Some combinatorial arrays related to the Lotka-Volterra system

The purpose of this paper is to investigate the connection between the Lotka-Volterra system and combinatorics. We study several context-free grammars associated with the Lotka-Volterra system. Some combinatorial arrays, involving the Stirling numbers of the second kind and Eulerian numbers, are generated by these context-free grammars. In particular, we present grammatical characterization of some statistics on cyclically ordered partitions.Comment: 15 page

Criteria for robustness of heteroclinic cycles in neural microcircuits.

Copyright © 2011 Ashwin et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in Lotka-Volterra-type winnerless competition (WLC) models as well as in more general coupled and/or symmetric systems. It has been previously suggested that RHCs may be relevant to a range of neural activities, from encoding and binding to spatio-temporal sequence generation.The robustness or otherwise of such cycles depends both on the coupling structure and the internal structure of the neurons. We verify that robust heteroclinic cycles can appear in systems of three identical cells, but only if we require perturbations to preserve some invariant subspaces for the individual cells. On the other hand, heteroclinic attractors can appear robustly in systems of four or more identical cells for some symmetric coupling patterns, without restriction on the internal dynamics of the cells

Priming nonlinear searches for pathway identification

BACKGROUND: Dense time series of metabolite concentrations or of the expression patterns of proteins may be available in the near future as a result of the rapid development of novel, high-throughput experimental techniques. Such time series implicitly contain valuable information about the connectivity and regulatory structure of the underlying metabolic or proteomic networks. The extraction of this information is a challenging task because it usually requires nonlinear estimation methods that involve iterative search algorithms. Priming these algorithms with high-quality initial guesses can greatly accelerate the search process. In this article, we propose to obtain such guesses by preprocessing the temporal profile data and fitting them preliminarily by multivariate linear regression. RESULTS: The results of a small-scale analysis indicate that the regression coefficients reflect the connectivity of the network quite well. Using the mathematical modeling framework of Biochemical Systems Theory (BST), we also show that the regression coefficients may be translated into constraints on the parameter values of the nonlinear BST model, thereby reducing the parameter search space considerably. CONCLUSION: The proposed method provides a good approach for obtaining a preliminary network structure from dense time series. This will be more valuable as the systems become larger, because preprocessing and effective priming can significantly limit the search space of parameters defining the network connectivity, thereby facilitating the nonlinear estimation task

Hardware implementation of digital memcomputing on small-size FPGAs

Memcomputing is a novel computing paradigm beyond the von-Neumann one. Its digital version is designed for the efficient solution of combinatorial optimization problems, which emerge in various fields of science and technology. Previously, the performance of digital memcomputing machines (DMMs) was demonstrated using software simulations of their ordinary differential equations. Here, we present the first hardware realization of a DMM algorithm on a low-cost FPGA board. In this demonstration, we have implemented a Boolean satisfiability problem solver. To optimize the use of hardware resources, the algorithm was partially parallelized. The scalability of the present implementation is explored and our FPGA-based results are compared to those obtained using a python code running on a traditional (von-Neumann) computer, showing one to two orders of magnitude speed-up in time to solution. This initial small-scale implementation is projected to state-of-the-art FPGA boards anticipating further advantages of the hardware realization of DMMs over their software emulation

Being Interdisciplinary: Adventures in urban science and beyond

In Being Interdisciplinary, Alan Wilson draws on five decades as a leading figure in urban science to set out a systems approach to interdisciplinarity for those conducting research in this and other fields. He argues that most research is interdisciplinary at base, and that a systems perspective is particularly appropriate for collaboration because it fosters an outlook that sees beyond disciplines. There is a more subtle thread, too. A systems approach enables researchers to identify the game-changers of the past as a basis for thinking outside convention, for learning how to do something new and how to be ambitious, in a nutshell how to be creative. Ultimately, the ideas presented address how to do research. Building on this systems focus, the book first establishes the basics of interdisciplinarity. Then, by drawing on the author’s experience of doing interdisciplinary research, and working from his personal toolkit, it offers general principles and a framework from which researchers can build their own interdisciplinary toolkit, with elements ranging from explorations of game-changers in research to superconcepts. In the last section, the book tackles questions of managing and organising research from individual to institutional scales. Alan Wilson deploys his wide experience – researcher in urban science, university professor and vice-chancellor, civil servant and institute director – to build the narrative. While his experience in urban science provides the illustrations, the principles apply across many research fields

Being Interdisciplinary

In Being Interdisciplinary, Alan Wilson draws on five decades as a leading figure in urban science to set out a systems approach to interdisciplinarity for those conducting research in this and other fields. He argues that most research is interdisciplinary at base, and that a systems perspective is particularly appropriate for collaboration because it fosters an outlook that sees beyond disciplines. There is a more subtle thread, too. A systems approach enables researchers to identify the game-changers of the past as a basis for thinking outside convention, for learning how to do something new and how to be ambitious, in a nutshell how to be creative. Ultimately, the ideas presented address how to do research. Building on this systems focus, the book first establishes the basics of interdisciplinarity. Then, by drawing on the author’s experience of doing interdisciplinary research, and working from his personal toolkit, it offers general principles and a framework from which researchers can build their own interdisciplinary toolkit, with elements ranging from explorations of game-changers in research to superconcepts. In the last section, the book tackles questions of managing and organising research from individual to institutional scales. Alan Wilson deploys his wide experience – researcher in urban science, university professor and vice-chancellor, civil servant and institute director – to build the narrative. While his experience in urban science provides the illustrations, the principles apply across many research fields

How the other half lives: CRISPR-Cas's influence on bacteriophages

CRISPR-Cas is a genetic adaptive immune system unique to prokaryotic cells used to combat phage and plasmid threats. The host cell adapts by incorporating DNA sequences from invading phages or plasmids into its CRISPR locus as spacers. These spacers are expressed as mobile surveillance RNAs that direct CRISPR-associated (Cas) proteins to protect against subsequent attack by the same phages or plasmids. The threat from mobile genetic elements inevitably shapes the CRISPR loci of archaea and bacteria, and simultaneously the CRISPR-Cas immune system drives evolution of these invaders. Here we highlight our recent work, as well as that of others, that seeks to understand phage mechanisms of CRISPR-Cas evasion and conditions for population coexistence of phages with CRISPR-protected prokaryotes.Comment: 24 pages, 8 figure

Discrete nondeterministic modeling of biochemical networks

The ideas expressed in this work pertain to biochemical modeling. We explore our technique, the Nondeterministic Waiting Time algorithm, for modeling molecular signaling cascades. The algorithm is presented with pseudocode along with an explanation of its implementation. The entire source code can be found in the Appendices. This algorithm builds on earlier work from the lab of Dr. Andrei Nun, the advisor for this dissertation. We discuss several important extensions including: (i) a heap with special maintenance functions for sorting reaction waiting times, (ii) a nondeterministic component for handling reaction competition, and (iii) a memory enhancement allowing slower reactions to compete with faster reactions. Several example systems are provided for comparisons between modeling with systems of ordinary differential equations, the Gillespie Algorithm, and our Nondeterministic Waiting Time algorithm. Our algorithm has a unique ability to exhibit behavior similar to the solutions to systems of ordinary differential equations for certain models and parameter choices, but it also has the nondeterministic component which yields results similar stochastic methods (e.g., the Gillespie Algorithm). Next, we turn our attention to the Fas-mediated apoptotic signaling cascade. Fas signaling has important implications in the research of cancer, autoimmune and neurodegenerative disorders. We provide an exhaustive account of results from the Nondeterministic Waiting Time algorithm in comparison to solutions to the system of ordinary differential equations described by another modeling group. Our work with the Fas pathway led us to explore a new model, focusing on the effects of HIV-1 proteins on the Fas signaling cascade. There is extensive information in the literature on the effects of the HIV-1 proteins on this pathway. The model described in this work represents the first attempt ever made in modeling Fas-induced apoptosis in latently infected T cells. There are several extensions for the Fas model discussed at the end of the work. Calcium signaling would be an interesting avenue to investigate, building on some recent results reported in the literature. For the HIV model, there are several extensions discussed. We also suggest a new direction for the Nondeterministic Waiting Time algorithm exploring parallelization options