## Algorithms and Complexity in Mathematics, Epistemology and Science

### 5 May 2015 - 8 May 2015

ACMES (Algorithms and Complexity in Mathematics, Epistemology and Science) is a multidisciplinary conference that focuses on a combination of the science of reliability and uncertainty quantification with conceptual and foundational issues concerning reliability in the application of scientific theories to real phenomena. The conference integrates longer talks from six leading computational scientists and philosophers of science with shorter computational research contributions from others, including graduate students, in computational science and epistemology of science.

ACMES is held in conjunction with Southern Ontario Numerical Analysis Day (SONAD). Read more about ACMES.

### INVITED TALKS

**Anouk Barberousse, History and Philsophy of Science, Université Lille 1, France
Community Modeling Systems as a Challenge to Reliability**

Climate computer simulations involve large teams of researchers who have to collaborate on designing and using computer programmes. Several disciplines are concerned: statistical physics, hydrodynamics, geologists, applied mathematicians, computer scientists, etc. In order to better understand how reliable knowledge is produced via climate simulations, I shall focus on several examples of community modelling involving different types of collaboration, from more centralized to more open ones, and I shall examine in each case how reliability is achieved. At first view, it might seem that reliability is directly related with centralization; however, as climate modeling is subject to the time constraint, which demands the results to come at a quick pace, centralized modes of collaboration may not be the most efficient ones.

**Robert Batterman, Department of Philosophy, University of Pittsburgh
Asymptotics, Minimal Models, Multiscale Techniques**

Much of applied mathematical modeling involves appeal to simple, “toy,” or “minimal” models. A minimal model is one that “most economically caricatures the essential physics.” [N. Goldenfeld] The requirement of economy is important and it is what allows one to draw (at least some) comparisons between various examples from across the sciences. Thus, the fruitfly drosophila, is a minimal model for human biological evolution, the ascidians (sea squirts) are minimal models for some aspects of human developmental biology, lattice gas models function as mimimal models for certain investigations into the nature of fluid flow, and we shouldn’t forget the importance of the Ising model and its various generalizations for understand phase transitions in both fluids and magnets. This talk addresses the question of how it is possible that such extreme caricatures can play explanatory and sometimes predictive roles in our attempts to model more complex and real systems.

**Max Gunzburger, Department of Applied Mathematics, Florida State University
Uncertainty Quantification for Complex Systems**

UQ efforts for complex systems such as those governed by partial differential equations require computationally expensive means to determine the uncertainties of system outputs from given uncertainty information about system inputs. This effort suffers from the dreaded “curse of dimensionality:” the explosive growth in computational expense as the number of uncertain variables increases and/or the desired accuracy of approximations improves. We discuss several probabilistically based approaches for dealing with such UQ problems as well as model calibration, design, and control problems and to applications for risk quantification and rare events.

**Ursula Martin, Department of Computer Science, Oxford
Mathematical Practice, Crowdsourcing and Social Machines**

Mathematical practice is an emerging interdisciplinary field which draws on philosophy, social science and ethnography, and the input of mathematicians themselves, to understand how mathematics is produced. Online mathematical activity provides a rich source of data for empirical investigation of mathematical practice – for example the community question answering system mathoverflow contains around 40,000 mathematical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Such investigations show the importance of “soft” aspects such as analogy and creativity, alongside formal deduction, in the production of mathematics, and give us new ways to think about the possible complementary roles of people and machines in creating new mathematical knowledge.

Social machines are new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. I present progress on a research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, which is being pursued at Oxford under an EPSRC Fellowship.

**Jesús Sanz-Serna, Department of Applied Mathematics, Universidad Carlos III de Madrid
The Power of Randomness**

Many phenomena around us are random and mathematics, as a pattern-seeking science, has succeeded in making sense of them. Unfortunately our minds do not operate in ways that allow us to be in tune with randomness. My talk will be a series of examples that make apparent the difficulties we all face when dealing with probability; these examples, while mathematically very simple, will hopefully be thought-provoking.

**Mark Wilson, Department of Philosophy, University of Pittsburgh
Approximation’s Hidden Hand**

Language often works most efficiently if it practices a division of descriptive labor, in which different semantic chores are parceled out to different representations operating in coordinated harmony. In this talk, I’ll discuss how satellite “approximations” of a finite element stripe played a central but acknowledged role in keeping the development of classical mechanics moving forward in a profitable way.