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Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
In the crowded eukaryotic nucleus, euchromatin and heterochromatin segregate into distinct compartments, a phenomenon often attributed to homotypic interactions mediated by liquid liquid phase separation of chromatin associated proteins.…
Patchwork learning arises as a new and challenging data collection paradigm where both samples and features are observed in fragmented subsets. Due to technological limits, measurement expense, or multimodal data integration, such patchwork…
Motivated by a non-random but clustered distribution of SNPs, we introduce a phenomenological model to account for the clustering properties of SNPs in the human genome. The phenomenological model is based on a preferential mutation to the…
Much of the on-going statistical analysis of DNA sequences is focused on the estimation of characteristics of coding and non-coding regions that would possibly allow discrimination of these regions. In the current approach, we concentrate…
We investigate a densely packed, non-random arrangement of forty-six chromosomes (46,XY) in human nuclei. Here, we model systems-level chromosomal crosstalk by unifying intrinsic parameters (chromosomal length and number of genes) across…
Continuous periodogram power spectral analyses of fractal fluctuations of frequency distributions of bases A, C, G, T in Drosophila DNA show that the power spectra follow the universal inverse power-law form of the statistical normal…
Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Remarkably, analogous high-dimensional, highly-interconnected computational architectures also…
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…
We use a coarse-grained model of DNA-functionalized particles to understand the role of DNA chain length on their self-assembly. We find that the increasing chain length for a given particle size decreases the propensity to form ordered…
The formation of DNA loops by proteins and protein complexes that bind at distal DNA sites plays a central role in many cellular processes, such as transcription, recombination, and replication. Here we review the basic thermodynamic…
Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation)…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localised clusters, suggesting a simple mechanism…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
Recent progress has been made in the understanding of the physical properties of chromatin -- the dense complex of DNA and histone proteins that occupies the nuclei of plant and animal cells. Here I will focus on the two lowest levels of…
Cancer is a number of related yet highly heterogeneous diseases. Correct identification of cancer subtypes is critical for clinical decisions. The advance in sequencing technologies has made it possible to study cancer based on abundant…
An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to…