2,896,033 research outputs found
The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules
Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical
systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when
moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in
the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems
is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with
evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper
bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary
between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new
simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution
to the SAT problem
Length P Systems with a Lone Traveler
In this paper we consider P systems with linear membrane structures (only
one membrane is elementary) with at most one object. We raise and attack the question
about the computational power of such systems, depending on the number of membrane
labels, kinds of rules used, and some other possible restrictions
Membrane Fission: A Computational Complexity Perspective
Membrane fission is a process by which a biological membrane is split into two new ones in the manner
that the content of the initial membrane is separated and distributed between the new membranes. Inspired by this
biological phenomenon, membrane separation rules were considered in membrane computing. In this work, we
investigate cell-like P systems with symport/antiport rules and membrane separation rules from a computational
complexity perspective. Specifically, we establish a limit on the efficiency of such P systems which use communication
rules of length at most two, and we prove the computational efficiency of this kind of models when using
communication rules of length at most three. Hence, a sharp borderline between tractability and NP–hardness
is provided in terms of the length of communication rules.Ministerio de Economía y Competitividad TIN2012-3743
Distance dependence of angular correlations in dense polymer solutions
Angular correlations in dense solutions and melts of flexible polymer chains
are investigated with respect to the distance between the bonds by
comparing quantitative predictions of perturbation calculations with numerical
data obtained by Monte Carlo simulation of the bond-fluctuation model. We
consider both monodisperse systems and grand-canonical (Flory-distributed)
equilibrium polymers. Density effects are discussed as well as finite chain
length corrections. The intrachain bond-bond correlation function is
shown to decay as for \xi \ll r \ll \r^* with being
the screening length of the density fluctuations and a novel
length scale increasing slowly with (mean) chain length .Comment: 17 pages, 5 figures, accepted for publication at Macromolecule
Rigorous Inequalities between Length and Time Scales in Glassy Systems
Glassy systems are characterized by an extremely sluggish dynamics without
any simple sign of long range order. It is a debated question whether a correct
description of such phenomenon requires the emergence of a large correlation
length. We prove rigorous bounds between length and time scales implying the
growth of a properly defined length when the relaxation time increases. Our
results are valid in a rather general setting, which covers finite-dimensional
and mean field systems.
As an illustration, we discuss the Glauber (heat bath) dynamics of p-spin
glass models on random regular graphs. We present the first proof that a model
of this type undergoes a purely dynamical phase transition not accompanied by
any thermodynamic singularity.Comment: 24 pages, 3 figures; published versio
Lower Bounds for Real Solutions to Sparse Polynomial Systems
We show how to construct sparse polynomial systems that have non-trivial
lower bounds on their numbers of real solutions. These are unmixed systems
associated to certain polytopes. For the order polytope of a poset P this lower
bound is the sign-imbalance of P and it holds if all maximal chains of P have
length of the same parity. This theory also gives lower bounds in the real
Schubert calculus through sagbi degeneration of the Grassmannian to a toric
variety, and thus recovers a result of Eremenko and Gabrielov.Comment: 31 pages. Minor revision
A Note on a New Class of APCol Systems
We introduce a new acceptance mode for APCol systems (Automaton-like P
colonies), variants of P colonies where the environment of the agents is given by a string
and during functioning the agents change their own states and process the string similarly
to automata. In case of the standard variant, the string is accepted if it can be reduced
to the empty word. In this paper, we de ne APCol systems where the agents verify their
environment, a model resembling multihead nite automata. In this case, a string of
length n is accepted if during every halting computation the length of the environmental
string in the con gurations does not change and in the course of the computation every
agent applies a rule to a symbol on position i of some of the environmental strings for
every i, 1 < i < n at least once. We show that these verifying APCol systems simulate
one-way multihead nite automata
On Solutions to Some Polynomial Congruences in Small Boxes
We use bounds of mixed character sum to study the distribution of solutions
to certain polynomial systems of congruences modulo a prime . In particular,
we obtain nontrivial results about the number of solution in boxes with the
side length below , which seems to be the limit of more general
methods based on the bounds of exponential sums along varieties
- …