Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Introduction to the Modeling and Analysis of Complex Systems

Keep up to date on Introduction to Modeling and Analysis of Complex Systems at http://bingweb.binghamton.edu/~sayama/textbook/! Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example. This textbook is available for purchase in both grayscale and color via Amazon.com and CreateSpace.com.https://knightscholar.geneseo.edu/oer-ost/1013/thumbnail.jp

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

The stability of model ecosystems

Ecologists would like to understand how complexity persists in nature. In this thesis I have taken two fundamentally different routes to study ecosystem stability of model ecosystems: classical community ecology and classical population ecology. In community ecology models, we can study the mathematical mechanisms of stability in general, large model ecosystems. In population ecology models, fewer species are studied but greater detail of species interactions can be incorporated. Within these alternative contexts, this thesis contributes to two consuming issues concerning the stability of ecological systems: the ecosystem stability-complexity debate; and the causes of cyclic population dynamics. One of the major unresolved issues in community ecology is the relationship between ecosystem stability and complexity. In 1958 Charles Elton made the conjecture that the stability of an ecological system was coupled to its complexity and this could be a “wise principle of co-existence between man and nature” with which ecologists could argue the case for the conservation of nature for all species, including man. The earliest and simplest model systems were randomly constructed and exhibited a negative association between stability and complexity. This finding sparked the stability-complexity debate and initiated the search for organising principles that enhanced stability in real ecosystems. One of the universal laws of ecology is that ecosystems contain many rare and few common species. In this thesis, I present analytical arguments and numerical results to show that the stability of an ecosystem can increase with complexity when the abundance distribution is characterized by a skew towards many rare species. This work adds to the growing number of conditions under which the negative stability - complexity relationship can been inverted in theoretical studies. While there is growing evidence that the stability-complexity debate is progressing towards a resolution, community ecology has become increasingly subject to major criticism. A long-standing criticism is the reliance on local stability analysis. There is growing recognition that a global property called permanence is a more satisfactory definition of ecosystem stability because it tests only whether species can coexist. Here I identify and explain a positive correlation between the probability of local stability and permanence, which suggests local stability is a better measure of species coexistence than previously thought. While this offers some relief, remaining issues cause the stability-complexity debate to evade clear resolution and leave community ecology in a poor position to argue for the conservation of natural diversity for the benefit of all species. In classical population ecology, a major unresolved issue is the cause of non-equilibrium population dynamics. In this thesis, I use models to study the drivers of cyclic dynamics in Scottish populations of mountain hares (Lepus timidus), for the first time in this system. Field studies currently favour the hypothesis that parasitism by a nematode Trichostrongylus retortaeformis drives the hare cycles, and theory predicts that the interaction should induce cycling. Initially I used a simple, strategic host-parasite model parameterised using available empirical data to test the superficial concordance between theory and observation. I find that parasitism could not account for hare cycles. This verdict leaves three options: either the parameterisation was inadequate, there were missing important biological details or simply that parasites do not drive host cycles. Regarding the first option, reliable information for some hare-parasite model parameters was lacking. Using a rejection-sampling approach motivated by Bayesian methods, I identify the most likely parameter set to predict observed dynamics. The results imply that the current formulation of the hare-parasite model can only generate realistic dynamics when parasite effects are significantly larger than current empirical estimates, and I conclude it is likely that the model contains an inadequate level of detail. The simple strategic model was mathematically elegant and allowed mathematical concepts to be employed in analysis, but the model was biologically naïve. The second model is the antipode of the first, an individual based model (IBM) steeped in biological reality that can only be studied by simulation. Whilst most highly detailed tactical models are developed as a predictive tool, I instead structurally perturb the IBM to study the ecological processes that may drive population cycles in mountain hares. The model allows delayed responses to life history by linking maternal body size and parasite infection to the future survival and fecundity of offspring. By systematically removing model structure I show that these delayed life history effects are weakly destabilising and allow parameters to lie closer to empirical estimates to generate observed hare population cycles. In a third model I structurally modify the simple strategic host-parasite model to make it spatially explicit by including diffusion of mountain hares and corresponding advection of parasites (transportation with host). From initial simulations I show that the spatially extended host-parasite equations are able to generate periodic travelling waves (PTWs) of hare and parasite abundance. This is a newly documented behaviour in these widely used host-parasite equations. While PTWs are a new potential scenario under which cyclic hare dynamics could be explained, further mathematical development is required to determine whether adding space can generate realistic dynamics with parameters that lie closer to empirical estimates. In the general thesis discussion I deliberate on whether a hare-parasite model has been identified which can be considered the right balance between abstraction and relevant detail for this system