On the Herbrand-Kleene universe for nondeterministic computations

AbstractFor nondeterministic recursive equations over an arbitrary signature of function symbols including the nondeterministic choice operator “or” the interpretation is factorized according to the techniques developed by the present author (1982). It is shown that one can either associate an infinite tree with the equations, then interpret the function symbol “or” as a nondeterministic choice operator and so mapping the tree onto a set of infinite trees and then interpret these trees. Or one can interpret the recursive equation directly yielding a set-valued function. Both possibilities lead to the same result, i.e., one obtains a commuting diagram. However, one has to use more refined techniques than just powerdomains. This explains and solves a problem posed by Nivat (1980). Basically, the construction gives a generalization of the powerdomain approach applicable to arbitrary nonflat (nondiscrete) algebraic domains

A Pseudo-Analyzer Approach to Formal Group Laws Not of Operad Type

AbstractFormal group schemes, associated to affine group schemes or Lie groups by completion, can be described by classical formal group laws. More generally, cogroup objects in categories of complete algebras (e.g., associative) are described by group laws for operads or analyzers. M. Lazard has introduced analyzers to study formal group laws and group law chunks (truncated formal power series). A main example of a type of generalized formal group laws not given by an operad or analyzer are group laws corresponding to noncommutative complete Hopf algebras. To cover this case and other types of group laws, pseudo-analyzers are introduced. We point out differences to the (quadratic) operad case; e.g., there is no classification of group laws by Koszul duality. On the other hand we show how pseudo-analyzer cohomology can be used to describe extension of group law chunks

Invariant types in model theory

We study how the product of global invariant types interacts with the preorder of domination, i.e. semi-isolation by a small type, and the induced equivalence relation, domination-equivalence. We provide sufficient conditions for the latter to be a congruence with respect to the product, and show that this holds in various classes of theories. In this case, we develop a general theory of the quotient semigroup, the domination monoid, and carry out its computation in several cases of interest. Notably, we reduce its study in o-minimal theories to proving generation by 1-types, and completely characterise it in the case of Real Closed Fields. We also provide a full characterisation for the theory of dense meet-trees, and moreover show that the domination monoid is well-defined in certain expansions of it by binary relations. We give an example of a theory where the domination monoid is not commutative, and of one where it is not well-defined, correcting some overly general claims in the literature. We show that definability, finite satisfiability, generic stability, and weak orthogonality to a fixed type are all preserved downwards by domination, hence are domination-equivalence invariants. We study the dependence on the choice of monster model of the quotient of the space of global invariant types by domination-equivalence, and show that if the latter does not depend on the former then the theory under examination is NIP

Annual Report of the University, 1992-1993, Volumes 1-4

SIGNIFICANT DEVELOPMENTS Preparation, approval by President Peck, delivery to NMCHE of UNM\u27s response to House Memorials 38 and 25 (on minorities and women). Development and packaging of a presentation on minorities at UNM to Hispanic community people and organizations. Renewal of faculty instructional workload report and other information for use by President Peck and others in the President\u27s Council in testimony to the legislature on accountability by faculty. Significant workload and contributions to WICHE\u27s Diversity Project: - responses to long questionnaire - projected demographics - substitution for O. Forbes on planning for diversity Reprogramming of obsolete computer program of the University of Southern California\u27s Faculty Planning Model. Work remains incomplete. Support and staff work for University Planning Council, Faculty Senate Long Range Planning Committee, Senate President, Senate Budget Committee, Student Learning Outcomes Assessment Committee, Admissions and Registration Committee, Staff Council; Graduate Petition and grade Review Subcommittee Service to NMCHE\u27s Outcomes Assessment Advisory Group; NMCHE\u27s review group on diversity plans Service on Albuquerque Business/Education Compact Conducted several special data analyses to provide user outcome information for the Center for Academic Program Support (CAPS). Wrote reports to summarize analyses. Served in an advisory capacity to VP Zuniga Forbes for the two surveys (Campus Climate for Diversity, ACT Student Opinion Survey) and helped to draw the sample for the ACT survey. Conducted secondary analyses and prepared report of all analyses of the Freshman Survey (CIRP) for VP Zuniga Forbes. Gave presentation of CIRP findings to the Regents Subcommittee on Student Affairs. Conducted secondary analyses and prepared report of all analyses of the Campus Climate for Diversity Survey for VP Zuniga Forbes

The compositional and evolutionary logic of metabolism

Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which layers of that system emerged. Metabolism also serves as the foundation in other hierarchies, at least up to cellular integration including bioenergetics and molecular replication, and trophic ecology. The recapitulation of patterns first seen in metabolism, in these higher levels, suggests metabolism as a source of causation or constraint on many forms of organization in the biosphere. We identify as modules widely reused subsets of chemicals, reactions, or functions, each with a conserved internal structure. At the small molecule substrate level, module boundaries are generally associated with the most complex reaction mechanisms and the most conserved enzymes. Cofactors form a structurally and functionally distinctive control layer over the small-molecule substrate. Complex cofactors are often used at module boundaries of the substrate level, while simpler ones participate in widely used reactions. Cofactor functions thus act as "keys" that incorporate classes of organic reactions within biochemistry. The same modules that organize the compositional diversity of metabolism are argued to have governed long-term evolution. Early evolution of core metabolism, especially carbon-fixation, appears to have required few innovations among a small number of conserved modules, to produce adaptations to simple biogeochemical changes of environment. We demonstrate these features of metabolism at several levels of hierarchy, beginning with the small-molecule substrate and network architecture, continuing with cofactors and key conserved reactions, and culminating in the aggregation of multiple diverse physical and biochemical processes in cells.Comment: 56 pages, 28 figure