Abstract: We consider the dynamics of a reaction-diffusion system on a multigraph. The species share the same set of nodes but can access different links to explore the embedding spatial support. By acting on the topology of the networks we can control the ability of the system to self-organise in macroscopic patterns, emerging as a symmetry breaking instability of an homogeneous fixed point. Two different cases study are considered: on the one side, we produce a global modification of the networks, starting from the limiting setting where species are hosted on the same graph. On the other, we consider the effect of inserting just one additional single link to differentiate the two graphs. In both cases, patterns can be generated or destroyed, as follows the imposed, small, topological perturbation. Approximate analytical formulae allows to grasp the essence of the phenomenon and can potentially inspire innovative control strategies to shape the macroscopic dynamics on multigraph networks.

Abstract: Complex biological systems such as cells, tissues, or diseases are comprised of numerous interactive, multi-scale networks with redundant, convergent and divergent signaling pathways including numerous positive and negative feedback loops. Computational tools that integrate multiple types of data from high-throughput experiments to elucidate critical patterns and derive predictions are the key to understanding such complex systems. While the advent of high-throughput technologies and the resultant abundance of data have increased the demand for data-driven analytics, comprehensive and computationally efficient methods for learning and predictive modeling of complex biological systems remain elusive. Capturing statistical regularities, with minimal assumptions about the structure in the data, is particularly difficult in biological systems due to their stochastic nature and residual multi-scale interdependencies. Modeling the latent interactions that characterize many biological systems also presents a significant challenge to popular modeling approaches often limited to representing linear statistical regularities, stationary data distributions and/or the use of annotated data via supervised learning methods. In this paper, we introduce a new computational framework and algorithm designed for unsupervised learning and model construction in high-throughput biological data applications. The proposed framework uses an underlying Bayesian nonparametric model that that can effectively infer long-range temporal dependencies from heterogeneous data streams and produce grammatical rules used for real-time in-silico modeling, behavior recognition and prediction. We present initial results for two unsupervised learning tasks using unlabeled live-cell imaging data from experiments performed on the Large Scale Digital Cell Analysis System (LSDCAS), namely cellular event identification and large-scale spatio-temporal behavior recognition. We demonstrate increases in accuracy and precision over current expert methods, the efficient asymptotic computational complexity of the proposed learning algorithm and its suitability for real-time predictive analytics.

Abstract: Some natural complex sequences when structurally analyzed have discrete morphemes, e.g. root consonants in Semitic languages and genetic exons in DNA molecules. Despite considerable approaches, such as Two Level Morphology of Kimmo Koskenniemi in linguistics and A New Kind of Science of Stephen Wolfram in physics, the existing formalisms applied for parsing these complex sequences are computationally inefficient. This presentation reports such a formalism called Shuffle Morphology where the sequences of a complex system, here Classical Arabic, is deshuffled into a few discrete morphemes on a finite set of shuffling discrete patterns for verbs and nouns. The extent to which Shuffle Morphology can handle the complexity of the morpho-syntax of Classical Arabic is evaluated in terms of the simplicity of its description of the language. This formalism is implemented as a set of templatic regular expressions in MOBIN Knowledge-Based System to morpho-syntactically analyze Classical Arabic texts. The descriptive simplicity of Shuffle Morphology is measured in terms of Kolmogorov Complexity defined as the length of the shortest computer program that morphologically analyses the language. Implemented in Perl, MOBIN has the source size of nearly 0.5 MB and the effectiveness of 96% in generating morpho-syntactically tagged corpora. This efficiency is just one-eighth of 4MB size of the source of Buckwalter Arabic Morphological Analyzer (BAMA version 2.0), also implemented in Perl and used for tagging Arabic corpora distributed at LDC centre in University of Pennsylvania. Although BAMA, newly re-implemented as SAMA (Standard Arabic Morphological Analyzer), uses three lists for prefixes, suffixes and stems, supplemented by three morphological compatibility tables, generates the tagged corpora highly ambiguously. Further development of Shuffle Morphology employing semi-supervised machine learning schemes is expected to compute efficiently other Semitic languages. It is also expected to increase considerably effectiveness and efficiency in computing DNA sequences.