Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

Isotactics as a foundation for alignment and abstraction of behavioral models

There are many use cases in business process management that require the comparison of behavioral models. For instance, verifying equivalence is the basis for assessing whether a technical workflow correctly implements a business process, or whether a process realization conforms to a reference process. This paper proposes an equivalence relation for models that describe behaviors based on the concurrency semantics of net theory and for which an alignment relation has been defined. This equivalence, called isotactics, preserves the level of concurrency of aligned operations. Furthermore, we elaborate on the conditions under which an alignment relation can be classified as an abstraction. Finally, we show that alignment relations induced by structural refinements of behavioral models are indeed behavioral abstractions

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and firings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our first result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and have infinitely many states, but we show how they can be refined to get an equivalent finitely-branching model. In it, states are equipped with symmetries, which are essential for the existence of a minimal, often finite-state, model. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework: we model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Then we define a well-behaved category of coalgebras. Our coalgebraic model is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin

On the discovery of social roles in large scale social systems

The social role of a participant in a social system is a label conceptualizing the circumstances under which she interacts within it. They may be used as a theoretical tool that explains why and how users participate in an online social system. Social role analysis also serves practical purposes, such as reducing the structure of complex systems to rela- tionships among roles rather than alters, and enabling a comparison of social systems that emerge in similar contexts. This article presents a data-driven approach for the discovery of social roles in large scale social systems. Motivated by an analysis of the present art, the method discovers roles by the conditional triad censuses of user ego-networks, which is a promising tool because they capture the degree to which basic social forces push upon a user to interact with others. Clusters of censuses, inferred from samples of large scale network carefully chosen to preserve local structural prop- erties, define the social roles. The promise of the method is demonstrated by discussing and discovering the roles that emerge in both Facebook and Wikipedia. The article con- cludes with a discussion of the challenges and future opportunities in the discovery of social roles in large social systems

Using ACL2 to Verify Loop Pipelining in Behavioral Synthesis

Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis. Certifying the loop pipelining algorithm is challenging because there is a huge semantic gap between the input sequential design and the output pipelined implementation making it infeasible to verify their equivalence with automated sequential equivalence checking techniques. We discuss our ongoing effort using ACL2 to certify loop pipelining transformation. The completion of the proof is work in progress. However, some of the insights developed so far may already be of value to the ACL2 community. In particular, we discuss the key invariant we formalized, which is very different from that used in most pipeline proofs. We discuss the needs for this invariant, its formalization in ACL2, and our envisioned proof using the invariant. We also discuss some trade-offs, challenges, and insights developed in course of the project.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Behavioral Communities and the Atomic Structure of Networks

We develop a theory of `behavioral communities' and the `atomic structure' of networks. We define atoms to be groups of agents whose behaviors always match each other in a set of coordination games played on the network. This provides a microfoundation for a method of detecting communities in social and economic networks. We provide theoretical results characterizing such behavior-based communities and atomic structures and discussing their properties in large random networks. We also provide an algorithm for identifying behavioral communities. We discuss applications including: a method of estimating underlying preferences by observing behavioral conventions in data, and optimally seeding diffusion processes when there are peer interactions and homophily. We illustrate the techniques with applications to high school friendship networks and rural village networks

Structural, item, and test generalizability of the psychopathology checklist - revised to offenders with intellectual disabilities

The Psychopathy Checklist–Revised (PCL-R) is the most widely used measure of psychopathy in forensic clinical practice, but the generalizability of the measure to offenders with intellectual disabilities (ID) has not been clearly established. This study examined the structural equivalence and scalar equivalence of the PCL-R in a sample of 185 male offenders with ID in forensic mental health settings, as compared with a sample of 1,212 male prisoners without ID. Three models of the PCL-R’s factor structure were evaluated with confirmatory factor analysis. The 3-factor hierarchical model of psychopathy was found to be a good fit to the ID PCL-R data, whereas neither the 4-factor model nor the traditional 2-factor model fitted. There were no cross-group differences in the factor structure, providing evidence of structural equivalence. However, item response theory analyses indicated metric differences in the ratings of psychopathy symptoms between the ID group and the comparison prisoner group. This finding has potential implications for the interpretation of PCL-R scores obtained with people with ID in forensic psychiatric settings