103,722 research outputs found
Forward and Backward Bisimulations for Chemical Reaction Networks
We present two quantitative behavioral equivalences over species of a
chemical reaction network (CRN) with semantics based on ordinary differential
equations. Forward CRN bisimulation identifies a partition where each
equivalence class represents the exact sum of the concentrations of the species
belonging to that class. Backward CRN bisimulation relates species that have
the identical solutions at all time points when starting from the same initial
conditions. Both notions can be checked using only CRN syntactical information,
i.e., by inspection of the set of reactions. We provide a unified algorithm
that computes the coarsest refinement up to our bisimulations in polynomial
time. Further, we give algorithms to compute quotient CRNs induced by a
bisimulation. As an application, we find significant reductions in a number of
models of biological processes from the literature. In two cases we allow the
analysis of benchmark models which would be otherwise intractable due to their
memory requirements.Comment: Extended version of the CONCUR 2015 pape
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
Challenges in Quantitative Abstractions for Collective Adaptive Systems
Like with most large-scale systems, the evaluation of quantitative properties
of collective adaptive systems is an important issue that crosscuts all its
development stages, from design (in the case of engineered systems) to runtime
monitoring and control. Unfortunately it is a difficult problem to tackle in
general, due to the typically high computational cost involved in the analysis.
This calls for the development of appropriate quantitative abstraction
techniques that preserve most of the system's dynamical behaviour using a more
compact representation. This paper focuses on models based on ordinary
differential equations and reviews recent results where abstraction is achieved
by aggregation of variables, reflecting on the shortcomings in the state of the
art and setting out challenges for future research.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
Unprecedented Zeolite-Like Framework Topology Constructed from Cages with 3-Rings in a Barium Oxonitridophosphate
A novel oxonitridophosphate, Ba19P36O6+xN66-xCl8+x(x≈4.54), has been synthesized by heating a multicomponent reactant mixture consisting of phosphoryl triamide OP(NH2)3, thiophosphoryl triamide SP(NH2)3, BaS, and NH4Cl enclosed in an evacuated and sealed silica glass ampule up to 750°C. Despite the presence of side phases, the crystal structure was elucidated ab initio from high-resolution synchrotron powder diffraction data (λ=39.998 pm) applying the charge flipping algorithm supported by independent symmetry information derived from electron diffraction (ED) and scanning transmission electron microscopy (STEM). The compound crystallizes in the cubic space group Fm3c (no. 226) with a = 2685.41(3) pm and Z = 8. As confirmed by Rietveld refinement, the structure comprises all-side vertex sharing P(O,N)4 tetrahedra forming slightly distorted 3846812 cages representing a novel composite building unit (CBU). Interlinked through their 4-rings and additional 3-rings, the cages build up a 3D network with a framework density FD = 14.87 T/1000 Å3 and a 3D 8-ring channel system. Ba2+ and Clˉ as extra-framework ions are located within the cages and channels of the framework. The structuralmodel is corroborated by 31P double-quantum(DQ) /single-quantum (SQ) and triple-quantum (TQ) /single-quantum (SQ) 2D correlation MAS NMR spectroscopy. According to 31P{1H} C-REDOR NMR measurements, the H content is less than one H atom per unit cell
Thermodynamic graph-rewriting
We develop a new thermodynamic approach to stochastic graph-rewriting. The
ingredients are a finite set of reversible graph-rewriting rules called
generating rules, a finite set of connected graphs P called energy patterns and
an energy cost function. The idea is that the generators define the qualitative
dynamics, by showing which transformations are possible, while the energy
patterns and cost function specify the long-term probability of any
reachable graph. Given the generators and energy patterns, we construct a
finite set of rules which (i) has the same qualitative transition system as the
generators; and (ii) when equipped with suitable rates, defines a
continuous-time Markov chain of which is the unique fixed point. The
construction relies on the use of site graphs and a technique of `growth
policy' for quantitative rule refinement which is of independent interest. This
division of labour between the qualitative and long-term quantitative aspects
of the dynamics leads to intuitive and concise descriptions for realistic
models (see the examples in S4 and S5). It also guarantees thermodynamical
consistency (AKA detailed balance), otherwise known to be undecidable, which is
important for some applications. Finally, it leads to parsimonious
parameterizations of models, again an important point in some applications
Syntactic Markovian Bisimulation for Chemical Reaction Networks
In chemical reaction networks (CRNs) with stochastic semantics based on
continuous-time Markov chains (CTMCs), the typically large populations of
species cause combinatorially large state spaces. This makes the analysis very
difficult in practice and represents the major bottleneck for the applicability
of minimization techniques based, for instance, on lumpability. In this paper
we present syntactic Markovian bisimulation (SMB), a notion of bisimulation
developed in the Larsen-Skou style of probabilistic bisimulation, defined over
the structure of a CRN rather than over its underlying CTMC. SMB identifies a
lumpable partition of the CTMC state space a priori, in the sense that it is an
equivalence relation over species implying that two CTMC states are lumpable
when they are invariant with respect to the total population of species within
the same equivalence class. We develop an efficient partition-refinement
algorithm which computes the largest SMB of a CRN in polynomial time in the
number of species and reactions. We also provide an algorithm for obtaining a
quotient network from an SMB that induces the lumped CTMC directly, thus
avoiding the generation of the state space of the original CRN altogether. In
practice, we show that SMB allows significant reductions in a number of models
from the literature. Finally, we study SMB with respect to the deterministic
semantics of CRNs based on ordinary differential equations (ODEs), where each
equation gives the time-course evolution of the concentration of a species. SMB
implies forward CRN bisimulation, a recently developed behavioral notion of
equivalence for the ODE semantics, in an analogous sense: it yields a smaller
ODE system that keeps track of the sums of the solutions for equivalent
species.Comment: Extended version (with proofs), of the corresponding paper published
at KimFest 2017 (http://kimfest.cs.aau.dk/
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