Random walks in the history of life.
Ontology highlight
ABSTRACT:
SUBMITTER: Cornette JL
PROVIDER: S-EPMC314160 | biostudies-literature | 2004 Jan
REPOSITORIES: biostudies-literature
Publications
Random walks in the history of life.
Cornette James L JL Lieberman Bruce S BS
Proceedings of the National Academy of Sciences of the United States of America 20031218 1
The simplest null hypothesis for evolutionary time series is that the observed data follow a random walk. We examined whether aspects of Sepkoski's compilation of marine generic diversity depart from a random walk by using statistical tests from econometrics. Throughout most of the Phanerozoic, the random-walk null hypothesis is not rejected for marine diversity, accumulated origination or accumulated extinction, suggesting that either these variables were correlated with environmental variables ...[more]
Similar Datasets
Project description:In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them. We first discuss the ideal case of a constant sampling interval and short-tailed distributions of rest and move durations, and provide an exact analytical calculation of the fraction of correctly sampled trajectories. Further insights are obtained with simulations using more realistic long-tailed rest duration distributions showing that this fraction is dramatically reduced for real cases. We test our results for real human mobility with high-resolution GPS trajectories, where a constant sampling interval allows one to recover at best 18% of the movements, while over-evaluating the average trip length by a factor of 2. Using a sampling interval extracted from real communication data, we recover only 11% of the moves, a value that cannot be increased above 16% even with ideal algorithms. These figures call for a more cautious use of data in quantitative studies of individuals' movements.
| S-EPMC5832728 | biostudies-literature
Project description:Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to know the proportion contributions of each direct treatment comparison to each network treatment effect. The construction of proportion contributions is based on the observation that each row of the hat matrix represents a so-called "evidence flow network" for each treatment comparison. However, the existing algorithm used to calculate these values is associated with ambiguity according to the selection of paths. In this article, we present a novel analogy between NMA and random walks. We use this analogy to derive closed-form expressions for the proportion contributions. A random walk on a graph is a stochastic process that describes a succession of random "hops" between vertices which are connected by an edge. The weight of an edge relates to the probability that the walker moves along that edge. We use the graph representation of NMA to construct the transition matrix for a random walk on the network of evidence. We show that the net number of times a walker crosses each edge of the network is related to the evidence flow network. By then defining a random walk on the directed evidence flow network, we derive analytically the matrix of proportion contributions. The random-walk approach has none of the associated ambiguity of the existing algorithm.
| S-EPMC9311228 | biostudies-literature
Project description:In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.
| S-EPMC4740897 | biostudies-literature
Project description:Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be used for tasks such as multi-label classification and link prediction. The performance of the node2vec algorithm in these applications is considered to depend on properties of random walks that the algorithm uses. In the present study, we theoretically and numerically analyse random walks used by the node2vec. Those random walks are second-order Markov chains. We exploit the mapping of its transition rule to a transition probability matrix among directed edges to analyse the stationary probability, relaxation times in terms of the spectral gap of the transition probability matrix, and coalescence time. In particular, we show that node2vec random walk accelerates diffusion when walkers are designed to avoid both backtracking and visiting a neighbour of the previously visited node but do not avoid them completely.
| S-EPMC7735314 | biostudies-literature
Project description:Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node's weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods including the baseline win-loss differential method in sparse networks.
| S-EPMC4269436 | biostudies-literature
Project description:Mechanism(s) that control whether individual human primordial ovarian follicles (PFs) remain dormant, or begin to grow, are all but unknown. One of our groups has recently shown that activation of the Integrated Stress Response (ISR) pathway can slow follicular granulosa cell proliferation by activating cell cycle checkpoints. Those data suggest that the ISR is active and fluctuates according to local conditions in dormant PFs. Because cell cycle entry of (pre)granulosa cells is required for PF growth activation (PFGA), we propose that rare ISR checkpoint resolution allows individual PFs to begin to grow. Fluctuating ISR activity within individual PFs can be described by a random process. In this article, we model ISR activity of individual PFs by one-dimensional random walks (RWs) and monitor the rate at which simulated checkpoint resolution and thus PFGA threshold crossing occurs. We show that the simultaneous recapitulation of (i) the loss of PFs over time within simulated subjects, and (ii) the timing of PF depletion in populations of simulated subjects equivalent to the distribution of the human age of natural menopause can be produced using this approach. In the RW model, the probability that individual PFs grow is influenced by regionally fluctuating conditions, that over time manifests in the known pattern of PFGA. Considered at the level of the ovary, randomness appears to be a key, purposeful feature of human ovarian aging.
| S-EPMC9406804 | biostudies-literature
Project description:Composite correlated random walks (CCRW) have been posited as a potential replacement for Lévy walks and it has also been suggested that CCRWs have been mistaken for Lévy walks. Here I test an alternative, emerging hypothesis: namely that some organisms approximate Lévy walks as an innate CCRW. It is shown that the tri-modal CCRW found to describe accurately the movement patterns of mussels (Mytilus edulis) during spatial pattern formation in mussel beds can be regarded as being the first three levels in a hierarchy of nested movement patterns which if extended indefinitely would correspond to a Lévy walk whose characteristic (power-law) exponent is tuned to nearly minimize the time required to form patterned beds. The mussels realise this Lévy walk to good approximation across a biologically meaningful range of scales. This demonstrates that the CCRW not only describes mussel movement patterns, it explains them.
| S-EPMC3957148 | biostudies-other
Project description:Large-scale network mining and analysis is key to revealing the underlying dynamics of networks, not easily observable before. Lately, there is a fast-growing interest in learning low-dimensional continuous representations of networks that can be utilized to perform highly accurate and scalable graph mining tasks. A family of these methods is based on performing random walks on a network to learn its structural features and providing the sequence of random walks as input to a deep learning architecture to learn a network embedding. While these methods perform well, they can only operate on static networks. However, in real-world, networks are evolving, as nodes and edges are continuously added or deleted. As a result, any previously obtained network representation will now be outdated having an adverse effect on the accuracy of the network mining task at stake. The naive approach to address this problem is to re-apply the embedding method of choice every time there is an update to the network. But this approach has serious drawbacks. First, it is inefficient, because the embedding method itself is computationally expensive. Then, the network mining task outcome obtained by the subsequent network representations are not directly comparable to each other, due to the randomness involved in the new set of random walks involved each time. In this paper, we propose EvoNRL, a random-walk based method for learning representations of evolving networks. The key idea of our approach is to first obtain a set of random walks on the current state of network. Then, while changes occur in the evolving network's topology, to dynamically update the random walks in reserve, so they do not introduce any bias. That way we are in position of utilizing the updated set of random walks to continuously learn accurate mappings from the evolving network to a low-dimension network representation. Moreover, we present an analytical method for determining the right time to obtain a new representation of the evolving network that balances accuracy and time performance. A thorough experimental evaluation is performed that demonstrates the effectiveness of our method against sensible baselines and varying conditions.
| S-EPMC7081665 | biostudies-literature
Project description:Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.
| S-EPMC4491834 | biostudies-literature
Project description:Measuring similarities between objects based on their attributes has been an important problem in many disciplines. Object-attribute associations can be depicted as links on a bipartite graph. A similarity measure can be thought as a unipartite projection of this bipartite graph. The most widely used bipartite projection techniques make assumptions that are not often fulfilled in real life systems, or have the focus on the bipartite connections more than on the unipartite connections. Here, we define a new similarity measure that utilizes a practical procedure to extract unipartite graphs without making a priori assumptions about underlying distributions. Our similarity measure captures the relatedness between two objects via the likelihood of a random walker passing through these nodes sequentially on the bipartite graph. An important aspect of the method is that it is robust to heterogeneous bipartite structures and it controls for the transitivity similarity, avoiding the creation of unrealistic homogeneous degree distributions in the resulting unipartite graphs. We test this method using real world examples and compare the obtained results with alternative similarity measures, by validating the actual and orthogonal relations between the entities.
| S-EPMC4143196 | biostudies-literature