4,729 research outputs found
A Stochastic Approach to Shortcut Bridging in Programmable Matter
In a self-organizing particle system, an abstraction of programmable matter,
simple computational elements called particles with limited memory and
communication self-organize to solve system-wide problems of movement,
coordination, and configuration. In this paper, we consider a stochastic,
distributed, local, asynchronous algorithm for "shortcut bridging", in which
particles self-assemble bridges over gaps that simultaneously balance
minimizing the length and cost of the bridge. Army ants of the genus Eciton
have been observed exhibiting a similar behavior in their foraging trails,
dynamically adjusting their bridges to satisfy an efficiency trade-off using
local interactions. Using techniques from Markov chain analysis, we rigorously
analyze our algorithm, show it achieves a near-optimal balance between the
competing factors of path length and bridge cost, and prove that it exhibits a
dependence on the angle of the gap being "shortcut" similar to that of the ant
bridges. We also present simulation results that qualitatively compare our
algorithm with the army ant bridging behavior. Our work gives a plausible
explanation of how convergence to globally optimal configurations can be
achieved via local interactions by simple organisms (e.g., ants) with some
limited computational power and access to random bits. The proposed algorithm
also demonstrates the robustness of the stochastic approach to algorithms for
programmable matter, as it is a surprisingly simple extension of our previous
stochastic algorithm for compression.Comment: Published in Proc. of DNA23: DNA Computing and Molecular Programming
- 23rd International Conference, 2017. An updated journal version will appear
in the DNA23 Special Issue of Natural Computin
Complexity of evolutionary equilibria in static fitness landscapes
A fitness landscape is a genetic space -- with two genotypes adjacent if they
differ in a single locus -- and a fitness function. Evolutionary dynamics
produce a flow on this landscape from lower fitness to higher; reaching
equilibrium only if a local fitness peak is found. I use computational
complexity to question the common assumption that evolution on static fitness
landscapes can quickly reach a local fitness peak. I do this by showing that
the popular NK model of rugged fitness landscapes is PLS-complete for K >= 2;
the reduction from Weighted 2SAT is a bijection on adaptive walks, so there are
NK fitness landscapes where every adaptive path from some vertices is of
exponential length. Alternatively -- under the standard complexity theoretic
assumption that there are problems in PLS not solvable in polynomial time --
this means that there are no evolutionary dynamics (known, or to be discovered,
and not necessarily following adaptive paths) that can converge to a local
fitness peak on all NK landscapes with K = 2. Applying results from the
analysis of simplex algorithms, I show that there exist single-peaked
landscapes with no reciprocal sign epistasis where the expected length of an
adaptive path following strong selection weak mutation dynamics is
even though an adaptive path to the optimum of length less
than n is available from every vertex. The technical results are written to be
accessible to mathematical biologists without a computer science background,
and the biological literature is summarized for the convenience of
non-biologists with the aim to open a constructive dialogue between the two
disciplines.Comment: 14 pages, 3 figure
Cellular Automata Applications in Shortest Path Problem
Cellular Automata (CAs) are computational models that can capture the
essential features of systems in which global behavior emerges from the
collective effect of simple components, which interact locally. During the last
decades, CAs have been extensively used for mimicking several natural processes
and systems to find fine solutions in many complex hard to solve computer
science and engineering problems. Among them, the shortest path problem is one
of the most pronounced and highly studied problems that scientists have been
trying to tackle by using a plethora of methodologies and even unconventional
approaches. The proposed solutions are mainly justified by their ability to
provide a correct solution in a better time complexity than the renowned
Dijkstra's algorithm. Although there is a wide variety regarding the
algorithmic complexity of the algorithms suggested, spanning from simplistic
graph traversal algorithms to complex nature inspired and bio-mimicking
algorithms, in this chapter we focus on the successful application of CAs to
shortest path problem as found in various diverse disciplines like computer
science, swarm robotics, computer networks, decision science and biomimicking
of biological organisms' behaviour. In particular, an introduction on the first
CA-based algorithm tackling the shortest path problem is provided in detail.
After the short presentation of shortest path algorithms arriving from the
relaxization of the CAs principles, the application of the CA-based shortest
path definition on the coordinated motion of swarm robotics is also introduced.
Moreover, the CA based application of shortest path finding in computer
networks is presented in brief. Finally, a CA that models exactly the behavior
of a biological organism, namely the Physarum's behavior, finding the
minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From
software to wetware. Springer, 201
Complexity, parallel computation and statistical physics
The intuition that a long history is required for the emergence of complexity
in natural systems is formalized using the notion of depth. The depth of a
system is defined in terms of the number of parallel computational steps needed
to simulate it. Depth provides an objective, irreducible measure of history
applicable to systems of the kind studied in statistical physics. It is argued
that physical complexity cannot occur in the absence of substantial depth and
that depth is a useful proxy for physical complexity. The ideas are illustrated
for a variety of systems in statistical physics.Comment: 21 pages, 7 figure
Modelling DNA Origami Self-Assembly at the Domain Level
We present a modelling framework, and basic model parameterization, for the
study of DNA origami folding at the level of DNA domains. Our approach is
explicitly kinetic and does not assume a specific folding pathway. The binding
of each staple is associated with a free-energy change that depends on staple
sequence, the possibility of coaxial stacking with neighbouring domains, and
the entropic cost of constraining the scaffold by inserting staple crossovers.
A rigorous thermodynamic model is difficult to implement as a result of the
complex, multiply connected geometry of the scaffold: we present a solution to
this problem for planar origami. Coaxial stacking and entropic terms,
particularly when loop closure exponents are taken to be larger than those for
ideal chains, introduce interactions between staples. These cooperative
interactions lead to the prediction of sharp assembly transitions with notable
hysteresis that are consistent with experimental observations. We show that the
model reproduces the experimentally observed consequences of reducing staple
concentration, accelerated cooling and absent staples. We also present a
simpler methodology that gives consistent results and can be used to study a
wider range of systems including non-planar origami
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