œ½„­»± …€»³¹ƒ¼...

download œ½„­»± …€»³¹ƒ¼ µ€·µ±ƒ¼­½± ±€Œ „·½ •ƒ· ±¹

of 84

  • date post

    23-Feb-2017
  • Category

    Science

  • view

    454
  • download

    0

Embed Size (px)

Transcript of œ½„­»± …€»³¹ƒ¼...

  • :

    / kgiann@ionio.gr

    23 2016

    ,

    QUIT- Quantum and UnconventIonal CompuTing group

    0

  • (Bio-inspired models) QUIT- Quantum and UnconventIonal CompuTing group

    http://quit.di.ionio.gr/

    1

    http://quit.di.ionio.gr/

  • standard computation

  • 2 ( 30).

    Alan Turing.

    KurtGdel, Alonzo Church, Stephen Kleene ..

    40 50.

    3

  • .

    . .

    , -.

    4

  • (dfa)

    .

    (Q, , : Q x Q, q0, F)

    q0

    1

    1

    00

    q1

    5

  • - (fa)

    , ( ).

    .

    (Q, , : Q x {} P(Q), q0, F)

    q0 q1

    1 1

    q2

    0,1

    0,1

    6

  • dfa nfa

    :

    .

    NFA DFA !

    7

  • (500 .. - 19 )

    ( 19 ) George Boole, Cantor ..

    ( 19 - 20)

    Frege, Russel, Hilbert ..

    8

  • (random processes).

    Poisson processes, ..

    (..) .

    10

  • * .

    * .

    P(Xn = xn|Xn1 = xn1 . . . X0 = x0) = P(Xn = xn|Xn1 = xn1)

    * birth processes, gambling, random walkers, queueing theory,information theory and information retrieval.

    11

  • markov

    i j

    pij = P(X1 = j|X0 = i)

    n p(n)ij = P(Xn = j|X0 = i)

    12

  • autonomous controlled fully partially observed

    13

  • pomdp

    . . (belief state). NP-complete

    14

  • 1, 2, . . . n

    X11 , X22 , . . .

    Xnn Y

    16

  • (...)

    18:32

    , , ; ; , .

    vs

    17

  • *

    * , .

    P(w) :=

    pAcc(w)n

    i=1(pi,wi,pi+1)pRun(w)

    ni=1(pi,wi,pi+1)

    . (1)

    18

  • pfa (probabilistic finite automata)

    Rabin (1963)

    Markov

    19

  • membrane computing

  • membrane computing

    Known as P systems with several proposed variants. Evolution depicted through rewriting rules on multisets of theform uv

    imitating natural chemical reactions, u, v are multisets of objects.

    The hierarchical status of membranes evolves by constantlycreating and destroying membranes, by membrane division etc.

    Represented either by a Venn diagram or a tree. Types of communication rules:

    symport rules (one-way passing through a membrane) antiport rules (two-way passing through a membrane)

    21

  • examples

    Membranes create hierarchical structures. Each membrane contains objects and rules.

    (a) Hierarchical nestedmembranes

    (b) With simple objects and rules

    22

  • p systems evolution and computation

    Via purely non deterministic, parallel rules.

    Characteristics of membrane systems: the membrane structure,multisets of objects and rules.

    They can be represented by a string of labelled matchingparentheses.

    Use of rules = transitions among configurations. A sequence of transitions is interpreted as computation. Accepted computations are those which halt and a successfulcomputation is associated with a result.

    23

  • p automata

    Variants of P systems with automata-like behaviour. Computation starts from an initial configuration. Acceptance is defined by a set of final states.

    They define a computable set of configurations satisfying certainconditions.

    The set of accepted input sequences forms the acceptedlanguage.

    A configuration of a P automaton with n membranes is definedas a n-tuple of multisets of object in each membrane.

    A run of a P automaton is defined as a process of altering itsconfigurations in each step.

    Transition function depends on the computational mode(maximally parallel mode, sequential mode, etc).

    24

  • rules used in membrane computing

    ...

    ...

    b)

    a)

    c) exo

    (a,in)aa(b,in)ba

    (a,out)cab

    cabbbba

    (a,out)caa

    cbbcca

    =

    =

    =

    25

  • a case study

    A biological model of mitochondrial fusion by Alexiou et al,expressed in BioAmbient calculus.

    Cell is divided into hierarchically nested ambients. 3 proteins are required (Mfn1, Mfn2 and OPA1) for the successfulfusion.

    Fusion can occur: by the merging of two membrane-bounded segments. when segments may enter or exit one another.

    Synchronized capabilities that can alter ambients state are:entry, exit, or merge of other compartments.

    26

  • our approach

    Every ambient membrane subsystem. Hierarchical structure of ambients membrane-like segments.

    Biomolecular rules from Bioambient calculus to P automatarewriting rules.

    Actions altering ambients state (entry, exit, or merge).

    Initial configuration:

    [[[[[[]AO1 []K ]PM1M2 ]RM1M2 ]GM1M2 ]OMOM1M2 [[[[[]BO1 ]PO1 ]RO1 ]GO1 ]IMOM1M2 ]skin/cell

    Final configuration:

    [[]PM1M2 []RM1M2 []GM1M2 []OMOM1M2 []PO1 []RO1 []GO1 []IMOM1M2 []K []AO1 []BO1 ]skin/cell

    27

  • the production of the the protein mfn1-mfn2

    Initial config. consecutive use of appropriate rule final config. and halt.

    Initial configuration: [[[[]PM1M2]RM1M2]GM1M2]OMOM1M2 Final configuration: []PM1M2[]RM1M2[]GM1M2[]OMOM1M2 Halting configuration through consecutive exo operations.

    [[[[]PM1M2 ]RM1M2 ]GM1M2 ]OMOM1M2exo [[[]PM1M2 ]RM1M2 ]GM1M2 []OMOM1M2

    exo

    [[]PM1M2 ]RM1M2 []GM1M2 []OMOM1M2exo []PM1M2 []RM1M2 []GM1M2 []OMOM1M2

    Similarly for the rest parts of the model.

    28

  • definition i

    A generic P system (of degree m, m 1) with the characteristics described above can be defined as a construct

    =(V, T, C, H, , w1 , ..., wm, (R1 , ..., Rm), (H1 , ..., Hm) i0) ,

    where

    1. V is an alphabet and its elements are called objects.

    2. T V is the output alphabet.

    3. C V, C T = are catalysts.

    4. H is the set {pino, exo, mate, drip} of membrane handling rules.

    5. is a membrane structure consisting of m membranes, with the membranes and the regions labeled in a one-to-one way withelements of a given set H.

    6. wi , 1 i m, are strings representing multisets over V associated with the regions 1,2, ... ,m of .

    7. Ri , 1 i m, are finite sets of evolution rules over the alphabet set V associated with the regions 1,2, ... , m of . These objectevolution rules have the form u v.

    8. Hi , 1 i m, are finite sets of membrane handling rules rules over the set H associated with the regions 1,2, ... , m of .

    9. i0 is a number between 1 and m and defines the initial configuration of each region of the P system.

    29

  • definition ii

    Formally, a one-way P automaton with n membranes (n 1) andantiport rules is a construct

    =(V, , P1, ..., Pn, c0, F),

    where:

    1. V is a finite alphabet of objects,2. is the underlying membrane structure of the automaton with

    n membranes,3. Pi is a finite set of antiport rules for membrane i with 1in

    without promoters/inhibitors, where each antiport rule is of theform (a, out; b, in) with a, b being multisets consisting ofelements of the set V,

    4. c0 is the initial configuration of , and5. F is the set of accepting configurations of .

    30

  • schematic view

    Figure: The step by step process through consecutive exo operations.

    31

  • schematic view

    32

  • discussion

    X Inherent compartmentalization, easy extensibility and directintuitive appearance for biologists.

    X Suitable in cases when few number of objects are involved orslow reactions.

    X Need for deeper understanding of mitochondrial fusion Connections with neurodegenerative diseases and malfunctions.

    X Probability theory and stochasticity (many biological functionsare of stochastic nature).

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fis1

    Drp1

    Mff Fi