arXiv subjects

Zhanshan Sam Ma

Publications and source records attributed to Zhanshan Sam Ma.

5 recordsLinked to original sources

arXiv2026

A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$

The replication dynamics (differential equation system) is the foundation of evolutionary game theory. When n=2, there are four possible types of replication dynamics. When n=3, there are 49 possible types of replication dynamics. However, when n>3, the classification of replication dynamics has not been solved. In this article, the sufficient and necessary conditions of the replication dynamics equation with a unique fixed point in the interior of simplex $S_n$(Int$S_n$) for $n\geq 2$ are presented. Furthermore, the different types of replication dynamics equations with a unique fixed point in IntSn is discussed.

q-bio.PE↗

arXiv2025

Six Decades Post-Discovery of Taylor's Power Law: From Ecological and Statistical Universality, Through Prime Number Distributions and Tipping-Point Signals, to Heterogeneity and Stability of Complex Networks

First discovered by L. R. Taylor (1961, Nature), Taylor's Power Law (TPL) correlates the mean (M) population abundances and the corresponding variances (V) across a set of insect populations using a power function (V=aM^b). TPL has demonstrated its 'universality' across numerous fields of sciences, social sciences, and humanities. This universality has inspired two main prongs of exploration: one from mathematicians and statisticians, who might instinctively respond with a convergence theorem similar to the central limit theorem of the Gaussian distribution, and another from biologists, ecologists, physicists, etc., who are more interested in potential underlying ecological or organizational mechanisms. Over the past six decades, TPL studies have produced a punctuated landscape with three relatively distinct periods (1960s-1980s; 1990s-2000s, and 2010s-2020s) across the two prongs of abstract and physical worlds. Eight themes have been identified and reviewed on this landscape, including population spatial aggregation and ecological mechanisms, TPL and skewed statistical distributions, mathematical/statistical mechanisms of TPL, sample vs. population TPL, population stability, synchrony, and early warning signals for tipping points, TPL on complex networks, TPL in macrobiomes, and in microbiomes. Three future research directions including fostering reciprocal interactions between the two prongs, heterogeneity measuring, and exploration in the context of evolution. The significance of TPL research includes practically, population fluctuations captured by TPL are relevant for agriculture, forestry, fishery, wildlife-conservation, epidemiology, tumor heterogeneity, earthquakes, social inequality, stock illiquidity, financial stability, tipping point events, etc.; theoretically, TPL is one form of power laws, which are related to phase transitions, universality, scale-invariance, etc.

q-bio.OT↗

arXiv2013

SparseAssembler2: Sparse k-mer Graph for Memory Efficient Genome Assembly

The formal version of our work has been published in BMC Bioinformatics and can be found here: http://www.biomedcentral.com/1471-2105/13/S6/S1 Motivation: To tackle the problem of huge memory usage associated with de Bruijn graph-based algorithms, upon which some of the most widely used de novo genome assemblers have been built, we released SparseAssembler1. SparseAssembler1 can save as much as 90% memory consumption in comparison with the state-of-art assemblers, but it requires rounds of denoising to accurately assemble genomes. In this paper, we introduce a new general model for genome assembly that uses only sparse k-mers. The new model replaces the idea of the de Bruijn graph from the beginning, and achieves similar memory efficiency and much better robustness compared with our previous SparseAssembler1. Results: We demonstrate that the decomposition of reads of all overlapping k-mers, which is used in existing de Bruijn graph genome assemblers, is overly cautious. We introduce a sparse k-mer graph structure for saving sparse k-mers, which greatly reduces memory space requirements necessary for de novo genome assembly. In contrast with the de Bruijn graph approach, we devise a simple but powerful strategy, i.e., finding links between the k-mers in the genome and traversing following the links, which can be done by saving only a few k-mers. To implement the strategy, we need to only select some k-mers that may not even be overlapping ones, and build the links between these k-mers indicated by the reads. We can traverse through this sparse k-mer graph to build the contigs, and ultimately complete the genome assembly. Since the new sparse k-mers graph shares almost all advantages of de Bruijn graph, we are able to adapt a Dijkstra-like breadth-first search algorithm to circumvent sequencing errors and resolve polymorphisms.

cs.DS↗

arXiv2012

A Note on Extending Taylor's Power Law for Characterizing Human Microbial Communities: Inspiration from Comparative Studies on the Distribution Patterns of Insects and Galaxies, and as a Case Study for Medical Ecology

Many natural patterns, such as the distributions of blood particles in a blood sample, proteins on cell surfaces, biological populations in their habitat, galaxies in the universe, the sequence of human genes, and the fitness in evolutionary computing, have been found to follow power law. Taylor's power law (Taylor 1961: Nature, 189:732-) is well recognized as one of the fundamental models in population ecology. A fundamental property of biological populations, which Taylor's power law reveals, is the near universal heterogeneity of population abundance distribution in habitat. Obviously, the heterogeneity also exists at the community level, where not only the distributions of population abundances but also the proportions of the species composition in the community are often heterogeneous. Nevertheless, existing community diversity indexes such as Shannon index and Simpson index can only measure "local" or "static" diversity in the sense that they are computed for each habitat at a specific time point, and the indexes alone do not reflect the diversity changes. In this note, I propose to extend the application scope of Taylor's power law to the studies of human microbial communities, specifically, the community heterogeneity at both population and community levels. I further suggested that population dispersion models such as Taylor (1980: Nature, 286, 53-), which is known to generate population distribution patterns consistent with the power law, should also be very useful for analyzing the distribution patterns of human microbes within the human body. Overall, I hope that the approach to human microbial community with the power law offers an example that ecological theories can play an important role in the emerging medical ecology, which aims at studying the ecology of human microbiome and its implications to human diseases and health, as well as in personalized medicine.

cs.CE↗

arXiv2011

SparseAssembler: de novo Assembly with the Sparse de Bruijn Graph

de Bruijn graph-based algorithms are one of the two most widely used approaches for de novo genome assembly. A major limitation of this approach is the large computational memory space requirement to construct the de Bruijn graph, which scales with k-mer length and total diversity (N) of unique k-mers in the genome expressed in base pairs or roughly (2k+8)N bits. This limitation is particularly important with large-scale genome analysis and for sequencing centers that simultaneously process multiple genomes. We present a sparse de Bruijn graph structure, based on which we developed SparseAssembler that greatly reduces memory space requirements. The structure also allows us to introduce a novel method for the removal of substitution errors introduced during sequencing. The sparse de Bruijn graph structure skips g intermediate k-mers, therefore reducing the theoretical memory space requirement to ~(2k/g+8)N. We have found that a practical value of g=16 consumes approximately 10% of the memory required by standard de Bruijn graph-based algorithms but yields comparable results. A high error rate could potentially derail the SparseAssembler. Therefore, we developed a sparse de Bruijn graph-based denoising algorithm that can remove more than 99% of substitution errors from datasets with a \leq 2% error rate. Given that substitution error rates for the current generation of sequencers is lower than 1%, our denoising procedure is sufficiently effective to safeguard the performance of our algorithm. Finally, we also introduce a novel Dijkstra-like breadth-first search algorithm for the sparse de Bruijn graph structure to circumvent residual errors and resolve polymorphisms.

cs.DS↗