Designing experimental conditions to use the Lotka-Volterra model to infer tumor cell line interaction types

The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures simultaneously. In addition to assessing each design for practical identifiability, we investigate how the predictive power of the model-i.e., its ability to fit data for initial ratios other than those to which it was calibrated-is affected by the choice of experimental design. The parallel calibration procedure is found to be optimal and is further tested on in silico data generated from a spatially-resolved cellular automaton model, which accounts for oxygen consumption and allows for variation in the intensity level of the interaction between the two cell lines. We use this study to highlight the care that must be taken when interpreting parameter estimates for the spatially-averaged Lotka-Volterra model when it is calibrated against data produced by the spatially-resolved cellular automaton model, since baseline competition for space and resources in the CA model may contribute to a discrepancy between the type of interaction used to generate the CA data and the type of interaction inferred by the LV model.Comment: 25 pages, 18 figure

2014 Conference Abstracts: Annual Undergraduate Research Conference at the Interface of Biology and Mathematics

Conference schedule and abstract book for the Sixth Annual Undergraduate Research Conference at the Interface of Biology and Mathematics Date: November 1-2, 2014Plenary Speakers: Joseph Tien, Associate Professor of Mathematics at The Ohio State University; and Jeremy Smith, Governor\u27s Chair at the University of Tennessee and Director of the University of Tennessee/Oak Ridge National Lab Center for Molecular Biophysic

AI-Assisted Discovery of Quantitative and Formal Models in Social Science

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we demonstrate the use of a machine learning system to aid the discovery of symbolic models that capture nonlinear and dynamical relationships in social science datasets. By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. Augmenting existing workflows with symbolic regression can help uncover novel relationships and explore counterfactual models during the scientific process. We propose that this AI-assisted framework can bridge parametric and non-parametric models commonly employed in social science research by systematically exploring the space of nonlinear models and enabling fine-grained control over expressivity and interpretability.Comment: 19 pages, 4 figure

Dinamica delle popolazioni: modelli deterministici di Lotka-Volterra

Lo scopo di questo lavoro di tesi è quello di analizzare i modelli deterministici di dinamica delle popolazioni, dal primo e più semplice modello Malthusiano per la descrizione del comportamento dinamico di un insieme di individui considerati pressoché identici, fino ad arrivare allo studio dei sistemi del tipo preda-predatore trattati grazie al famoso modello di Lotka-Volterra. Tale modello è stato studiato nella sua versione base, in cui esso descrive la dinamica di interazione tra due specie compresenti nello stesso ambiente, sia da un punto di vista puramente matematico sia tramite simulazioni numeriche. Successivamente il modello è stato complicato per descrivere in modo migliore sistemi reali in cui non sono disponibili risorse infinite per lo sviluppo degli individui grazie all’utilizzo di un termine derivato dal modello di crescita logistica. Successivamente si è passati allo studio di un’ultima complicazione del modello, trattando i sistemi a più specie, esponendo il costrutto matematico definente tali sistemi, da un punto di vista puramente teorico per il caso ad N specie, mentre invece è stato approfondito il caso particolare del tipo preda-preda-predatore studiandone le proprietà dinamiche è commentando le soluzioni ricavate nuovamente tramite simulazione. Infine, i modelli precedentemente esposti sono stati utilizzati per operare un confronto con alcuni dati provenienti da due ricerche appartenenti a due ambiti scientifici diversi

A DECISION SUPPORT SYSTEM FOR THE SPATIAL CONTROL OF INVASIVE BIOAGENTS

A Decision Support System (DSS) is developed and applied to the spatial control of invasive bioagents, exemplified in this study by the resident Canada goose species (Branta Canadensis) in the Anacostia River system of the District of Columbia. The DSS incorporates a model of goose movement that responds to resource distribution; a twocompartment Expert System (ES) that identifies the causes of goose congregation in hotspots (Diagnosis ES) and prescribes strategies for goose population control (Prescription ES); and a Geographic Information System (GIS) that stores, analyzes, and displays geographic data. The DSS runs on an HP xw8600 64-bit Workstation running Window XP Operating System. The mathematical model developed in this study simulates goose-resource dynamics using partial differential equations - solved numerically using the Finite Element Method (FEM). MATLAB software (v. 7.1) performed all simulations. ArcGIS software (v. 9.3) produced by Environmental Systems Research Institute (ESRI) was used to store and manipulate georeferenced data for mapping, image processing, data management, and hotspot analysis. The rule-based Expert Systems (ES) were implemented within the GIS via ModelBuilder, a modular and intuitive Graphical User Interface (GUI) of ArcGIS software. The Diagnosis ES was developed in three steps. The first step was to acquire knowledge about goose biology through a literature search and discussions with human experts. The second step was to formalize the knowledge acquired in step 1 in the form of logical sentences (IF-THEN statements) representing the goose invasion diagnosis rules. Finally, in the third step, the rules were translated into decision trees. The Prescription ES was developed by following the same steps as in the development of the Diagnosis ES, the major difference being that, in this case, knowledge was acquired relative to goose control strategies rather than overpopulation causes; and additionally, knowledge was formalized based on the Diagnosis and on other local factors. Results of the DSS application indicate that high accessibility to food and water resources is the most likely cause of the congregation of geese in the critical areas identified by the model. Other causes include high accessibility to breeding and nesting habitats, and supplementary, artificial food provided by people in urban areas. The DSS prescribed the application of chemical repellents at feeding sites as a goose control strategy (GCS) to reduce the quality of the food resources consumed by resident Canada geese, and therefore the densities of geese in the infested locations. Two other prescribed GCSs are egg destruction and harvest of breeding adult geese, both of which have direct impacts on the goose populations by reducing their densities at hotspots or slowing down their increase. Enclosing small wetlands with fencing and banning the feeding of geese in urban areas are other GCSs recommended by the ES. Model simulations predicted that these strategies would reduce goose densities at hotspots by over 90%. It is suggested that further research is needed to investigate the use of similar systems for the management of other invasive bioagents in ecologically similar environments

Bridging the Gap

The concept of resilience has arisen as a “new way of thinking”, becoming a response to both the causes and effects of ongoing global challenges. As it strongly stresses cities’ transformative potential, resilience’s final purpose is to prevent and manage unforeseen events and improve communities’ environmental and social quality. Although the resilience theory has been investigated in depth, several methodological challenges remain, mainly related to the concept’s practical sphere. As a matter of fact, resilience is commonly criticised for being too ambiguous and empty of meaning. At the same time, turning resilience into practice is not easy to do. This will arguably be one of the most impactful global issues for future research on resilience. The Special Issue “Bridging the Gap: The Measure of Urban Resilience” falls under this heading, and it seeks to synthesise state-of-the-art knowledge of theories and practices on measuring resilience. The Special Issue collected 11 papers that address the following questions: “What are the theoretical perspectives of measuring urban resilience? What are the existing methods for measuring urban resilience? What are the main features that a technique for measuring urban resilience needs to have? What is the role of measuring urban resilience in operationalising cities’ ability to adapt, recover and benefit from shocks?

Mathematical Manipulative Models: In Defense of Beanbag Biology

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education

Collaborating with the Behaving Machine: simple adaptive dynamical systems for generative and interactive music

Situated at the intersection of interactive computer music and generative art, this thesis is inspired by research in Artificial Life and Autonomous Robotics and applies some of the principles and methods of these fields in a practical music context. As such the project points toward a paradigm for computer music research and performance which comple- ments current mainstream approaches and develops upon existing creative applications of Artificial Life research. Many artists have adopted engineering techniques from the field of Artificial Life research as they seem to support a richer interactive experience with computers than is often achieved in digital interactive art. Moreover, the low level aspects of life which the research programme aims to model are often evident in these artistic appropriations in the form of bizarre and abstract but curiously familiar digital forms that somehow, despite their silicon make-up, appear to accord with biological convention. The initial aesthetic motivation for this project was very personal and stemmed from interests in adaptive systems and improvisation and a desire to unite the two. In sim- ple terms, I wanted to invite these synthetic critters up on stage and play with them. There has been some similar research in the musical domain, but this has focused on a very small selection of specific models and techniques which have been predominantly applied as compositional tools rather than for use in live generative music. This thesis considers the advantages of the Alife approach for contemporary computer musicians and offers specific examples of simple adaptive systems as components for both compo- sitional and performance tools. These models have been implemented in a range of generative and interactive works which are described here. These include generative sound installations, interactive instal- lations and a performance system for collaborative man-machine improvisation. Public response at exhibitions and concerts suggests that the approach taken here holds much promise