Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...

Given a positive integer M and real number x∈(0,1], we call q∈(1,M+1] univoque simply normal base of x if there exists unique sequence (di)∈{0,1,…,M}N such that x=∑i=1∞diq−i. Similarly, is called irregular x=∑i=1∞diq−i the (di) has no digit frequency. Let USN(x) UIr(x) be sets bases x, respectively. In this paper show for any x∈(0,1] both have full Hausdorff dimension. Furthermore, given finite...

In prior work [7] we considered networks of agents who have knowledge bases in first order logic, and report facts to their neighbors that are in their common languages and are provable from their knowledge bases, in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider’s sen...

We present discriminative Gaifman models, a novel family of relational machine learning models. Gaifman models learn feature representations bottom up from representations of locally connected and bounded-size regions of knowledge bases (KBs). Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of overfittin...

The history of tea is poorly known, mainly due to the questionable identification of decayed tea plants in archaeological samples. This paper attempts to test the utility of calciphytoliths (calcium oxalate crystals) for the identification of tea in archaeological samples. It provides the first survey of the macropatterns of calciphytoliths in several species of Theaceae and common non-Theaceae...

With increased application of fuzzy logic in complex control systems, there is a need for a structured methodological approach in the development of fuzzy logic systems. Current fuzzy logic systems are developed based on individualistic bases and cannot face the challenge of interacting with other (fuzzy) systems in a dynamic environment. In this chapter a method for development of fuzzy system...

A significant obstacle to the development of intelligent natural language processing systems is the lack of rich knowledge bases containing representations of world knowledge. For experimental systems it is common practice to construct small knowledge bases by hand; however, this approach does not scale well to large systems. An alternative is to attempt to extract the desired information from ...

Ab initio quantum mechanical calculations at the MP2 level were used for an extensive study concerning the stability of hydrogen-bonded complexes formed by pyrrole and thiophene, which are the most common building blocks of conducting polymers, and DNA bases. Results indicated that very stable complexes were formed with pyrrole, which shows a clear tendency to form specific hydrogen-bonding int...

We formalize the problem of recovering the evolutionary history of a set of genomes that are related to an unseen common ancestor genome by operations of speciation, deletion, insertion, duplication, and rearrangement of segments of bases. The problem is examined in the limit as the number of bases in each genome goes to infinity. In this limit, the chromosomes are represented by continuous cir...

Knowledge compilation is a common technique for propositional logic knowledge bases. A given knowledge base is transformed into a normal form, for which queries can be answered efficiently. This precompilation step is expensive, but it only has to be performed once. We apply this technique to knowledge bases defined in the Description Logic ALC. We discuss an efficient satisfiability test as we...