Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview
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paper_title: The Fokker-Planck equation

paper_content:

An arrangement for retaining a heart valve in a passageway of a cardiovascular system, and a heart valve useable therewith. The retaining arrangement includes an annular arrangement surrounding the circular heart valve and engaging it so as to be radially expandable and contractable relative thereto while securely holding the heart valve in place. The annular arrangement may include a single overlapping loop or a plurality of arcuate segments, all of which could slidingly engage a circumferentially extending flange on the outside of the heart valve. The heart valve includes a plurality of circular elements interfitting in a single plane to close the valve and extending axially relative to each other to open the valve and hence permit fluid flow through the passageway.
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paper_title: The Algorithmic Beauty of Plants

paper_content:

1 Graphical modeling using L-systems.- 1.1 Rewriting systems.- 1.2 DOL-systems.- 1.3 Turtle interpretation of strings.- 1.4 Synthesis of DOL-systems.- 1.4.1 Edge rewriting.- 1.4.2 Node rewriting.- 1.4.3 Relationship between edge and node rewriting.- 1.5 Modeling in three dimensions.- 1.6 Branching structures.- 1.6.1 Axial trees.- 1.6.2 Tree OL-systems.- 1.6.3 Bracketed OL-systems.- 1.7 Stochastic L-systems.- 1.8 Context-sensitive L-systems.- 1.9 Growth functions.- 1.10 Parametric L-systems.- 1.10.1 Parametric OL-systems.- 1.10.2 Parametric 2L-systems.- 1.10.3 Turtle interpretation of parametric words.- 2 Modeling of trees.- 3 Developmental models of herbaceous plants.- 3.1 Levels of model specification.- 3.1.1 Partial L-systems.- 3.1.2 Control mechanisms in plants.- 3.1.3 Complete models.- 3.2 Branching patterns.- 3.3 Models of inflorescences.- 3.3.1 Monopodial inflorescences.- 3.3.2 Sympodial inflorescences.- 3.3.3 Polypodial inflorescences.- 3.3.4 Modified racemes.- 4 Phyllotaxis.- 4.1 The planar model.- 4.2 The cylindrical model.- 5 Models of plant organs.- 5.1 Predefined surfaces.- 5.2 Developmental surface models.- 5.3 Models of compound leaves.- 6 Animation of plant development.- 6.1 Timed DOL-systems.- 6.2 Selection of growth functions.- 6.2.1 Development of nonbranching filaments.- 6.2.2 Development of branching structures.- 7 Modeling of cellular layers.- 7.1 Map L-systems.- 7.2 Graphical interpretation of maps.- 7.3 Microsorium linguaeforme.- 7.4 Dryopteris thelypteris.- 7.5 Modeling spherical cell layers.- 7.6 Modeling 3D cellular structures.- 8 Fractal properties of plants.- 8.1 Symmetry and self-similarity.- 8.2 Plant models and iterated function systems.- Epilogue.- Appendix A Software environment for plant modeling.- A.1 A virtual laboratory in botany.- A.2 List of laboratory programs.- Appendix B About the figures.- Turtle interpretation of symbols.
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paper_title: The Fokker-Planck equation

paper_content:

An arrangement for retaining a heart valve in a passageway of a cardiovascular system, and a heart valve useable therewith. The retaining arrangement includes an annular arrangement surrounding the circular heart valve and engaging it so as to be radially expandable and contractable relative thereto while securely holding the heart valve in place. The annular arrangement may include a single overlapping loop or a plurality of arcuate segments, all of which could slidingly engage a circumferentially extending flange on the outside of the heart valve. The heart valve includes a plurality of circular elements interfitting in a single plane to close the valve and extending axially relative to each other to open the valve and hence permit fluid flow through the passageway.
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paper_title: Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations.

paper_content:

Summary: Cellerator describes single and multi-cellular signal transduction networks (STN) with a compact, optionally palette-driven, arrow-based notation to represent biochemical reactions and transcriptional activation. Multicompartment systems are represented as graphs with STNs embedded in each node. Interactions include massaction, enzymatic, allosteric and connectionist models. Reactions are translated into differential equations and can be solved numerically to generate predictive time courses or output as systems of equations that can be read by other programs. Cellerator simulations are fully extensible and portable to any operating system that supports Mathematica, and can be indefinitely nested within larger data structures to produce highly scaleable models. Availability: Cellerator can be licensed free of charge to noncommercial academic, U.S. government, and nonprofit users. Details and sample notebooks are available at http:
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paper_title: Tracking Cell Signals in Fluorescent Images

paper_content:

In this paper we present the techniques for tracking cell signal in GFP (Green Fluorescent Protein) images of growing cell colonies. We use such tracking for both data extraction and dynamic modeling of intracellular processes. The techniques are based on optimization of energy functions, which simultaneously determines cell correspondences, while estimating the mapping functions. In addition to spatial mappings such as affine and Thin-Plate Spline mapping, the cell growth and cell division histories must be estimated as well. Different levels of joint optimization are discussed. The most unusual tracking feature addressed in this paper is the possibility of one-to-two correspondences caused by cell division. A novel extended softassign algorithm for solutions of one-to-many correspondences is detailed in this paper. The techniques are demonstrated on three sets of data: growing bacillus Subtillus and e-coli colonies and a developing plant shoot apical meristem. The techniques are currently used by biologists for data extraction and hypothesis formation.
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Title: Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview

Section 1: Introduction
Description 1: Write an introduction about probabilistic models and how they can be unified within the framework of Stochastic Parameterized Grammars (SPGs) and Dynamical Grammars (DGs).

Section 2: Syntax Definition
Description 2: Describe the formal syntax of Stochastic Parameterized Grammars, including rule structure, parameter types, and probability rate functions.

Section 3: Semantic Maps
Description 3: Explain the semantics function Ψ for continuous-time and discrete-time stochastic processes derived from the grammar.

Section 4: Operator Algebra
Description 4: Detail the operator algebra used to define the semantics, including creation and annihilation operators and their implications for probability conservation.

Section 5: Continuous-time Semantics
Description 5: Define the continuous-time semantics of the grammar, particularly focusing on the time evolution operator and probability inflow/outflow.

Section 6: Discrete-time SPG Semantics
Description 6: Elaborate on the discrete-time semantics, discussing the operator H and how it conditions probability distribution over discrete rule-firing events.

Section 7: Time-ordered Product Expansion
Description 7: Introduce the time-ordered product expansion tool and its application in generating simulation algorithms and Feynman diagram expansions.

Section 8: Relation between Semantic Maps
Description 8: Discuss the relation between continuous-time and discrete-time semantic maps and the conditions under which they converge.

Section 9: Discussion: Transformations of SPGs
Description 9: Explore transformations of SPGs that preserve semantic properties, with a focus on syntactic transformations and inference algorithms.

Section 10: Examples and Reductions
Description 10: Provide examples of other frameworks that can be expressed or reduced to SPGs, including biochemical reaction networks, logic programs, graph grammars, and differential equations.

Section 11: Discussion: Relevance to Artificial Intelligence and Computational Science
Description 11: Discuss the relevance of SPGs and DGs to AI and computational science, including their applications in machine learning, multiscale modeling, and the construction of mathematical models.

Section 12: Conclusion
Description 12: Summarize the established syntax and semantics for the probabilistic modeling language and its applicability to various fields and models.