8 research outputs found
Probability 1 computation with chemical reaction networks
The computational power of stochastic chemical reaction networks (CRNs) varies significantly with the output convention and whether or not error is permitted. Focusing on probability 1 computation, we demonstrate a striking difference between stable computation that converges to a state where the output cannot change, and the notion of limit-stable computation where the output eventually stops changing with probability 1. While stable computation is known to be restricted to semilinear predicates (essentially piecewise linear), we show that limit-stable computation encompasses the set of predicates ϕ:N→{0,1} in Δ^0_2 in the arithmetical hierarchy (a superset of Turing-computable). In finite time, our construction achieves an error-correction scheme for Turing universal computation. We show an analogous characterization of the functions f:N→N computable by CRNs with probability 1, which encode their output into the count of a certain species. This work refines our understanding of the tradeoffs between error and computational power in CRNs
Probability 1 computation with chemical reaction networks
The computational power of stochastic chemical reaction networks (CRNs) varies significantly with the output convention and whether or not error is permitted. Focusing on probability 1 computation, we demonstrate a striking difference between stable computation that converges to a state where the output cannot change, and the notion of limit-stable computation where the output eventually stops changing with probability 1. While stable computation is known to be restricted to semilinear predicates (essentially piecewise linear), we show that limit-stable computation encompasses the set of predicates ϕ:N→{0,1} in Δ^0_2 in the arithmetical hierarchy (a superset of Turing-computable). In finite time, our construction achieves an error-correction scheme for Turing universal computation. We show an analogous characterization of the functions f:N→N computable by CRNs with probability 1, which encode their output into the count of a certain species. This work refines our understanding of the tradeoffs between error and computational power in CRNs
Methods for construction and analysis of computational models in systems biology: applications to the modelling of the heat shock response and the self-assembly of intermediate filaments
Systems biology is a new, emerging and rapidly developing, multidisciplinary
research field that aims to study biochemical and biological systems from
a holistic perspective, with the goal of providing a comprehensive, system-
level understanding of cellular behaviour. In this way, it addresses one of
the greatest challenges faced by contemporary biology, which is to compre-
hend the function of complex biological systems. Systems biology combines
various methods that originate from scientific disciplines such as molecu-
lar biology, chemistry, engineering sciences, mathematics, computer science
and systems theory. Systems biology, unlike “traditional” biology, focuses
on high-level concepts such as: network, component, robustness, efficiency,
control, regulation, hierarchical design, synchronization, concurrency, and
many others. The very terminology of systems biology is “foreign” to “tra-
ditional” biology, marks its drastic shift in the research paradigm and it
indicates close linkage of systems biology to computer science.
One of the basic tools utilized in systems biology is the mathematical
modelling of life processes tightly linked to experimental practice. The stud-
ies contained in this thesis revolve around a number of challenges commonly
encountered in the computational modelling in systems biology. The re-
search comprises of the development and application of a broad range of
methods originating in the fields of computer science and mathematics for
construction and analysis of computational models in systems biology. In
particular, the performed research is setup in the context of two biolog-
ical phenomena chosen as modelling case studies: 1) the eukaryotic heat
shock response and 2) the in vitro self-assembly of intermediate filaments,
one of the main constituents of the cytoskeleton. The range of presented
approaches spans from heuristic, through numerical and statistical to ana-
lytical methods applied in the effort to formally describe and analyse the
two biological processes. We notice however, that although applied to cer-
tain case studies, the presented methods are not limited to them and can
be utilized in the analysis of other biological mechanisms as well as com-
plex systems in general. The full range of developed and applied modelling
techniques as well as model analysis methodologies constitutes a rich mod-
elling framework. Moreover, the presentation of the developed methods,
their application to the two case studies and the discussions concerning
their potentials and limitations point to the difficulties and challenges one
encounters in computational modelling of biological systems. The problems
of model identifiability, model comparison, model refinement, model inte-
gration and extension, choice of the proper modelling framework and level
of abstraction, or the choice of the proper scope of the model run through
this thesis
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
Contemporary Natural Philosophy and Philosophies - Part 2
Modern technology has eliminated barriers posed by geographic distances between people around the globe, making the world more interdependent. However, in spite of global collaboration within research domains, fragmentation among research fields persists and even escalates. Disintegrated knowledge has become subservient to the competition in the technological and economic race, leading in the direction chosen not by reason and intellect but rather by the preferences of politics and markets. To restore the authority of knowledge in guiding humanity, we have to reconnect its scattered isolated parts and offer an evolving and diverse but shared vision of objective reality connecting the sciences and other knowledge domains and informed by and in communication with ethical and esthetic thinking and being. This collection of articles responds to the second call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with the rest of the knowledge-producing and knowledge-consuming communities in an inclusive, extended natural-philosophic, human-centric manner. In this process of reconnection, scientific and philosophical investigations enrich each other, with sciences informing philosophies about the best current knowledge of the world, both natural and human-made, while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences
Contemporary Natural Philosophy and Philosophies—Part 2
This is a short presentation by the Guest Editors of the series of Special Issues of the journal Philosophies under the common title "Contemporary Natural Philosophy and Philosophies" in which we present Part 2. The series will continue, and the call for contributions to the next Special Issue will appear shortly