2,896,033 research outputs found

    The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

    Get PDF
    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

    Get PDF
    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

    Get PDF
    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

    Full text link
    Angular correlations in dense solutions and melts of flexible polymer chains are investigated with respect to the distance rr 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 P(r)P(r) is shown to decay as P(r)1/r3P(r) \sim 1/r^3 for \xi \ll r \ll \r^* with ξ\xi being the screening length of the density fluctuations and rN1/3r^* \sim N^{1/3} a novel length scale increasing slowly with (mean) chain length NN.Comment: 17 pages, 5 figures, accepted for publication at Macromolecule

    Rigorous Inequalities between Length and Time Scales in Glassy Systems

    Full text link
    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

    Get PDF
    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

    Get PDF
    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

    Full text link
    We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime pp. In particular, we obtain nontrivial results about the number of solution in boxes with the side length below p1/2p^{1/2}, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties
    corecore