Time Complexity Research Articles

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.

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.

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.

A linear time algorithm for linearizing quadratic and higher-order shortest path problems

AbstractAn instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP (LinQSPP) decides whether a given QSPP instance is linearizable and determines the corresponding SPP instance in the positive case. We provide a novel linear time algorithm for the LinQSPP on acyclic digraphs which runs considerably faster than the previously best algorithm. The algorithm is based on a new insight revealing that the linearizability of the QSPP for acyclic digraphs can be seen as a local property. Our approach extends to the more general higher-order shortest path problem.

A complexity efficient penta-diagonal quantum smoothing filter for bio-medical signal denoising: a study on ECG

Extracting information-bearing signal from a noisy environment has been a practical challenge in both classical and quantum computing formalism, especially in critical signal processing applications. To filter out the effect of noise, we propose a quantum smoothing filter built upon quantum formalism-based circuits applied for electrocardiogram signal denoising. The proposed quantum filter is a conceptually novel framework with an advantage in computational complexity as compared to the existing classical filters, such as discrete wavelet transform and empirical mode decomposition, whereas it achieves similar performance metrics for the accuracy of the filter. Further, we exploit the penta-diagonal Toeplitz structure of the smoothing filter, which gives approximately 48%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$48\\%$$\\end{document} gate cost reduction for 10 qubit circuit compared to the standard Hamiltonian simulation without structure. The run-time complexity using the quantum matrix inversion technique for the structured matrix is given by O~κ2poly(logN)εP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{{\\mathscr {O}}}\\left( \\frac{\\kappa ^2 \ ext {poly}(\\log {N})}{\\varepsilon _P}\\right)$$\\end{document} for condition number κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document} of the N×N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\ imes N$$\\end{document} filter matrix within precision εP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon _P$$\\end{document}. Embedding fixed sparsity of the banded matrix, the quantum filter shows potentially better run-time complexity than classical filtering techniques. For the quantifiable research results of our work, we have shown several performance metrics, such as mean-square error and peak signal-to-noise ratio analysis, with a bound of error due to observation noise, simulation error and quantum measurement uncertainty.

Adaptive temporal compression for reduction of computational complexity in human behavior recognition

The research on video analytics especially in the area of human behavior recognition has become increasingly popular recently. It is widely applied in virtual reality, video surveillance, and video retrieval. With the advancement of deep learning algorithms and computer hardware, the conventional two-dimensional convolution technique for training video models has been replaced by three-dimensional convolution, which enables the extraction of spatio-temporal features. Specifically, the use of 3D convolution in human behavior recognition has been the subject of growing interest. However, the increased dimensionality has led to challenges such as the dramatic increase in the number of parameters, increased time complexity, and a strong dependence on GPUs for effective spatio-temporal feature extraction. The training speed can be considerably slow without the support of powerful GPU hardware. To address these issues, this study proposes an Adaptive Time Compression (ATC) module. Functioning as an independent component, ATC can be seamlessly integrated into existing architectures and achieves data compression by eliminating redundant frames within video data. The ATC module effectively reduces GPU computing load and time complexity with negligible loss of accuracy, thereby facilitating real-time human behavior recognition.

Low-Resolution Optimization for an Unmanned Aerial Vehicle Communication Network under a Passive Reconfigurable Intelligent Surface and Active Reconfigurable Intelligent Surface

This paper investigates the optimization of an unmanned aerial vehicle (UAV) network serving multiple downlink users equipped with single antennas. The network is enhanced by the deployment of either a passive reconfigurable intelligent surface (RIS) or an active RIS. The objective is to jointly design the UAV’s trajectory and the low-bit, quantized, RIS-programmable coefficients to maximize the minimum user rate in a multi-user scenario. To address this optimization challenge, an alternating optimization framework is employed, leveraging the successive convex approximation (SCA) method. Specifically, for the UAV trajectory design, the original non-convex optimization problem is reformulated into an equivalent convex problem through the introduction of slack variables and appropriate approximations. On the other hand, for the RIS-programmable coefficient design, an efficient algorithm is developed using a penalty-based approximation approach. To solve the problems with the proposed optimization, high-performance optimization tools such as CVX are utilized, despite their associated high time complexity. To mitigate this complexity, a low-complexity algorithm is specifically tailored for the optimization of passive RIS-programmable reflecting elements. This algorithm relies solely on closed-form expressions to generate improved feasible points, thereby reducing the computational burden while maintaining reasonable performance. Extensive simulations are created to validate the performance of the proposed algorithms. The results demonstrate that the active RIS-based approach outperforms the passive RIS-based approach. Additionally, for the passive RIS-based algorithms, the low-complexity variant achieves a reduced time complexity with a moderate loss in performance.

Graph semantic similarity-based automatic assessment for programming exercises

This paper proposes an algorithm for the automatic assessment of programming exercises. The algorithm assigns assessment scores based on the program dependency graph structure and the program semantic similarity, but does not actually need to run the student’s program. By calculating the node similarity between the student’s program and the teacher’s reference programs in terms of structure and program semantics, a similarity matrix is generated and the optimal similarity node path of this matrix is identified. The proposed algorithm achieves improved computational efficiency, with a time complexity of O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2)$$\\end{document} for a graph with n nodes. The experimental results show that the assessment algorithm proposed in this paper is more reliable and accurate than several comparison algorithms, and can be used for scoring programming exercises in C/C++, Java, Python, and other languages.

A Theory of Alternating Paths and Blossoms from the Perspective of Minimum Length

The Micali–Vazirani (MV) algorithm for finding a maximum cardinality matching in general graphs, which was published in 1980, remains to this day the most efficient known algorithm for the problem. The current paper gives the first complete and correct proof of this algorithm. The MV algorithm resorts to finding minimum-length augmenting paths. However, such paths fail to satisfy an elementary property, called breadth first search honesty in this paper. In the absence of this property, an exponential time algorithm appears to be called for—just for finding one such path. On the other hand, the MV algorithm accomplishes this and additional tasks in linear time. The saving grace is the various “footholds” offered by the underlying structure, which the algorithm uses in order to perform its key tasks efficiently. The theory expounded in this paper elucidates this rich structure and yields a proof of correctness of the algorithm. It may also be of independent interest as a set of well-knit graph-theoretic facts. Funding: This work was supported in part by the National Science Foundation [Grant CCF-2230414].

Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes

We introduce and analyse an efficient decoder for quantum Tanner codes that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight \(O(\sqrt{n\log n})\) . We also work on the link between quantum Tanner codes and the Lifted Product codes of Panteleev and Kalachev, and show that our decoder can be adapted to the latter. The decoding algorithm alternates between sequential and parallel procedures and converges in linear time.

Quantum Fourier networks for solving parametric PDEs

Many real-world problems, like modelling environment dynamics, physical processes, time series etc involve solving partial differential equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture called Fourier neural operator (FNO) proved to be capable of learning solutions of given PDE families for any initial conditions as input. However, it results in a time complexity linear in the number of evaluations of the PDEs while testing. Given the advancements in quantum hardware and the recent results in quantum machine learning methods, we exploit the running efficiency offered by these and propose quantum algorithms inspired by the classical FNO, which result in time complexity logarithmic in the number of evaluations and are expected to be substantially faster than their classical counterpart. At their core, we use the unary encoding paradigm and orthogonal quantum layers and introduce a new quantum Fourier transform in the unary basis. We propose three different quantum circuits to perform a quantum FNO. The proposals differ in their depth and their similarity to the classical FNO. We also benchmark our proposed algorithms on three PDE families, namely Burgers’ equation, Darcy’s flow equation and the Navier–Stokes equation. The results show that our quantum methods are comparable in performance to the classical FNO. We also perform an analysis on small-scale image classification tasks where our proposed algorithms are at par with the performance of classical convolutional neural networks, proving their applicability to other domains as well.

Multi-Connectivity for Multicast Video Streaming in Cellular Networks

The escalating demand for high-quality video streaming poses a major challenge for communication networks today. Catering to these bandwidth-hungry video streaming services places a huge burden on the limited spectral resources of communication networks, limiting the resources available for other services as well. Large volumes of video traffic can lead to severe network congestion, particularly during live streaming events, which require sending the same content to a large number of users simultaneously. For such applications, multicast transmission can effectively combat network congestion while meeting the demands of all the users by serving groups of users requesting the same content over shared spectral resources. Streaming services can further benefit from multi-connectivity, which allows users to receive content from multiple base stations simultaneously. Integrating multi-connectivity within multicast streaming can improve the system resource utilization while also providing seamless connectivity to multicast users. Toward this end, this work studied the impact of using multi-connectivity (MC) alongside wireless multicast for meeting the resource requirements of video streaming. Our findings show that MC substantially enhances the performance of multicast streaming, particularly benefiting cell-edge users who often experience poor channel conditions. We especially considered the number of users that can be simultaneously served by multi-connected multicast systems. It was observed that about 60% of the users that are left unserved under single-connectivity multicast are successfully served using the same resources by employing multi-connectivity in multicast transmissions. We prove that the optimal resource allocation problem for MC multicast is NP-hard. As a solution, we present a greedy approximation algorithm with an approximation factor of (1−1/e). Furthermore, we establish that no other polynomial-time algorithm can offer a superior approximation. To generate realistic video traffic patterns in our simulations, we made use of traces from actual videos. Our results clearly demonstrate that multi-connectivity leads to significant enhancements in the performance of multicast streaming.

DIRECT: Dual Interpretable Recommendation with Multi-aspect Word Attribution

Recommending products to users with intuitive explanations helps improve the system in transparency, persuasiveness, and satisfaction. Existing interpretation techniques include post-hoc methods and interpretable modeling. The former category could quantitatively analyze input contribution to model prediction but has limited interpretation faithfulness, while the latter could explain model internal mechanisms but may not directly attribute model predictions to input features. In this study, we propose a novel D ual I nterpretable Rec ommenda t ion model called DIRECT, which integrates ideas of the two interpretation categories to inherit their advantages and avoid limitations. Specifically, DIRECT makes use of item descriptions as explainable evidence for recommendation. First, similar to the post-hoc interpretation, DIRECT could attribute the prediction of a user preference score to textual words of the item descriptions. The attribution of each word is related to its sentiment polarity and word importance, where a word is important if it corresponds to an item aspect that the user is interested in. Second, to improve the interpretability of embedding space, we propose to extract high-level concepts from embeddings, where each concept corresponds to an item aspect. To learn discriminative concepts, we employ a concept-bottleneck layer, and maximize the coding rate reduction on word-aspect embeddings by leveraging a word-word affinity graph extracted from a pre-trained language model. In this way, DIRECT simultaneously achieves faithful attribution and usable interpretation of embedding space. We also show that DIRECT achieves linear inference time complexity regarding the length of item reviews. We conduct experiments including ablation studies on five real-world datasets. Quantitative analysis, visualizations, and case studies verify the interpretability of DIRECT. Our code is available at: https://github.com/JacksonWuxs/DIRECT .

Global Receptive Field Designed Complex-Valued Convolutional Neural Network Equalizer for Optical Fiber Communications

In this paper, an improved complex-valued convolutional neural network (CvCNN) structure to be placed at the received side is proposed for nonlinearity compensation in a coherent optical system. This complex-valued global convolutional kernel-assisted convolutional neural network equalizer (CvGNN) has been verified in terms of Q-factor performance and complexity compared to seven other related nonlinear equalizers based on both the 64 QAM experimental platform and the QPSK numerical platform. The global convolution operation of the proposed CvGNN is more suitable for the calculation process of perturbation coefficients, and the global receptive field can also be more effective at extracting effective information from perturbation feature maps. The introduction of CvCNN can directly focus on the complex-valued perturbation feature maps themselves without separately processing the real and imaginary parts, which is more in line with the waveform-dependent physical characteristics of optical signals. Based on the experimental platform, compared with the real-valued neural network with small convolutional kernel (RvCNNC), the proposed CvGNNC improves the Q-factor by ∼2.95 dB at the optimal transmission power, while reducing the time complexity by ∼44.7%.

NDI-PPO: Node degree increment-based proximal policy optimization method for employment community discovery in online social networks

Purpose: aiming at the limitations of pre-input parameters in the complex network overlapping community discovery algorithm based on tag propagation in real networks and the problems of tag redundancy, method: a node degree increment-based proximal policy optimization method for community discovery in online social networks is proposed (named NDI-PPO). Process: by applying the cohesion idea and introducing the concept of modularity increment, a social network great community is constructed from the bottom up according to the criteria of community division. For the problem that the number of iterative steps is sensitive to the strategy gradient algorithm, we adopt an improved PPO to improve the efficiency of feature extraction. In label updating, the maximum clique is used as the core unit to update the labels and weights of the maximum maximum clique adjacent nodes from the center to the periphery using intimacy, and the weights of the non-maximum maximum clique adjacent nodes are updated by means of the maximum weight. In the post-processing stage, the adaptive threshold method is used to remove the noise in the node label, which effectively overcomes the limitation of the number of pre-input overlapping communities in the real network. Result: The simulation results show that the proposed community discovery algorithm NDI-PPO is superior to other advanced algorithms, the time complexity is greatly reduced, and it is suitable for community discovery in large social networks.

Menstrual Temporality: Cyclic Bodies in a Linear World

ABSTRACT In this paper I will explore a phenomenology of the menstrual cycle, focusing on the cycle’s rhythm as a form of lived temporality. Drawing on the work of Henri Lefebvre and Thomas Fuchs I will outline a key connection between embodiment and rhythmic temporality more generally, before applying this analysis to the rhythm of the menstrual cycle specifically. I will consider the phenomenology of the experience of cycling through the phases of pre-ovulation, ovulation, pre-menstruation and menstruation as a pattern, or specifically an embodied rhythm that constitutes a form of lived temporality. I will consider a way that the subject may potentially be alienated from this rhythm as a result of a dominant cultural narrative of “linear time”. I will argue further that this dissonance between the menstrual body and the contemporary world tends to be compounded by a lack of “menstrual literacy” in education and culture.