220 research outputs found
Negative Interactions in Irreversible Self-Assembly
This paper explores the use of negative (i.e., repulsive) interaction the
abstract Tile Assembly Model defined by Winfree. Winfree postulated negative
interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu,
and Yin explored their power in the context of reversible attachment
operations. We explore the power of negative interactions with irreversible
attachments, and we achieve two main results. Our first result is an
impossibility theorem: after t steps of assembly, Omega(t) tiles will be
forever bound to an assembly, unable to detach. Thus negative glue strengths do
not afford unlimited power to reuse tiles. Our second result is a positive one:
we construct a set of tiles that can simulate a Turing machine with space bound
s and time bound t, while ensuring that no intermediate assembly grows larger
than O(s), rather than O(s * t) as required by the standard Turing machine
simulation with tiles
Computational Complexity of Atomic Chemical Reaction Networks
Informally, a chemical reaction network is "atomic" if each reaction may be
interpreted as the rearrangement of indivisible units of matter. There are
several reasonable definitions formalizing this idea. We investigate the
computational complexity of deciding whether a given network is atomic
according to each of these definitions.
Our first definition, primitive atomic, which requires each reaction to
preserve the total number of atoms, is to shown to be equivalent to mass
conservation. Since it is known that it can be decided in polynomial time
whether a given chemical reaction network is mass-conserving, the equivalence
gives an efficient algorithm to decide primitive atomicity.
Another definition, subset atomic, further requires that all atoms are
species. We show that deciding whether a given network is subset atomic is in
, and the problem "is a network subset atomic with respect to a
given atom set" is strongly -.
A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et
al., further requires that each species has a sequence of reactions splitting
it into its constituent atoms. We show that there is a to decide whether a given network is reachably atomic, improving
upon the result of Adleman et al. that the problem is . We
show that the reachability problem for reachably atomic networks is
-.
Finally, we demonstrate equivalence relationships between our definitions and
some special cases of another existing definition of atomicity due to Gnacadja
Leaderless deterministic chemical reaction networks
This paper answers an open question of Chen, Doty, and Soloveichik [1], who
showed that a function f:N^k --> N^l is deterministically computable by a
stochastic chemical reaction network (CRN) if and only if the graph of f is a
semilinear subset of N^{k+l}. That construction crucially used "leaders": the
ability to start in an initial configuration with constant but non-zero counts
of species other than the k species X_1,...,X_k representing the input to the
function f. The authors asked whether deterministic CRNs without a leader
retain the same power.
We answer this question affirmatively, showing that every semilinear function
is deterministically computable by a CRN whose initial configuration contains
only the input species X_1,...,X_k, and zero counts of every other species. We
show that this CRN completes in expected time O(n), where n is the total number
of input molecules. This time bound is slower than the O(log^5 n) achieved in
[1], but faster than the O(n log n) achieved by the direct construction of [1]
(Theorem 4.1 in the latest online version of [1]), since the fast construction
of that paper (Theorem 4.4) relied heavily on the use of a fast, error-prone
CRN that computes arbitrary computable functions, and which crucially uses a
leader.Comment: arXiv admin note: substantial text overlap with arXiv:1204.417
DNA as a universal substrate for chemical kinetics
Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka–Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions
The field of algorithmic self-assembly is concerned with the design and
analysis of self-assembly systems from a computational perspective, that is,
from the perspective of mathematical problems whose study may give insight into
the natural processes through which elementary objects self-assemble into more
complex ones. One of the main problems of algorithmic self-assembly is the
minimum tile set problem (MTSP), which asks for a collection of types of
elementary objects (called tiles) to be found for the self-assembly of an
object having a pre-established shape. Such a collection is to be as concise as
possible, thus minimizing supply diversity, while satisfying a set of stringent
constraints having to do with the termination and other properties of the
self-assembly process from its tile types. We present a study of what we think
is the first practical approach to MTSP. Our study starts with the introduction
of an evolutionary heuristic to tackle MTSP and includes results from extensive
experimentation with the heuristic on the self-assembly of simple objects in
two and three dimensions. The heuristic we introduce combines classic elements
from the field of evolutionary computation with a problem-specific variant of
Pareto dominance into a multi-objective approach to MTSP.Comment: Minor typos correcte
Optimization of oil field development based on a 3D reservoir model obtained as a result of history matching
The paper proposes an approach to optimizing the development of oil fields. The objective function includes weighted squares of development target indicators and regularizing terms, in which the coefficients are searched adaptively. Regularizing terms ensure the fulfillment of restrictions on the optimized parameters and the rapid convergence of the optimization process. When minimizing the objective function, linearization of the target indicators is performed, and the values of the optimized parameters at the next iteration are sought by solving the system of linear algebraic equations obtained from minimizing the quadratic functional. The values of the target indicators and their sensitivity to the parameters being optimized are calculated by fluid dynamic 3D modeling for the oil reservoir model obtained as a result of history matching for the period preceding the optimization period. Calculations are performed in a distributed computing system consisting of multi-core personal computers. To test the proposed approach, a model of a high-viscosity oil field in Tatarstan was used. The optimization was carried out with various weighting factors and desired oil recovery values in the corresponding target indicator. It is shown that the optimized plans provide more efficient development of the oil field compared to the plan used in practice. At the same time, the optimal plan, built on the basis of a reservoir model history-matched at an early stage of development, optimizes development for a model history-matched throughout the entire period of field development. This allows us to conclude that development plans obtained from a model history-matched using a short time period will optimize production characteristics for a real field to about the same extent. The time for solving optimization problems containing about 500 parameters in a distributed computing system was about a day
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/
Integrated information increases with fitness in the evolution of animats
One of the hallmarks of biological organisms is their ability to integrate
disparate information sources to optimize their behavior in complex
environments. How this capability can be quantified and related to the
functional complexity of an organism remains a challenging problem, in
particular since organismal functional complexity is not well-defined. We
present here several candidate measures that quantify information and
integration, and study their dependence on fitness as an artificial agent
("animat") evolves over thousands of generations to solve a navigation task in
a simple, simulated environment. We compare the ability of these measures to
predict high fitness with more conventional information-theoretic processing
measures. As the animat adapts by increasing its "fit" to the world,
information integration and processing increase commensurately along the
evolutionary line of descent. We suggest that the correlation of fitness with
information integration and with processing measures implies that high fitness
requires both information processing as well as integration, but that
information integration may be a better measure when the task requires memory.
A correlation of measures of information integration (but also information
processing) and fitness strongly suggests that these measures reflect the
functional complexity of the animat, and that such measures can be used to
quantify functional complexity even in the absence of fitness data.Comment: 27 pages, 8 figures, one supplementary figure. Three supplementary
video files available on request. Version commensurate with published text in
PLoS Comput. Bio
Probabilistic reasoning with a bayesian DNA device based on strand displacement
We present a computing model based on the DNA strand displacement technique which performs Bayesian inference. The model will take single stranded DNA as input data, representing the presence or absence of a specific molecular signal (evidence). The program logic encodes the prior probability of a disease and the conditional probability of a signal given the disease playing with a set of different DNA complexes and their ratios. When the input and program molecules interact, they release a different pair of single stranded DNA species whose relative proportion represents the application of Bayes? Law: the conditional probability of the disease given the signal. The models presented in this paper can empower the application of probabilistic reasoning in genetic diagnosis in vitro
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