only a third of Notch ON hubs progress to a state with nascent transcription, which correlates with polymerase II and core Mediator recruitment. This probability is increased by a second signal. The discovery that target-gene transcription is probabilistic has far-reaching implications because it implies that stochastic differences in Notch pathway output can arise downstream of receptor activation.

Computing Pareto-Optimal and Almost Envy-Free Allocations of Indivisible Goods

We study the problem of fair and efficient allocation of a set of indivisible goods to agents with additive valuations using the popular fairness notions of envy-freeness up to one good (EF1) and equitability up to one good (EQ1) in conjunction with Pareto-optimality (PO). There exists a pseudo-polynomial time algorithm to compute an EF1+PO allocation and a non-constructive proof of the existence of allocations that are both EF1 and fractionally Pareto-optimal (fPO), which is a stronger notion than PO. We present a pseudopolynomial time algorithm to compute an EF1+fPO allocation, thereby improving the earlier results. Our techniques also enable us to show that an EQ1+fPO allocation always exists when the values are positive and that it can be computed in pseudo-polynomial time. We also consider the class of k-ary instances where k is a constant, i.e., each agent has at most k different values for the goods. For such instances, we show that an EF1+fPO allocation can be computed in strongly polynomial time. When all values are positive, we show that an EQ1+fPO allocation for such instances can be computed in strongly polynomial time. Next, we consider instances where the number of agents is constant and show that an EF1+PO (likewise, an EQ1+PO) allocation can be computed in polynomial time. These results significantly extend the polynomial-time computability beyond the known cases of binary or identical valuations. We also design a polynomial-time algorithm that computes a Nash welfare maximizing allocation when there are constantly many agents with constant many different values for the goods. Finally, on the complexity side, we show that the problem of computing an EF1+fPO allocation lies in the complexity class PLS.

Expected Shapley-Like Scores of Boolean functions: Complexity and Applications to Probabilistic Databases

Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf values. In this work we adapt these Shapley-like scores to probabilistic settings, the objective being to compute their expected value. We show that the computations of expected Shapley values and of the expected values of Boolean functions are interreducible in polynomial time, thus obtaining the same tractability landscape. We investigate the specific tractable case where Boolean functions are represented as deterministic decomposable circuits, designing a polynomial-time algorithm for this setting. We present applications to probabilistic databases through database provenance, and an effective implementation of this algorithm within the ProvSQL system, which experimentally validates its feasibility over a standard benchmark.

An Efficient Semantic Segmentation Method for Remote-Sensing Imagery Using Improved Coordinate Attention

Semantic segmentation stands as a prominent domain within remote sensing that is currently garnering significant attention. This paper introduces a pioneering semantic segmentation model based on TransUNet architecture with improved coordinate attention for remote-sensing imagery. It is composed of an encoding stage and a decoding stage. Notably, an enhanced and improved coordinate attention module is employed by integrating two pooling methods to generate weights. Subsequently, the feature map undergoes reweighting to accentuate foreground information and suppress background information. To address the issue of time complexity, this paper introduces an improvement to the transformer model by sparsifying the attention matrix. This reduces the computing expense of calculating attention, making the model more efficient. Additionally, the paper uses a combined loss function that is designed to enhance the training performance of the model. The experimental results conducted on three public datasets manifest the efficiency of the proposed method. The results indicate that it excels in delivering outstanding performance for semantic segmentation tasks pertaining to remote-sensing images.

Efficient Feature Matching for Large-scale Images based on Cascade Hash and Local Geometric Constraint

Abstract. Feature matching plays a crucial role in 3D reconstruction to provide correspondences between overlapped images. The accuracy and efficiency of feature matching significantly impact the performance of 3D reconstruction. The widely used framework with the exhaustive nearest neighbor searching (NNS) between descriptors and RANSAC-based geometric estimation is, however, low-efficient and unreliable for large-scale UAV images. Inspired by indexing-based NNS, this paper implements an efficient feature matching method for large-scale images based on Cascade Hashing and local geometric constraints. Our proposed method improves upon traditional feature matching approaches by introducing a combination of image retrieval, data scheduling, and GPU-accelerated Cascade Hashing. Besides, it utilizes a local geometric constraint to filter matching results within a matching framework. On the one hand, the GPU-accelerated Cascade Hashing technique generates compact and discriminative hash codes based on image features, facilitating the rapid completion of the initial matching process, and significantly reducing the search space and time complexity. On the other hand, after the initial matching is completed, the method employs a local geometric constraint to filter the initial matching results, enhancing the accuracy of the matching results. This forms a three-tier framework based on data scheduling, GPU-accelerated Cascade Hashing, and local geometric constraints. We conducted experiments using two sets of large-scale UAV image data, comparing our method with SIFTGPU to evaluate its performance in initial matching, outlier rejection, and 3D reconstruction. The results demonstrate that our method achieves a feature matching speed 2.0 times that of SIFTGPU while maintaining matching accuracy and producing comparable reconstruction results. This suggests that our method holds promise for efficiently addressing large-scale image matching.

Sharp threshold for embedding balanced spanning trees in random geometric graphs

AbstractA rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph . In particular, we find the sharp threshold for balanced binary trees. More generally, we show that all sequences of balanced trees with uniformly bounded degrees and height tending to infinity appear above a sharp threshold, and none of these appears below the same value. Our results hold more generally for geometric graphs satisfying a mild condition on the distribution of their vertex set, and we provide a polynomial time algorithm to find such trees.