Methodological Fundamentalism: or why Batterman’s Different Notions of ‘Fundamentalism’ may not make a Difference

I argue that the distinctions Robert Batterman (2004) presents between ‘epistemically fundamental’ versus ‘ontologically fundamental’ theoretical approaches can be subsumed by methodologically fundamental procedures. I characterize precisely what is meant by a methodologically fundamental procedure, which involves, among other things, the use of multilinear graded algebras in a theory’s formalism. For example, one such class of algebras I discuss are the Clifford (or Geometric) algebras. Aside from their being touted by many as a “unified mathematical language for physics,” (Hestenes (1984, 1986) Lasenby, et. al. (2000)) Finkelstein (2001, 2004) and others have demonstrated that the techniques of multilinear algebraic ‘expansion and contraction’ exhibit a robust regularizablilty. That is to say, such regularization has been demonstrated to remove singularities, which would otherwise appear in standard field-theoretic, mathematical characterizations of a physical theory. I claim that the existence of such methodologically fundamental procedures calls into question one of Batterman’s central points, that “our explanatory physical practice demands that we appeal essentially to (infinite) idealizations” (2003, 7) exhibited, for example, by singularities in the case of modeling critical phenomena, like fluid droplet formation. By way of counterexample, in the field of computational fluid dynamics (CFD), I discuss the work of Mann & Rockwood (2003) and Gerik Scheuermann, (2002). In the concluding section, I sketch a methodologically fundamental procedure potentially applicable to more general classes of critical phenomena appearing in fluid dynamics

Review of research in feature-based design

Research in feature-based design is reviewed. Feature-based design is regarded as a key factor towards CAD/CAPP integration from a process planning point of view. From a design point of view, feature-based design offers possibilities for supporting the design process better than current CAD systems do. The evolution of feature definitions is briefly discussed. Features and their role in the design process and as representatives of design-objects and design-object knowledge are discussed. The main research issues related to feature-based design are outlined. These are: feature representation, features and tolerances, feature validation, multiple viewpoints towards features, features and standardization, and features and languages. An overview of some academic feature-based design systems is provided. Future research issues in feature-based design are outlined. The conclusion is that feature-based design is still in its infancy, and that more research is needed for a better support of the design process and better integration with manufacturing, although major advances have already been made

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

Symbolic modeling of structural relationships in the Foundational Model of Anatomy

The need for a sharable resource that can provide deep anatomical knowledge and support inference for biomedical applications has recently been the driving force in the creation of biomedical ontologies. Previous attempts at the symbolic representation of anatomical relationships necessary for such ontologies have been largely limited to general partonomy and class subsumption. We propose an ontology of anatomical relationships beyond class assignments and generic part-whole relations and illustrate the inheritance of structural attributes in the Digital Anatomist Foundational Model of Anatomy. Our purpose is to generate a symbolic model that accommodates all structural relationships and physical properties required to comprehensively and explicitly describe the physical organization of the human body

Investigating complex networks with inverse models: analytical aspects of spatial leakage and connectivity estimation

Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated connectivity estimation may be affected by spatial leakage, an artifact of inverse modeling that limits the interpretability of network analysis. This paper investigates general analytical aspects pertaining to this issue. First, the existence of spatial leakage is derived from the topological structure of inverse operators. Then, the geometry of spatial leakage is modeled and used to define a geometric correction scheme, which limits spatial leakage effects in connectivity estimation. Finally, this new approach for network analysis is compared analytically to existing methods based on linear regressions, which are shown to yield biased coupling estimates.Comment: 19 pages, 4 figures, including 5 appendices; v2: minor edits, 1 appendix added; v3: expanded version, v4: minor edit

Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes

We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of symmetry for radial manifold shapes, we develop spectral Galerkin methods based on hyperinterpolation with Lebedev quadratures for $L^2$-projection to spherical harmonics. We demonstrate our methods by investigating hydrodynamic responses as the surface geometry is varied. Relative to the case of a sphere, we find significant changes can occur in the observed hydrodynamic flow responses as exhibited by quantitative and topological transitions in the structure of the flow. We present numerical results based on the Rayleigh-Dissipation principle to gain further insights into these flow responses. We investigate the roles played by the geometry especially concerning the positive and negative Gaussian curvature of the interface. We provide general approaches for taking geometric effects into account for investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure