Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.

The surface electromyography-force relationship during isometric dorsiflexion in males and females

This study evaluated sex-related differences in the tibialis anterior (TA) surface electromyography (EMG) to force relationship. One-hundred participants (50 males and 50 females) performed three isometric contractions at 20, 40, 60, 80, and 100% of maximal voluntary contraction (MVC) in an apparatus designed to isolate the action of the dorsiflexors. The surface EMG signal was amplified (lOOOx), band-pass filtered (10-500Hz), and sampled at 2048 Hz. The load cell signal was low-passed filtered at 100 Hz and sampled at the same rate. Males were stronger than females {P <0.05). However, there was no significant difference in root-mean-square (RMS) values between sexes {P <0.05). Both sexes exhibited a quadratic increase in RMS across force levels (P <0.05). The mean power frequency (MNF) for males was greater than for females {P <0.05). Males and females exhibited a linear increase in both frequency measures up to 80% of MVC (P <0.05). Between 80 and 100% MVC, the frequency values for the females plateaued while males showed a decrease {P <0.05). The magnitude of the difference in MNF between males and females was consistent with sex-specific TA physiology. In general, the pattern of means for RMS and MNF between males and females revealed no sex-related differences in the surface EMG/force relationship. We therefore conclude that there are no sex-related differences in the gradation of muscle force.

Cognitive set, absorption, and achievement as moderators of the perceptual closure effect in picture priming /

The present study examined individual differences in Absorption and fantasy, as well as in Achiievement and achievement striving as possible moderators of the perceptual closure effect found by Snodgrass and Feenan (1990). The study also examined whether different instructions (experiential versus instrumental) interact with the personality variables to moderate the relationship between priming and subsequent performance on a picture completion task. 1 28 participants completed two sessions, one to fill out the MPQ and NEO personality inventories and the other to complete the experimental task. The experimental task consisted of a priming phase and a test phase, with pictures presented on a computer screen for both phases. Participants were shown 30 pictures in the priming phase, and then shovm the 30 primed pictures along with 30 new pictures for the test phase. Participants were randomly assigned to receive one of the two different instruction sets for the task. Two measures of performance were calculated, most fragmented measure and threshold. Results of the present study confirm that a five-second exposure time is long enough to produce the perceptual closure effect. The analysis of the two-way interaction effects indicated a significant quadratic interaction of Absorption with priming level on threshold performance. The results were in the opposite direction of predictions. Possible explanations for the Absorption results include lack of optimal conditions, lack of intrinsic motivation and measurement problems. Primary analyses also revealed two significant between-subject effects of fantasy and achievement striving on performance collapsed across priming levels. These results suggest that fantasy has a beneficial effect on performance at test for pictures primed at all levels, whereas achievement striving seems to have an adverse effect on performance at test for pictures primed at all levels. Results of the secondary analyses with a revised threshold performance measure indicated a significant quadratic interaction of Absorption, condition and priming level. In the experiential condition, test performance, based on Absorption scores for pictures primed at level 4, showed a positive slope and performance for pictures primed at levels 1 and 7 based on Absorption showed a negative slope. The reverse effect was found in the instrumental condition. The results suggest that Absorption, in combination with experiential involvement, may affect implicit memory. A second significant result of the secondary analyses was a linear three-way interaction of Achievement, condition and priming level on performance. Results suggest that as Achievement scores increased, test performance improved for less fragmented primed pictures in the instrumental condition and test performance improved for more highly fragmented primes in the experiential condition. Results from the secondary analyses suggest that the revised threshold measure may be more sensitive to individual differences. Results of the exploratory analyses with Openness to Experience, Conscientiousness and agentic positive emotionality (PEM-A) measures indicated no significant effects of any of these personality variables. Results suggest that facets of the scales may be more useful with regard to perceptual research, and that future research should examine narrowly focused personality traits as opposed to broader constructs.

Analysis Of The A11a22 X 11a11 And A 33a22 X 1 electronic transitions in selenocarbonyl difluoride

The absorption spectrum of F2CSe in the 18800-21900 cm-1 region has been recorded at -770 C and 220 C under the conditions of medium resolution. The responsible electronic promotion is TI* + n excitation which leads to 3A2 and lA2 excited states. Progressions in vI', v2', v3" v4' and v4" have been identified in the spectrum and have been analyzed in terms of vibronic transitions between a planar ground state and a nQnplanar excited state. The - 3 - 1 - 1 - 1 origins of the a A2 + X Al and A A2 + X Al systems were assigned to the bands at 19018 cm-l and 19689 cm-l . This has given a singlet-triplet splittl. n g lA2 - 3A2 P f 671 cm -1 The out-of-plane wagging levels were found to be anharmonic. 1 -1 Barrier heights of 2483 cm- and 2923 cm were obtained for the lA2 and 3A2 upper states from a fitting of the energy levels of a Lorentzian-quadratic function to the observed levels in the out-of-plane wagging modes. 1 3 For the A2 and A2 states nonplanar equilibrium angles of 30.10 and 31.40 have been evaluated respectively. i

ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

RelMDD-A Library for Manipulating Relations Based on MDDs

Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.