385 research outputs found
Self-replication and evolution of DNA crystals
Is it possible to create a simple physical system that is capable of replicating itself? Can such a system evolve interesting behaviors, thus allowing it to adapt to a wide range of environments? This paper presents a design for such a replicator constructed exclusively from synthetic DNA. The basis for the replicator is crystal growth: information is stored in the spatial arrangement of monomers and copied from layer to layer by templating. Replication is achieved by fragmentation of crystals, which produces new crystals that carry the same information. Crystal replication avoids intrinsic problems associated with template-directed mechanisms for replication of one-dimensional polymers. A key innovation of our work is that by using programmable DNA tiles as the crystal monomers, we can design crystal growth processes that apply interesting selective pressures to the evolving sequences. While evolution requires that copying occur with high accuracy, we show how to adapt error-correction techniques from algorithmic self-assembly to lower the replication error rate as much as is required
Quantum Optimization Problems
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for
an NP optimization problem that searches an optimal value among
exponentially-many outcomes of polynomial-time computations. This paper expands
his framework to a quantum optimization problem using polynomial-time quantum
computations and introduces the notion of an ``universal'' quantum optimization
problem similar to a classical ``complete'' optimization problem. We exhibit a
canonical quantum optimization problem that is universal for the class of
polynomial-time quantum optimization problems. We show in a certain relativized
world that all quantum optimization problems cannot be approximated closely by
quantum polynomial-time computations. We also study the complexity of quantum
optimization problems in connection to well-known complexity classes.Comment: date change
Rapid solution of problems by nuclear-magnetic-resonance quantum computation
We offer an improved method for using a nuclear-magnetic-resonance quantum
computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the
application of the NMRQC are exponential diminishment of density-matrix
elements with the number of bits, threatening weak signal levels, and the high
cost of preparing a suitable starting state. A third obstacle is a heretofore
unnoticed restriction on measurement operators available for use by an NMRQC.
Variations on the function classes of the Deutsch-Jozsa problem are introduced,
both to extend the range of problems advantageous for quantum computation and
to escape all three obstacles to use of an NMRQC. By adapting it to one such
function class, the Deutsch-Jozsa problem is made solvable without exponential
loss of signal. The method involves an extra work bit and a polynomially more
involved Oracle; it uses the thermal-equilibrium density matrix systematically
for an arbitrary number of spins, thereby avoiding both the preparation of a
pseudopure state and temporal averaging.Comment: 19 page
Solving the subset-sum problem with a light-based device
We propose a special computational device which uses light rays for solving
the subset-sum problem. The device has a graph-like representation and the
light is traversing it by following the routes given by the connections between
nodes. The nodes are connected by arcs in a special way which lets us to
generate all possible subsets of the given set. To each arc we assign either a
number from the given set or a predefined constant. When the light is passing
through an arc it is delayed by the amount of time indicated by the number
placed in that arc. At the destination node we will check if there is a ray
whose total delay is equal to the target value of the subset sum problem (plus
some constants).Comment: 14 pages, 6 figures, Natural Computing, 200
Exact Cover with light
We suggest a new optical solution for solving the YES/NO version of the Exact
Cover problem by using the massive parallelism of light. The idea is to build
an optical device which can generate all possible solutions of the problem and
then to pick the correct one. In our case the device has a graph-like
representation and the light is traversing it by following the routes given by
the connections between nodes. The nodes are connected by arcs in a special way
which lets us to generate all possible covers (exact or not) of the given set.
For selecting the correct solution we assign to each item, from the set to be
covered, a special integer number. These numbers will actually represent delays
induced to light when it passes through arcs. The solution is represented as a
subray arriving at a certain moment in the destination node. This will tell us
if an exact cover does exist or not.Comment: 20 pages, 4 figures, New Generation Computing, accepted, 200
The Nondeterministic Waiting Time Algorithm: A Review
We present briefly the Nondeterministic Waiting Time algorithm. Our technique
for the simulation of biochemical reaction networks has the ability to mimic
the Gillespie Algorithm for some networks and solutions to ordinary
differential equations for other networks, depending on the rules of the
system, the kinetic rates and numbers of molecules. We provide a full
description of the algorithm as well as specifics on its implementation. Some
results for two well-known models are reported. We have used the algorithm to
explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells
Computational depth complexity of measurement-based quantum computation
We prove that one-way quantum computations have the same computational power
as quantum circuits with unbounded fan-out. It demonstrates that the one-way
model is not only one of the most promising models of physical realisation, but
also a very powerful model of quantum computation. It confirms and completes
previous results which have pointed out, for some specific problems, a depth
separation between the one-way model and the quantum circuit model. Since
one-way model has the same computational power as unbounded quantum fan-out
circuits, the quantum Fourier transform can be approximated in constant depth
in the one-way model, and thus the factorisation can be done by a polytime
probabilistic classical algorithm which has access to a constant-depth one-way
quantum computer. The extra power of the one-way model, comparing with the
quantum circuit model, comes from its classical-quantum hybrid nature. We show
that this extra power is reduced to the capability to perform unbounded
classical parity gates in constant depth.Comment: 12 page
Knowledge politics and new converging technologies: a social epistemological perspective
The “new converging technologies” refers to the prospect of advancing the human condition by the integrated study and application of nanotechnology, biotechnology, information technology and the cognitive sciences - or “NBIC”. In recent years, it has loomed large, albeit with somewhat different emphases, in national science policy agendas throughout the world. This article considers the political and intellectual sources - both historical and contemporary - of the converging technologies agenda. Underlying it is a fluid conception of humanity that is captured by the ethically challenging notion of “enhancing evolution”
A common algebraic description for probabilistic and quantum computations
AbstractThrough the study of gate arrays we develop a unified framework to deal with probabilistic and quantum computations, where the former is shown to be a natural special case of the latter. On this basis we show how to encode a probabilistic or quantum gate array into a sum-free tensor formula which satisfies the conditions of the partial trace problem, and vice-versa; that is, given a tensor formula F of order n×1 over a semiring S plus a positive integer k, deciding whether the kth partial trace of the matrix valSn,n(F·FT) fulfills a certain property. We use this to show that a certain promise version of the sum-free partial trace problem is complete for the class pr- BPP (promise BPP) for formulas over the semiring (Q+,+,·) of the positive rational numbers, for pr-BQP (promise BQP) in the case of formulas defined over the field (Q+,+,·), and if the promise is given up, then completeness for PP is shown, regardless whether tensor formulas over positive rationals or rationals in general are used. This suggests that the difference between probabilistic and quantum polytime computers may ultimately lie in the possibility, in the latter case, of having destructive interference between computations occurring in parallel. Moreover, by considering variants of this problem, classes like ⊕P, NP, C=P, its complement co-C=P, the promise version of Valiant's class UP, its generalization promise SPP, and unique polytime US can be characterized by carrying the problem properties and the underlying semiring
The Complexity of Computing Minimal Unidirectional Covering Sets
Given a binary dominance relation on a set of alternatives, a common thread
in the social sciences is to identify subsets of alternatives that satisfy
certain notions of stability. Examples can be found in areas as diverse as
voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08]
proved that it is NP-hard to decide whether an alternative is contained in some
inclusion-minimal upward or downward covering set. For both problems, we raise
this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and
provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other
natural problems regarding minimal or minimum-size covering sets are hard or
complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of
our results is that neither minimal upward nor minimal downward covering sets
(even when guaranteed to exist) can be computed in polynomial time unless P=NP.
This sharply contrasts with Brandt and Fischer's result that minimal
bidirectional covering sets (i.e., sets that are both minimal upward and
minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure
- …