49,626 research outputs found
Latin directed triple systems
Abstract It is well known that given a Steiner triple system then a quasigroup can be formed by defining an operation · by the identities x · x = x and x · y = z where z is the third point in the block containing the pair {x, y}. The same is true for a Mendelsohn triple system where the pair (x, y) is considered to be ordered. But it is not true in general for directed triple systems. However directed triple systems which form quasigroups under this operation do exist. We call these Latin directed triple systems and in this paper begin the study of their existence and properties
Types of directed triple systems
We introduce three types of directed triple systems. Two of these, Mendelsohn directed triple systems and Latin directed triple systems, have previously appeared in the literature but we prove further results about them. The third type, which we call skewed directed triple systems, is new and we determine the existence spectrum to be v ≡ 1 (mod 3), v ≠ 7, except possibly for v = 22, as well as giving enumeration results for small orders
Storing RDF as a Graph
RDF is the first W3C standard for enriching information resources of the Web with detailed meta data. The semantics of RDF data is defined using a RDF schema. The most expressive language for querying RDF is RQL, which enables querying of semantics. In order to support RQL, a RDF storage system has to map the RDF graph model onto its storage structure. Several storage systems for RDF data have been developed, which store the RDF data as triples in a relational database. To evaluate an RQL query on those triple structures, the graph model has to be rebuilt from the triples.
In this paper, we presented a new approach to store RDF data as a graph in a object-oriented database. Our approach avoids the costly rebuilding of the graph and efficiently queries the storage structure directly. The advantages of our approach have been shown by performance test on our prototype implementation OO-Store
An enumeration of equilateral triangle dissections
We enumerate all dissections of an equilateral triangle into smaller
equilateral triangles up to size 20, where each triangle has integer side
lengths. A perfect dissection has no two triangles of the same side, counting
up- and down-oriented triangles as different. We computationally prove W. T.
Tutte's conjecture that the smallest perfect dissection has size 15 and we find
all perfect dissections up to size 20.Comment: Final version sent to journal
Enriching Knowledge Bases with Counting Quantifiers
Information extraction traditionally focuses on extracting relations between
identifiable entities, such as . Yet, texts
often also contain Counting information, stating that a subject is in a
specific relation with a number of objects, without mentioning the objects
themselves, for example, "California is divided into 58 counties". Such
counting quantifiers can help in a variety of tasks such as query answering or
knowledge base curation, but are neglected by prior work. This paper develops
the first full-fledged system for extracting counting information from text,
called CINEX. We employ distant supervision using fact counts from a knowledge
base as training seeds, and develop novel techniques for dealing with several
challenges: (i) non-maximal training seeds due to the incompleteness of
knowledge bases, (ii) sparse and skewed observations in text sources, and (iii)
high diversity of linguistic patterns. Experiments with five human-evaluated
relations show that CINEX can achieve 60% average precision for extracting
counting information. In a large-scale experiment, we demonstrate the potential
for knowledge base enrichment by applying CINEX to 2,474 frequent relations in
Wikidata. CINEX can assert the existence of 2.5M facts for 110 distinct
relations, which is 28% more than the existing Wikidata facts for these
relations.Comment: 16 pages, The 17th International Semantic Web Conference (ISWC 2018
Anticipation as prediction in the predication of data types
Every object in existence has its type. Every subject in language has its predicate. Every intension in logic has its extension. Each therefore has two levels but with the fundamental problem of the relationship between the two. The formalism of set theory cannot guarantee the two are co-extensive. That has to be imposed by the axiom of extensibility, which is inadequate for types as shown by Bertrand Russell's rami ed type theory, for language as by Henri Poincar e's impredication and for intension unless satisfying Port Royal's de nitive concept. An anticipatory system is usually de ned to contain its own future state. What is its type? What is its predicate? What is its extension? Set theory can well represent formally the weak anticipatory system, that is in a model of itself. However we have previously shown that the metaphysics of process category theory is needed to represent strong anticipation. Time belongs to extension not intension. The apparent prediction of strong anticipation is really in the structure of its predication. The typing of anticipation arises from a combination of and | respectively (co) multiplication of the (co)monad induced by adjointness of the system's own process. As a property of cartesian closed categories this predication has signi cance for all typing in general systems theory including even in the de nition of time itself
Minors for alternating dimaps
We develop a theory of minors for alternating dimaps --- orientably embedded
digraphs where, at each vertex, the incident edges (taken in the order given by
the embedding) are directed alternately into, and out of, the vertex. We show
that they are related by the triality relation of Tutte. They do not commute in
general, though do in many circumstances, and we characterise the situations
where they do. The relationship with triality is reminiscent of similar
relationships for binary functions, due to the author, so we characterise those
alternating dimaps which correspond to binary functions. We give a
characterisation of alternating dimaps of at most a given genus, using a finite
set of excluded minors. We also use the minor operations to define simple Tutte
invariants for alternating dimaps and characterise them. We establish a
connection with the Tutte polynomial, and pose the problem of characterising
universal Tutte-like invariants for alternating dimaps based on these minor
operations.Comment: 51 pages, 7 figure
- …