Search results for "Theoretical Computer Science"
showing 10 items of 1151 documents
Finitary formal topologies and Stone’s representation theorem
2008
AbstractWe study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theorem for distributive lattices. We work within the framework of a minimalist foundation (as proposed by Maria Emilia Maietti and the second author). Both inductive and co-inductive methods are used in most proofs.
Sudoku – A Language Description Case Study
2009
A complete language description includes the structure as well as constraints, textual representation, graphical representation, and behaviour (transformation and execution). As a case study in language description, we consider Sudoku as a language, where a Sudoku puzzle is an instance of the language. Thus we are able to apply meta-model-based technologies for the creation of a language description for Sudoku, including correctness checking of a puzzle, and solving strategies. We identify what has to be expressed and how this can be done with the technology available today.
Two-dimensional filters for structured text
1997
The paper introduces a method for defining filters for structured text. In the method, the text structure is originally defined by a grammar consisting of a set of productions. To describe the information interests, a two-dimensional template is first created interactively from the grammar to show the structure of a set of textual elements, at a chosen level of detail. The template depicts the hierarchical structure of the elements and indicates also optionality, alternatives, and iteration in the structure. Then, the template is filled by constraints and annotations. The constraints allow giving conditions to the content of parts, to the position of parts in an ordered set of parts, and to…
Reflections towards a generative theory of musical parallelism
2010
Parallelism plays a core role in Lerdahl and Jackendoff's (1983) GTTM, as it rules the emergence of motivic, metrical, grouping and even formal structures. Due to the high amount of detail and complexity characterising associational structures, neither explicit model nor systematic methodology of parallelism-based structural inference has been included into the GTTM. This paper develops a methodological and computational answer to this problem founded on a computational modelling of pattern extraction operations. The paper focuses in particular on the methodological interest of the pattern mining formalism, and in particular its application to the formalisation of grouping and metrical str…
Graphical Models for Dependencies and Associations
1992
The role of graphical representations is described in distinguishing various special forms of independency structure that can arise with multivariate data, especially in observational studies in the social sciences. Conventions for constructing the graphs and strategies for analysing three sets of data are summarized. Finally some directions for desirable future work are outlined.
VoxelMages: a general-purpose graphical interface for designing geometries and processing DICOM images for PENELOPE
2016
The design and construction of geometries for Monte Carlo calculations is an error-prone, time-consuming, and complex step in simulations describing particle interactions and transport in the field of medical physics. The software VoxelMages has been developed to help the user in this task. It allows to design complex geometries and to process DICOM image files for simulations with the general-purpose Monte Carlo code PENELOPE in an easy and straightforward way. VoxelMages also allows to import DICOM-RT structure contour information as delivered by a treatment planning system. Its main characteristics, usage and performance benchmarking are described in detail.
Employing artificial neural networks to find reaction coordinates and pathways for self-assembly
2021
Capturing the autonomous self-assembly of molecular building blocks in computer simulations is a persistent challenge, requiring to model complex interactions and to access long time scales. Advanced sampling methods allow to bridge these time scales but typically require to construct accurate low-dimensional representations of the transition pathways. In this work, we demonstrate for the self-assembly of two single-stranded DNA fragments into a ring-like structure how autoencoder architectures based on unsupervised neural networks can be employed to reliably expose transition pathways and to provide a suitable low-dimensional representation. The assembly occurs as a two-step process throug…
Preventing Overlaps in Agglomerative Hierarchical Conceptual Clustering
2020
Hierarchical Clustering is an unsupervised learning task, whi-ch seeks to build a set of clusters ordered by the inclusion relation. It is usually assumed that the result is a tree-like structure with no overlapping clusters, i.e., where clusters are either disjoint or nested. In Hierarchical Conceptual Clustering (HCC), each cluster is provided with a conceptual description which belongs to a predefined set called the pattern language. Depending on the application domain, the elements in the pattern language can be of different nature: logical formulas, graphs, tests on the attributes, etc. In this paper, we tackle the issue of overlapping concepts in the agglomerative approach of HCC. We …
A Concept for Quantitative Comparison of Mathematical and Natural Language and its possible Effect on Learning
2017
Starting with the question whether there is a connection between the mathematical capabilities of a person and his or her mother tongue, we introduce a new modeling approach to quantitatively compare natural languages with mathematical language. The question arises from educational assessment studies that indicate such a relation. Texts written in natural languages can be deconstructed into a dependence graph, in simple cases a dependence tree. The same kind of deconstruction is also possible for mathematical texts. This gives an idea of how to quantitatively compare mathematical and natural language. To that end, we develop algorithms to define the distance between graphs. In this paper, w…
Multiple Hypotheses Testing
1993
The paper is mainly concerned with multiple testing procedures which control a given multiple level α. General concepts for this purpose are the closure test and a modification which is independent of the special structure of hypotheses and tests. We consider improvements of this modification using information about the logical dependences (redundancies) within the system of hypotheses and present an efficient algorithm. Finally, we discuss some problems which are specific for hierarchical systems of hypotheses, e.g. in model search.