32,636 research outputs found
Structural Analysis of Boolean Equation Systems
We analyse the problem of solving Boolean equation systems through the use of
structure graphs. The latter are obtained through an elegant set of
Plotkin-style deduction rules. Our main contribution is that we show that
equation systems with bisimilar structure graphs have the same solution. We
show that our work conservatively extends earlier work, conducted by Keiren and
Willemse, in which dependency graphs were used to analyse a subclass of Boolean
equation systems, viz., equation systems in standard recursive form. We
illustrate our approach by a small example, demonstrating the effect of
simplifying an equation system through minimisation of its structure graph
Modelling & analysis of hybrid dynamic systems using a bond graph approach
Hybrid models are those containing continuous and discontinuous behaviour. In constructing dynamic systems models, it is frequently desirable to abstract rapidly changing, highly nonlinear behaviour to a discontinuity. Bond graphs lend themselves to systems modelling by being multi-disciplinary and reflecting the physics of the system. One advantage is that they can produce a mathematical model in a form that simulates quickly and efficiently. Hybrid bond graphs are a logical development which could further improve speed and efficiency. A range of hybrid bond graph forms have been proposed which are suitable for either simulation or further analysis, but not both. None have reached common usage.
A Hybrid bond graph method is proposed here which is suitable for simulation as well as providing engineering insight through analysis. This new method features a distinction between structural and parametric switching. The controlled junction is used for the former, and gives rise to dynamic causality. A controlled element is developed for the latter. Dynamic causality is unconstrained so as to aid insight, and a new notation is proposed.
The junction structure matrix for the hybrid bond graph features Boolean terms to reflect the controlled junctions in the graph structure. This hybrid JSM is used to generate a mixed-Boolean state equation. When storage elements are in dynamic causality, the resulting system equation is implicit.
The focus of this thesis is the exploitation of the model. The implicit form enables application of matrix-rank criteria from control theory, and control properties can be seen in the structure and causal assignment. An impulsive mode may occur when storage elements are in dynamic causality, but otherwise there are no energy losses associated with commutation because this method dictates the way discontinuities are abstracted.
The main contribution is therefore a Hybrid Bond Graph which reflects the physics of commutating systems and offers engineering insight through the choice of controlled elements and dynamic causality. It generates a unique, implicit, mixed-Boolean system equation, describing all modes of operation. This form is suitable for both simulation and analysis
Construction and analysis of causally dynamic hybrid bond graphs
Engineering systems are frequently abstracted to models with discontinuous behaviour (such as a switch or contact),
and a hybrid model is one which contains continuous and discontinuous behaviours. Bond graphs are an established
physical modelling method, but there are several methods for constructing switched or ‘hybrid’ bond graphs, developed
for either qualitative ‘structural’ analysis or efficient numerical simulation of engineering systems. This article proposes a
general hybrid bond graph suitable for both. The controlled junction is adopted as an intuitive way of modelling a discontinuity in the model structure. This element gives rise to ‘dynamic causality’ that is facilitated by a new bond graph notation. From this model, the junction structure and state equations are derived and compared to those obtained by
existing methods. The proposed model includes all possible modes of operation and can be represented by a single set
of equations. The controlled junctions manifest as Boolean variables in the matrices of coefficients. The method is more
compact and intuitive than existing methods and dispenses with the need to derive various modes of operation from a
given reference representation. Hence, a method has been developed, which can reach common usage and form a platform for further study
Analysis of Boolean Equation Systems through Structure Graphs
We analyse the problem of solving Boolean equation systems through the use of
structure graphs. The latter are obtained through an elegant set of
Plotkin-style deduction rules. Our main contribution is that we show that
equation systems with bisimilar structure graphs have the same solution. We
show that our work conservatively extends earlier work, conducted by Keiren and
Willemse, in which dependency graphs were used to analyse a subclass of Boolean
equation systems, viz., equation systems in standard recursive form. We
illustrate our approach by a small example, demonstrating the effect of
simplifying an equation system through minimisation of its structure graph
Exploiting Query Structure and Document Structure to Improve Document Retrieval Effectiveness
In this paper we present a systematic analysis of document
retrieval using unstructured and structured queries within
the score region algebra (SRA) structured retrieval framework. The behavior of di®erent retrieval models, namely
Boolean, tf.idf, GPX, language models, and Okapi, is tested
using the transparent SRA framework in our three-level structured retrieval system called TIJAH. The retrieval models are implemented along four elementary retrieval aspects: element and term selection, element score computation, score combination, and score propagation.
The analysis is performed on a numerous experiments
evaluated on TREC and CLEF collections, using manually
generated unstructured and structured queries. Unstructured queries range from the short title queries to long title
+ description + narrative queries. For generating structured
queries we exploit the knowledge of the document structure
and the content used to semantically describe or classify
documents. We show that such structured information can
be utilized in retrieval engines to give more precise answers to user queries then when using unstructured queries
Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development
Progress in cell type reprogramming has revived the interest in Waddington's
concept of the epigenetic landscape. Recently researchers developed the
quasi-potential theory to represent the Waddington's landscape. The
Quasi-potential U(x), derived from interactions in the gene regulatory network
(GRN) of a cell, quantifies the relative stability of network states, which
determine the effort required for state transitions in a multi-stable dynamical
system. However, quasi-potential landscapes, originally developed for
continuous systems, are not suitable for discrete-valued networks which are
important tools to study complex systems. In this paper, we provide a framework
to quantify the landscape for discrete Boolean networks (BNs). We apply our
framework to study pancreas cell differentiation where an ensemble of BN models
is considered based on the structure of a minimal GRN for pancreas development.
We impose biologically motivated structural constraints (corresponding to
specific type of Boolean functions) and dynamical constraints (corresponding to
stable attractor states) to limit the space of BN models for pancreas
development. In addition, we enforce a novel functional constraint
corresponding to the relative ordering of attractor states in BN models to
restrict the space of BN models to the biological relevant class. We find that
BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics
of pancreas cell differentiation. This framework can also determine the genes'
influence on cell state transitions, and thus can facilitate the rational
design of cell reprogramming protocols.Comment: 24 pages, 6 figures, 1 tabl
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