TY - CONF
TI - Operads and Phylogenetic Trees
AU - Baez, John C.
AU - Otter, Nina
AB - We construct an operad $\mathrm{Phyl}$ whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of $\mathrm{Com}$, the operad for commutative semigroups, and $[0,\infty)$, the operad with unary operations corresponding to nonnegative real numbers, where composition is addition. We show that there is a homeomorphism between the space of $n$-ary operations of $\mathrm{Phyl}$ and $\mathcal{T}_n\times [0,\infty)^{n+1}$, where $\mathcal{T}_n$ is the space of metric $n$-trees introduced by Billera, Holmes and Vogtmann. Furthermore, we show that the Markov models used to reconstruct phylogenetic trees from genome data give coalgebras of $\mathrm{Phyl}$. These always extend to coalgebras of the larger operad $\mathrm{Com} + [0,\infty]$, since Markov processes on finite sets converge to an equilibrium as time approaches infinity. We show that for any operad $O$, its coproduct with $[0,\infty]$ contains the operad $W(O)$ constucted by Boardman and Vogt. To prove these results, we explicitly describe the coproduct of operads in terms of labelled trees.
DA - 2015///
PY - 2015
DP - Semantic Scholar
KW - Biology
KW - Coalgebras
ER -
TY - CONF
TI - Rule-Based Modelling, Symmetries, Refinements
AU - Danos, Vincent
AU - Feret, Jérôme
AU - Fontana, Walter
AU - Harmer, Russell
AU - Krivine, Jean
A2 - Fisher, Jasmin
T3 - Lecture Notes in Computer Science
AB - Rule-based modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexes -i.e., not to have to specify all the traits of the entitities partaking in a reaction but just those that matter- is the key to obtaining compact descriptions of what otherwise could be nearly infinite dimensional dynamical systems. This also makes these descriptions easier to read, write and modify.In the course of modelling a particular signalling system it will often happen that more traits matter in a given interaction than previously thought, and one will need to strengthen the conditions under which that interaction may happen. This is a process that we call rule refinement and which we set out in this paper to study. Specifically we present a method to refine rule sets in a way that preserves the implied stochastic semantics.This stochastic semantics is dictated by the number of different ways in which a given rule can be applied to a system (obeying the mass action principle). The refinement formula we obtain explains how to refine rules and which choice of refined rates will lead to a neutral refinement, i.e., one that has the same global activity as the original rule had (and therefore leaves the dynamics unchanged). It has a pleasing mathematical simplicity, and is reusable with little modification across many variants of stochastic graph rewriting. A particular case of the above is the derivation of a maximal refinement which is equivalent to a (possibly infinite) Petri net and can be useful to get a quick approximation of the dynamics and to calibrate models. As we show with examples, refinement is also useful to understand how different subpopulations contribute to the activity of a rule, and to modulate differentially their impact on that activity.
C1 - Berlin, Heidelberg
C3 - Formal Methods in Systems Biology
DA - 2008///
PY - 2008
DO - 10/dc5k68
DP - Springer Link
SP - 103
EP - 122
LA - en
PB - Springer
SN - 978-3-540-68413-8
KW - Biology
KW - Rewriting theory
KW - Systems biology
ER -
TY - CONF
TI - Applications of Categories to Biology and Cognition
AU - Ehresmann, Andrée C.
DA - 2018///
PY - 2018
DO - 10/ggdf93
DP - Semantic Scholar
KW - Biology
KW - Emergence
KW - Neuroscience
ER -
TY - CONF
TI - Cells as Machines: Towards Deciphering Biochemical Programs in the Cell
AU - Fages, François
A2 - Natarajan, Raja
T3 - Lecture Notes in Computer Science
AB - Systems biology aims at understanding complex biological processes in terms of their basic mechanisms at the molecular level in cells. The bet of applying theoretical computer science concepts and software engineering methods to the analysis of distributed biochemical reaction systems in the cell, designed by natural evolution, has led to interesting challenges in computer science, and new model-based insights in biology. In this paper, we review the development over the last decade of the biochemical abstract machine (Biocham) software environment for modeling cell biology molecular reaction systems, reasoning about them at different levels of abstraction, formalizing biological behaviors in temporal logic with numerical constraints, and using them to infer non-measurable kinetic parameter values, evaluate robustness, decipher natural biochemical processes and implement new programs in synthetic biology.
C1 - Cham
C3 - Distributed Computing and Internet Technology
DA - 2014///
PY - 2014
DO - 10/ggdf96
DP - Springer Link
SP - 50
EP - 67
LA - en
PB - Springer International Publishing
SN - 978-3-319-04483-5
ST - Cells as Machines
KW - Biology
KW - Rewriting theory
KW - Symbolic logic
KW - Systems biology
ER -
TY - CONF
TI - Machine Learning Biochemical Networks from Temporal Logic Properties
AU - Fages, François
AU - Calzone, Laurence
AU - Chabrier-Rivier, Nathalie
AU - Soliman, Sylvain
A2 - Priami, Corrado
A2 - Plotkin, Gordon
T3 - Lecture Notes in Computer Science
AB - One central issue in systems biology is the definition of formal languages for describing complex biochemical systems and their behavior at different levels. The biochemical abstract machine BIOCHAM is based on two formal languages, one rule-based language used for modeling biochemical networks, at three abstraction levels corresponding to three semantics: boolean, concentration and population; and one temporal logic language used for formalizing the biological properties of the system. In this paper, we show how the temporal logic language can be turned into a specification language. We describe two algorithms for inferring reaction rules and kinetic parameter values from a temporal specification formalizing the biological data. Then, with an example of the cell cycle control, we illustrate how these machine learning techniques may be useful to the modeler.
C1 - Berlin, Heidelberg
C3 - Transactions on Computational Systems Biology VI
DA - 2006///
PY - 2006
DO - 10/dd8
DP - Springer Link
SP - 68
EP - 94
LA - en
PB - Springer
SN - 978-3-540-46236-1
KW - Abstract machines
KW - Biology
KW - Classical ML
KW - Machine learning
KW - Symbolic logic
KW - Systems biology
ER -
TY - CONF
TI - Symetries and asymetries of the immune system response: A categorification approach
AU - Mascari, Jean-François
AU - Giacchero, Damien
AU - Sfakianakis, Nikolaos
T2 - 2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)
AB - A new modeling approach and conceptual framework to the immune system response and its dual role with respect to cancer is proposed based on Applied Category Theory. States of cells and pathogenes are structured as mathematical structures (categories), the interactions, at a given phase, between cells of the immune system and pathogenes, correspond to a pair of adjunctions (adjoint functors), the interaction process consisting of the sequential composition of an identification phase, a preparation phase and an activation phase is modeled by the composition of maps of adjunctions: the approach is illustrated by considering the Cancer-Immunity Cycle. A third dimension is needed to model Cancer Immunoediting. The categorical foundations of our approach is based on Marco Grandis and Rober Paré theory of Intercategories.
C3 - 2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)
DA - 2017/11//
PY - 2017
DO - 10/ggdnd3
DP - IEEE Xplore
SP - 1451
EP - 1454
ST - Symetries and asymetries of the immune system response
KW - Biology
KW - Sketchy
ER -