1,411 research outputs found
Prospects for Declarative Mathematical Modeling of Complex Biological Systems
Declarative modeling uses symbolic expressions to represent models. With such
expressions one can formalize high-level mathematical computations on models
that would be difficult or impossible to perform directly on a lower-level
simulation program, in a general-purpose programming language. Examples of such
computations on models include model analysis, relatively general-purpose
model-reduction maps, and the initial phases of model implementation, all of
which should preserve or approximate the mathematical semantics of a complex
biological model. The potential advantages are particularly relevant in the
case of developmental modeling, wherein complex spatial structures exhibit
dynamics at molecular, cellular, and organogenic levels to relate genotype to
multicellular phenotype. Multiscale modeling can benefit from both the
expressive power of declarative modeling languages and the application of model
reduction methods to link models across scale. Based on previous work, here we
define declarative modeling of complex biological systems by defining the
operator algebra semantics of an increasingly powerful series of declarative
modeling languages including reaction-like dynamics of parameterized and
extended objects; we define semantics-preserving implementation and
semantics-approximating model reduction transformations; and we outline a
"meta-hierarchy" for organizing declarative models and the mathematical methods
that can fruitfully manipulate them
Learning the Semantics of Manipulation Action
In this paper we present a formal computational framework for modeling
manipulation actions. The introduced formalism leads to semantics of
manipulation action and has applications to both observing and understanding
human manipulation actions as well as executing them with a robotic mechanism
(e.g. a humanoid robot). It is based on a Combinatory Categorial Grammar. The
goal of the introduced framework is to: (1) represent manipulation actions with
both syntax and semantic parts, where the semantic part employs
-calculus; (2) enable a probabilistic semantic parsing schema to learn
the -calculus representation of manipulation action from an annotated
action corpus of videos; (3) use (1) and (2) to develop a system that visually
observes manipulation actions and understands their meaning while it can reason
beyond observations using propositional logic and axiom schemata. The
experiments conducted on a public available large manipulation action dataset
validate the theoretical framework and our implementation
Grammar-based Representation and Identification of Dynamical Systems
In this paper we propose a novel approach to identify dynamical systems. The
method estimates the model structure and the parameters of the model
simultaneously, automating the critical decisions involved in identification
such as model structure and complexity selection. In order to solve the
combined model structure and model parameter estimation problem, a new
representation of dynamical systems is proposed. The proposed representation is
based on Tree Adjoining Grammar, a formalism that was developed from linguistic
considerations. Using the proposed representation, the identification problem
can be interpreted as a multi-objective optimization problem and we propose a
Evolutionary Algorithm-based approach to solve the problem. A benchmark example
is used to demonstrate the proposed approach. The results were found to be
comparable to that obtained by state-of-the-art non-linear system
identification methods, without making use of knowledge of the system
description.Comment: Submitted to European Control Conference (ECC) 201
Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice
Modeling Structure-Function Relationships in Synthetic DNA Sequences using Attribute Grammars
Recognizing that certain biological functions can be associated with specific DNA sequences has led various fields of biology to adopt the notion of the genetic part. This concept provides a finer level of granularity than the traditional notion of the gene. However, a method of formally relating how a set of parts relates to a function has not yet emerged. Synthetic biology both demands such a formalism and provides an ideal setting for testing hypotheses about relationships between DNA sequences and phenotypes beyond the gene-centric methods used in genetics. Attribute grammars are used in computer science to translate the text of a program source code into the computational operations it represents. By associating attributes with parts, modifying the value of these attributes using rules that describe the structure of DNA sequences, and using a multi-pass compilation process, it is possible to translate DNA sequences into molecular interaction network models. These capabilities are illustrated by simple example grammars expressing how gene expression rates are dependent upon single or multiple parts. The translation process is validated by systematically generating, translating, and simulating the phenotype of all the sequences in the design space generated by a small library of genetic parts. Attribute grammars represent a flexible framework connecting parts with models of biological function. They will be instrumental for building mathematical models of libraries of genetic constructs synthesized to characterize the function of genetic parts. This formalism is also expected to provide a solid foundation for the development of computer assisted design applications for synthetic biology
Usage-based and emergentist approaches to language acquisition
It was long considered to be impossible to learn grammar based on linguistic experience alone. In the past decade, however, advances in usage-based linguistic theory, computational linguistics, and developmental psychology changed the view on this matter. So-called usage-based and emergentist approaches to language acquisition state that language can be learned from language use itself, by means of social skills like joint attention, and by means of powerful generalization mechanisms. This paper first summarizes the assumptions regarding the nature of linguistic representations and processing. Usage-based theories are nonmodular and nonreductionist, i.e., they emphasize the form-function relationships, and deal with all of language, not just selected levels of representations. Furthermore, storage and processing is considered to be analytic as well as holistic, such that there is a continuum between children's unanalyzed chunks and abstract units found in adult language. In the second part, the empirical evidence is reviewed. Children's linguistic competence is shown to be limited initially, and it is demonstrated how children can generalize knowledge based on direct and indirect positive evidence. It is argued that with these general learning mechanisms, the usage-based paradigm can be extended to multilingual language situations and to language acquisition under special circumstances
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