132 research outputs found
Nested Balanced Incomplete Block Designs
If the blocks of a balanced incomplete block design (BIBD) with v treatments and with parameters (v; b1;r;k1) are each partitioned into sub-blocks of size k2, and the b2 =b1k1=k2 sub-blocks themselves constitute a BIBD with parameters (v; b2;r;k2), then the system of blocks, sub-blocks and treatments is, by de4nition, a nested BIBD (NBIBD). Whist tournaments are special types of NBIBD with k1 =2k2= 4. Although NBIBDs were introduced in the statistical literature in 1967 and have subsequently received occasional attention there, they are almost unknown in the combinatorial literature, except in the literature of tournaments, and detailed combinatorial studies of them have been lacking. The present paper therefore reviews and extends mathematical knowledge of NBIBDs. Isomorphism and automorphisms are defined for NBIBDs, and methods of construction are outlined. Some special types of NBIBD are de4ned and illustrated. A first-ever detailed table of NBIBDs with v⩜16, r⩜30 is provided; this table contains many newly discovered NBIBDs. © 2001 Elsevier Science B.V. All rights reserved
Methodological Fundamentalism: or why Battermanâs Different Notions of âFundamentalismâ may not make a Difference
I argue that the distinctions Robert Batterman (2004) presents between âepistemically fundamentalâ versus âontologically fundamentalâ 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 theoryâs 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 âunified mathematical language for physics,â (Hestenes (1984, 1986) Lasenby, et. al. (2000)) Finkelstein (2001, 2004) and others have demonstrated that the techniques of multilinear algebraic âexpansion and contractionâ 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 Battermanâs central points, that âour explanatory physical practice demands that we appeal essentially to (infinite) idealizationsâ (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
Evolution of Metabolic Networks: A Computational Framework
Background: The metabolic architectures of extant organisms share many key pathways such as the citric acid
cycle, glycolysis, or the biosynthesis of most amino acids. Several competing hypotheses for the evolutionary
mechanisms that shape metabolic networks have been discussed in the literature, each of which ïŹnds support
from comparative analysis of extant genomes. Alternatively, the principles of metabolic evolution can be studied
by direct computer simulation. This requires, however, an explicit implementation of all pertinent components: a
universe of chemical reaction upon which the metabolism is built, an explicit representation of the enzymes that
implement the metabolism, of a genetic system that encodes these enzymes, and of a ïŹtness function that can
be selected for.
Results: We describe here a simulation environment that implements all these components in a simpliïŹed ways so
that large-scale evolutionary studies are feasible. We employ an artiïŹcial chemistry that views chemical reactions as
graph rewriting operations and utilizes a toy-version of quantum chemistry to derive thermodynamic parameters.
Minimalist organisms with simple string-encoded genomes produce model ribozymes whose catalytic activity is
determined by an ad hoc mapping between their secondary structure and the transition state graphs that they
stabilize. Fitness is computed utilizing the ideas of metabolic ïŹux analysis. We present an implementation of the
complete system and ïŹrst simulation results.
Conclusions: The simulation system presented here allows coherent investigations into the evolutionary mechanisms of the ïŹrst steps of metabolic evolution using a self-consistent toy univers
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