Number Of Disjunctions Research Articles

A parameterized view on the complexity of dependence and independence logic

Abstract In this paper, we investigate the parameterized complexity of model checking for Dependence and Independence logic, which are well studied logics in the area of Team Semantics. We start with a list of nine immediate parameterizations for this problem, namely the number of disjunctions (i.e. splits)/(free) variables/universal quantifiers, formula-size, the tree-width of the Gaifman graph of the input structure, the size of the universe/team and the arity of dependence atoms. We present a comprehensive picture of the parameterized complexity of model checking and obtain a division of the problem into tractable and various intractable degrees. Furthermore, we also consider the complexity of the most important variants (data and expression complexity) of the model checking problem by fixing parts of the input.

Parameterised complexity of model checking and satisfiability in propositional dependence logic

Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be NP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is FPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture.

Mosses of the Dominican Republic: Species Catalogue, Elevation Distribution and Floristic Affinities

Abstract. The Dominican Republic moss flora stands out within the Caribbean countries because of the high species richness and number of disjuncts. The flora is comprised of 467 taxa in 207 genera, and 61 families. We report 62 new records and 82 disjuncts for this flora that shows affinity with other Greater Antilles and Central America. Within the context of the Caribbean and in terms of conservation, this flora is important because it represents both the highest reported moss species richness and 82 unique disjuncts within the West Indies.

Mining optimized gain rules for numeric attributes

Association rules are useful for determining correlations between attributes of a relation and have applications in the marketing, financial, and retail sectors. Furthermore, optimized association rules are an effective way to focus on the most interesting characteristics involving certain attributes. Optimized association rules are permitted to contain uninstantiated attributes and the problem is to determine instantiations such that either the support, confidence, or gain of the rule is maximized. In this paper, we generalize the optimized gain association rule problem by permitting rules to contain disjunctions over uninstantiated numeric attributes. Our generalized association rules enable us to extract more useful information about seasonal and local patterns involving the uninstantiated attribute. For rules containing a single numeric attribute, we present an algorithm with linear complexity for computing optimized gain rules. Furthermore, we propose a bucketing technique that can result in a significant reduction in input size by coalescing contiguous values without sacrificing optimality. We also present an approximation algorithm based on dynamic programming for two numeric attributes. Using recent results on binary space partitioning trees, we show that the approximations are within a constant factor of the optimal optimized gain rules. Our experimental results with synthetic data sets for a single numeric attribute demonstrate that our algorithm scales up linearly with the attribute's domain size as well as the number of disjunctions. In addition, we show that applying our optimized rule framework to a population survey real-life data set enables us to discover interesting underlying correlations among the attributes.

Mining optimized support rules for numeric attributes

Mining association rules on large data sets have received considerable attention in recent years. Association rules are useful for determining correlations between attributes of a relation and have applications in marketing, financial and retail sectors. Furthermore, optimized association rules are an effective way to focus on the most interesting characteristics involving certain attributes. Optimized association rules are permitted to contain uninstantiated attributes and the problem is to determine instantiations such that either the support, confidence or gain of the rule is maximized. In this paper, we generalize the optimized support association rule problem by permitting rules to contain disjunctions over uninstantiated numeric attributes. Our generalized association rules enable us to extract more useful information about seasonal and local patterns involving the uninstantiated attribute. For rules containing a single numeric attribute, we present a dynamic programming algorithm for computing optimized association rules. Furthermore, we propose bucketing technique for reducing the input size, and a divide and conquer strategy that improves the performance significantly without sacrificing optimality. We also present approximation algorithms based on dynamic programming for two numeric attributes. Our experimental results for a single numeric attribute indicate that our bucketing and divide and conquer enhancements are very effective in reducing the execution times and memory requirements of our dynamic programming algorithm. Furthermore, they show that our algorithms scale up almost linearly with the attribute's domain size as well as the number of disjunctions.

Geographic Variation in Eucalyptus diversifolia (Myrtaceae) and the Recognition of New Subspecies E. diversifolia subsp. hesperia and E. diversifolia subsp. megacarpa

Patterns of geographic variation in morphological and chemical characters are documented in Eucalyptus diversifolia Bonpl. (soap mallee, white coastal mallee). This species is found in coastal and subcoastal Australia from southern Western Australia to Cape Nelson (western Victoria), with a number of disjunctions in the intervening region. Morphological data from adult plants collected at field localities and seedlings grown under uniform conditions were analysed using univariate and multivariate methods, including oneway ANOVA, multiple comparison tests, non-metric multidimensional scaling (NMDS), nearest neighbour networks, and minimum spanning trees. Seedling material was tested for isozyme polymorphism, and adult leaf flavonoids were analysed using liquid chromatography. Morphological and chemical characters are also documented in E. aff. diversifolia, a closely related but unnamed taxon restricted to ironstone outcrops near Norseman (WA), and putative E. diversifolia- E. baxteri hybrids from Cape Nelson. Congruent patterns in data sets distinguish three groups of E. diversifolia adults and progeny: (1) those to the west of the Nullarbor disjunction; (2) South Australian populations to the east of this disjunction; and (3) those from Cape Nelson. Formal taxonomic recognition of the three forms at subspecific level is established, namely E. diversifolia subsp. diversifolia, E. diversifolia subsp. hesperia, and E. diversifolia subsp. megacarpa. Patterns of geographic affinity between populations are consistent with a hypothesis of genetic exchange between normally disjunct regional populations of E. diversifolia via coastal land-bridges exposed during periodic times of low sea level since the mid Tertiary.

On the distribution of tree weta in the North Island, New Zealand

The distribution in the North Island of three species of tree weta (Hemideina thoracica, H. crassidens and H. trewicki) is described from field surveys. The two most widespread species (H. thoracica and H. crassidens) were generally parapatric but the boundary between the two was rather complex with a number of disjunctions. Most notable were the relict populations of H. crassidens isolated on Mt Ruapehu (39°17'S) and Mt Taranaki (39°17'S). The main boundary between these two species crosses the North Island at approximately 40° 20’ S. A recently described species (H. trewicki), found only in the Hawkes Bay region, is sympatric with H. thoracica over much of its range. These weta probably developed into separate species after they became isolated by geophysical processes, and their subsequent distribution has been the result of recent climate‐related dispersal.

Alpine plants of phytogeographic interest on northwestern Vancouver Island

Forty-four alpine taxa of phytogeographic interest are reported for seven mountain peaks on northwestern Vancouver Island, and their distribution is discussed. These taxa include two of the Queen Charlotte Islands endemics, two of the Olympic Peninsula endemics, one new record for North America, five new records for Vancouver Island, and a number of disjuncts. The relation of the alpine flora of the Vancouver Island Ranges to other mountain systems and phytogeographic evidence for nonglaciated refugia on Vancouver Island are discussed.