We introduce the Dynamic Influence Network (DIN), a novel visual analytics technique for representing and analyzing rule-based models of protein-protein interaction networks. Rule-based modeling has proved instrumental in developing biological models that are concise, comprehensible, easily extensible, and that mitigate the combinatorial complexity of multi-state and multi-component biological molecules. Our technique visualizes the dynamics of these rules as they evolve over time. Using the data produced by KaSim, an open source stochastic simulator of rule-based models written in the Kappa language, DINs provide a node-link diagram that represents the influence that each rule has on the other rules. That is, rather than representing individual biological components or types, we instead represent the rules about them (as nodes) and the current influence of these rules (as links). Using our interactive DIN-Viz software tool, researchers are able to query this dynamic network to find meaningful patterns about biological processes, and to identify salient aspects of complex rule-based models. To evaluate the effectiveness of our approach, we investigate a simulation of a circadian clock model that illustrates the oscillatory behavior of the KaiC protein phosphorylation cycle.
Elmqvist and Tsigas @cite_11 introduce the Growing Squares and Growing Polygons techniques to explore causality, finding that they are significantly more useful than static graphs or Hesse diagrams for reasoning about systems. In these techniques, differently sized shapes are used to indicate information flow in a system of interacting processes, filling with different colors to represent the changing influence of the different processes.
@cite_11
2012703196 2018047324 2053190303 1495092270
Causality visualization is an important tool for many scientific domains that involve complex interactions between multiple entities (examples include parallel and distributed systems in computer science). However, traditional visualization techniques such as Hasse diagrams are not well-suited to large system executions, and users often have difficulties answering even basic questions using them, or have to spend inordinate amounts of time to do so. In this paper, we present the Growing Squares and Growing Polygons methods, two sibling visualization techniques that were designed to solve this problem by providing efficient 2D causality visualization through the use of color, texture, and animation. Both techniques have abandoned the traditional linear timeline and instead map the time parameter to the size of geometrical primitives representing the processes; in the Growing Squares case, each process is a color-coded square that receives color influences from other process squares as messages reach it; in the Growing Polygons case, each process is instead an n-sided polygon consisting of triangular sectors showing color-coded influences from the other processes. We have performed user studies of both techniques, comparing them with Hasse diagrams, and they have been shown to be significantly more efficient than old techniques, both in terms of objective performance as well as the subjective opinion of the test subjects (the Growing Squares technique is, however, only significantly more efficient for small systems). A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up in numerous and often surprising contexts in both fields. But, perhaps, we should start with a few words about graphs in general. They are, of course, one of the prime objects of study in Discrete Mathematics. However, graphs are among the most ubiquitous models of both natural and human-made structures. In the natural and social sciences they model relations among species, societies, companies, etc. In computer science, they represent networks of communication, data organization, computational devices as well as the flow of computation, and more. In mathematics, Cayley graphs are useful in Group Theory. Graphs carry a natural metric and are therefore useful in Geometry, and though they are “just” one-dimensional complexes, they are useful in certain parts of Topology, e.g. Knot Theory. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. The study of these models calls, then, for the comprehension of the significant structural properties of the relevant graphs. But are there nontrivial structural properties which are universally important? Expansion of a graph requires that it is simultaneously sparse and highly connected. Expander graphs were first defined by Bassalygo and Pinsker, and their existence first proved by Pinsker in the early ’70s. The property of being an expander seems significant in many of these mathematical, computational and physical contexts. It is not surprising that expanders are useful in the design and analysis of communication networks. What is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness. In mathematics, we will encounter e.g. their role in the study of metric embeddings, and in particular in work around the Baum-Connes Conjecture. Expansion is closely related to the convergence rates of Markov Chains, and so they play a key role in the study of Monte-Carlo algorithms in statistical mechanics and in a host of practical computational applications. The list of such interesting and fruitful connections goes on and on with so many applications we will not even Abstract Objects move, collide, flow, bend, heat up, cool down, stretch, compress, and boil. These and other things that cause changes in objects over time are intuitively characterized as processes . To understand commonsense physical reasoning and make programs that interact with the physical world as well as people do we must understand qualitative reasoning about processes, when they will occur, their effects, and when they will stop. Qualitative process theory defines a simple notion of physical process that appears useful as a language in which to write dynamical theories. Reasoning about processes also motivates a new qualitative representation for quantity in terms of inequalities, called the quantity space . This paper describes the basic concepts of qualitative process theory, several different kinds of reasoning that can be performed with them, and discusses its implications for causal reasoning. Several extended examples illustrate the utility of the theory, including figuring out that a boiler can blow up, that an oscillator with friction will eventually stop, and how to say that you can pull with a string, but not push with it. We introduce a mechanism called "morphing" for introducing structure or randomness into a wide variety of problems. We illustrate the usefulness of morphing by performing several different experimental studies. These studies identify the impact of a "small-world" topology on the cost of coloring graphs, of asymmetry on the cost of finding the optimal TSP tour, and of the dimensionality of space on the cost of finding the optimal TSP tour. We predict that morphing will find many other uses.